Interactions Between Current and Domain Wall Spin Structures

Interactions Between Current and Domain Wall Spin Structures Universität Konstanz

DISSERTATION ZUR ERLANGUNG DES AKADEMISCHEN GRADES DES DOKTORS DER NATURWISSENSCHAFTEN AN DER UNIVERSITÄT KONSTANZ MATHEMATISCH-NATURWISSENSCHAFTLICHE SEKTION FACHBEREICH PHYSIK VORGELEGT VON MARKUS LAUFENBERG

TAG DER MÜNDLICHEN PRÜFUNG: 26. JULI 2006 REFERENTEN: PROF. DR. ULRICH RÜDIGER PROF. DR. GÜNTER SCHATZ Konstanzer Online-Publikations-System (KOPS) URL: http://www.ub.uni-konstanz.de/kops/volltexte/2006/1955/

Summary In this thesis, the interaction between current and domain wall spin structures in the 3d-ferromagnets Ni80 Fe20 (permalloy) and Co as well as in the halfmetallic ferromagnets Fe3 O4 and CrO2 is investigated. Nanostructures of these materials with different shapes (rings, wires, rectangles) and different sizes and thicknesses are fabricated using molecular beam epitaxy, electron beam lithography, lift-off, as well as focused ion beam milling and various etching techniques. Samples designed for current injection and magnetoresistance measurements are electrically contacted with Au pads in an overlay process. First, the spin structure of domain walls in these materials is studied using x-ray magnetic circular dichroism photoemission electron microscopy (XMCDPEEM) with synchrotron light, because it is known that the wall spin structure influences the magnetoresistance and that spin transfer torque effects are closely related to the wall spin structure. Comprehensive domain wall type phase diagrams for 180◦ head-to-head domain walls are obtained and explained using micromagnetic theory. Thermally induced wall type transformations are studied, the wall width is determined as a function of the element width, and the dipolar coupling between adjacent walls is investigated. The domain wall spin structures and their dependence on the magnetocrystalline anisotropy in Fe 3 O4 and CrO2 structures are elucidated. The current- and field-induced domain wall motion in NiFe structures is studied at variable temperatures using measurements of the anisotropic magnetoresistance contribution of the domain wall. The Joule heating of the current is determined and discriminated from intrinsic spin torque effects. The domain wall velocity and current-induced transformations of the domain wall spin structures are studied using XMCD-PEEM. In CrO 2 , the magnetoresistance contributions are probed, the Joule heating is measured, and current-assisted domain wall motion is studied at low temperatures.

Zusammenfassung In dieser Arbeit wird die Wechselwirkung zwischen Strom und der Spinstruktur von Domänenwänden in den 3d-Ferromagneten Ni 80 Fe20 (Permalloy) und Co sowie in den halbmetallischen Ferromagneten Fe 3 O4 und CrO2 untersucht. Nanostrukturen aus diesen Materialien (Ringe, Drähte, Rechtecke etc.) verschiedener Größe und Dicke werden unter Einsatz von Molekularstrahlepitaxie, Elektronenstrahl-Lithographie, Lift-off-Technik sowie fokussiertem IonenstrahlMilling und chemischen Ätzprozessen hergestellt. Proben, die für Strominjektion und Magnetowiderstandsmessungen bestimmt sind, werden in einem Overlay-Prozess mit Goldkontakten elektrisch kontaktiert. Zunächst wird die Spinstruktur von Domänenwänden in diesen Materialien mit Hilfe von Photoemissionselektronenmikroskopie auf Basis von zirkularem Röntgendichroismus (XMCD-PEEM) mit Synchrotronstrahlung untersucht, weil bekannt ist, dass die Domänenwand-Spinstruktur den Magnetowiderstand beeinflusst und dass Spin-Transfer-Torque-Effekte in engem Bezug zur Spinstruktur stehen. Es ergeben sich Domänenwandtyp-Phasendiagramme für 180◦ Kopf-an-Kopf-Domänenwände, die mit Hilfe der Theorie des Mikromagnetismus bestätigt werden. Thermisch induzierte Wandtyp-Transformationen werden untersucht, die Wandbreite als Funktion der Strukturbreite ermittelt und die dipolare Kopplung benachbarter Domänenwände abgebildet. Die Domänenwand-Spinstrukturen und ihre Abhängigkeit von der magnetokristallinen Anisotropie in Fe3 O4 und CrO2 Strukturen wird untersucht. Strom- und feldinduzierte Domänenwandverschiebung in NiFe-Strukturen wird bei variablen Temperaturen über Messung des Domänenwandbeitrages zum anisotropen Magnetowiderstand studiert. Die Messung der Joulschen Erwärmung durch Strom erlaubt, thermische Effekte von intrinsischen SpinTorque-Effekten zu separieren. Die Domänenwandgeschwindigkeit und strominduzierte Transformationen der Domänenwand-Spinstruktur werden mit

iii XMCD-PEEM bestimmt. In CrO2 werden die verschiedenen Magnetowiderstandsbeiträge temperaturabhängig ermittelt, die Joulsche Erwärmung durch Strom gemessen und stromunterstützte Domänenwandverschiebung bei tiefen Temperaturen untersucht.

Contents Summary / Zusammenfassung

i

List of Figures

x

List of Acronyms

xi

Introduction

1

1

Theory

4

1.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

1.2

Microscopic Origins of Ferromagnetism . . . . . . . . . . . . . . .

5

1.2.1

Exchange Interaction . . . . . . . . . . . . . . . . . . . . . .

5

1.2.2

Localized Model and Mean Field Approximation . . . . .

5

1.2.3

Band Model of Ferromagnetism . . . . . . . . . . . . . . .

6

Micromagnetic Systems . . . . . . . . . . . . . . . . . . . . . . . .

8

1.3.1

Thermodynamics in Magnetism . . . . . . . . . . . . . . .

8

1.3.2

Energy Contributions . . . . . . . . . . . . . . . . . . . . .

9

1.3.3

Brown’s Equations and the Effective Field . . . . . . . . . .

12

Magnetization Dynamics . . . . . . . . . . . . . . . . . . . . . . . .

13

1.4.1

Landau-Lifshitz-Gilbert Equation . . . . . . . . . . . . . .

13

1.4.2

Micromagnetic Simulations . . . . . . . . . . . . . . . . . .

16

Spin Transfer Torque Model . . . . . . . . . . . . . . . . . . . . . .

17

1.5.1

Hydromagnetic Drag Force . . . . . . . . . . . . . . . . . .

17

1.5.2

s-d Exchange Force and Spin Transfer Torque . . . . . . . .

18

1.5.3

Landau-Lifshitz-Gilbert Equation with Spin Transfer Torque 20

1.5.4

Adiabatic and Non-adiabatic Spin Torque . . . . . . . . . .

21

1.5.5

Domain Wall Spin Structure Modifications . . . . . . . . .

24

1.3

1.4

1.5

CONTENTS

1.6

1.7 2

1.5.6

Critical Current Density and Domain Wall Velocity . . . .

1.5.7

Temperature Dependence of the Spin Torque and the Role

25

of Spinwaves . . . . . . . . . . . . . . . . . . . . . . . . . .

28

Magnetotransport and Magnetoresistance Effects . . . . . . . . . .

30

1.6.1

The "XMR-Zoo" . . . . . . . . . . . . . . . . . . . . . . . . .

30

1.6.2

Anisotropic Magnetoresistance (AMR) . . . . . . . . . . .

32

1.6.3

Intergrain Tunneling Magnetoresistance (ITMR) . . . . . .

33

1.6.4

Domain Wall Contributions to the Magnetoresistance . . .

33

Fe3 O4 and CrO2 : Halfmetallic Ferromagnets . . . . . . . . . . . .

35

Experimental Techniques 2.1

38

X-ray Magnetic Circular Dichroism Photoemission Electron Microscopy (XMCD-PEEM) . . . . . . . . . . . . . . . . . . . . . . . .

38

2.1.1

Photoelectron Emission Microscopy (PEEM) . . . . . . . .

38

2.1.2

Magnetic Circular Dichroism . . . . . . . . . . . . . . . . .

40

2.1.3

XMCD-PEEM with Synchrotron Light . . . . . . . . . . . .

41

Magnetoresistance Measurements . . . . . . . . . . . . . . . . . .

44

2.2.1

General Experimental Setup . . . . . . . . . . . . . . . . . .

44

2.2.2

Electrical Measurement Circuits . . . . . . . . . . . . . . .

49

2.2.3

Software "TransportLab" . . . . . . . . . . . . . . . . . . . .

52

PEEM with In-situ Current Pulse Injection . . . . . . . . . . . . . .

55

2.3.1

Pulse Injection Unit . . . . . . . . . . . . . . . . . . . . . . .

55

2.3.2

Sample Cartridge . . . . . . . . . . . . . . . . . . . . . . . .

57

2.4

Electron Holography . . . . . . . . . . . . . . . . . . . . . . . . . .

59

2.5

Scanning Electron Microscopy (SEM) . . . . . . . . . . . . . . . . .

60

2.6

Atomic and Magnetic Force Microscopy (AFM / MFM) . . . . . .

62

2.2

2.3

3

v

Magnetic Nanostructures – Fabrication and Properties

63

3.1

Introduction and Overview . . . . . . . . . . . . . . . . . . . . . .

63

3.2

Material Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

3.2.1

Molecular Beam Epitaxy of NiFe and Co Layers . . . . . .

65

3.2.2

Molecular Beam Epitaxy of Fe3 O4 Layers . . . . . . . . . .

66

3.2.3

Chemical Vapor Deposition of CrO 2 Layers . . . . . . . . .

67

Lithography and Pattern Transfer . . . . . . . . . . . . . . . . . . .

68

3.3.1

Electron Beam Lithography and Lift-off . . . . . . . . . . .

68

3.3.2

Nanostructures Patterned with Ion Milling . . . . . . . . .

70

3.3

CONTENTS

3.4

3.5 4

3.3.3

Focused Ion Beam Milling (FIB) . . . . . . . . . . . . . . .

70

3.3.4

Prepatterned Substrates . . . . . . . . . . . . . . . . . . . .

70

Properties of Films and Nanostructures . . . . . . . . . . . . . . .

71

3.4.1

NiFe and Co Samples . . . . . . . . . . . . . . . . . . . . .

72

3.4.2

Fe3 O4 Samples . . . . . . . . . . . . . . . . . . . . . . . . .

72

3.4.3

CrO2 Samples . . . . . . . . . . . . . . . . . . . . . . . . . .

73

Magnetic States and Switching of Ring Structures . . . . . . . . .

74

Domain Wall Spin Structures

76

4.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

4.2

Introduction to Domain Walls . . . . . . . . . . . . . . . . . . . . .

78

4.2.1

Domain Wall Spin Structures . . . . . . . . . . . . . . . . .

78

4.2.2

Domain Wall Widths . . . . . . . . . . . . . . . . . . . . . .

81

Domain Wall Type Phase Diagrams for NiFe and Co . . . . . . . .

82

4.3.1

Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . .

82

4.3.2

Walls in Thin and Wide Structures – Limits of the Description 86

4.3

4.4

Temperature Effects on Domain Wall Spin Structures . . . . . . .

88

4.5

Domain Wall Widths . . . . . . . . . . . . . . . . . . . . . . . . . .

91

4.6

Interacting Domain Walls and Wall Stray Fields . . . . . . . . . . .

94

4.6.1

Sample Fabrication and Experimental Techniques . . . . .

95

4.6.2

XMCD-PEEM Imaging of Interacting Domain Walls . . . .

96

4.6.3

Stray Field Mapping Using Electron Holography . . . . .

98

4.6.4

Energy Barrier Height Distribution for Vortex Nucleation .

99

4.7

5

vi

Spin Structure of Fe3 O4 Nanostructures . . . . . . . . . . . . . . . 101 4.7.1

Experimental Difficulties Encountered . . . . . . . . . . . . 101

4.7.2

XAS and XMCD Spectra . . . . . . . . . . . . . . . . . . . . 102

4.7.3

Spin Structure of Fe3 O4 Rings . . . . . . . . . . . . . . . . . 103

4.7.4

Spin Structure of Zigzag Wires for CIDM Experiments . . 107

4.7.5

Fe3 O4 Structures Capped with NiFe . . . . . . . . . . . . . 109

4.8

Spin Structure of CrO2 Nanostructures . . . . . . . . . . . . . . . . 109

4.9

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Interaction Between Domain Walls and Current

114

5.1

Introduction and Overview . . . . . . . . . . . . . . . . . . . . . . 114

5.2

Current- and Field-induced Domain Wall Motion at Constant Temperatures in NiFe . . . . . . . . . . . . . . . . . . . . . . . . . . 116

CONTENTS

5.3

vii

5.2.1

Sample Characterization . . . . . . . . . . . . . . . . . . . . 116

5.2.2

Current- and Field-induced Domain Wall Motion . . . . . 118

5.2.3

Joule Heating due to Current . . . . . . . . . . . . . . . . . 121

5.2.4

Comparison of Experiment and Theory . . . . . . . . . . . 122

5.2.5

Splitting of the Boundary for Domain Wall Motion . . . . 124

5.2.6

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Current-induced Domain Wall Motion and Transformations in NiFe Observed with XMCD-PEEM . . . . . . . . . . . . . . . . . . 126

5.4

6

5.3.1

Sample Fabrication and Experimental Setup . . . . . . . . 127

5.3.2

Domain Wall Spin Structure Transformations . . . . . . . . 128

5.3.3

Spin Structure Dependence of the Domain Wall Velocity . 132

5.3.4

Geometry Dependence of Wall Transformations . . . . . . 133

5.3.5

Geometry Dependence of the Domain Wall Velocity . . . . 135

Domain Walls in CrO2 . . . . . . . . . . . . . . . . . . . . . . . . . 139 5.4.1

Temperature Dependent Magnetoresistance . . . . . . . . 139

5.4.2

Magnetization Reversal in Wires With Constrictions . . . . 140

5.4.3

Joule Heating . . . . . . . . . . . . . . . . . . . . . . . . . . 142

5.4.4

Current-induced Domain Wall Motion Experiments . . . . 144

5.5

Current-induced Domain Wall Motion in Fe 3 O4 . . . . . . . . . . 146

5.6

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Conclusions and Outlook

A Resistance of Capped NiFe Wires

149 153

A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 A.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 154 A.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 B Work Performed at the INESC-MN in Lisbon

158

B.1 Introduction and Experimental Setup . . . . . . . . . . . . . . . . 158 B.2 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 B.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 B.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Bibliography

168

Publication List

192

List of Figures 1.1

Sketch of the band model of ferromagnetism . . . . . . . . . . . .

8

1.2

Current distribution causing the hydromagnetic drag effect . . . .

18

1.3

Results of micromagnetic simulations including spin torque . . .

22

1.4

Spinwave spectrum modified by current . . . . . . . . . . . . . . .

29

1.5

Schematics of the intergrain tunneling magnetoresistance . . . . .

33

1.6

AMR contribution of a domain wall . . . . . . . . . . . . . . . . .

34

1.7

Spin-dependent density of states for 3d-ferromagnets and halfmetallic ferromagnets . . . . . . . . . . . . . . . . . . . . . . .

35

2.1

X-PEEM and LEEM imaging modes . . . . . . . . . . . . . . . . .

39

2.2

X-ray magnetic circular dichroism . . . . . . . . . . . . . . . . . .

41

2.3

XAS and resulting XMCD spectra of Fe and Co . . . . . . . . . . .

42

2.4

Photographs of Elettra PEEM setup . . . . . . . . . . . . . . . . . .

43

2.5

Schematic cross section and top view of the CryoVac cryostat . . .

45

2.6

Schematics of the cooling system . . . . . . . . . . . . . . . . . . .

46

2.7

Photograph and schematics of the vector field system . . . . . . .

47

2.8

Schematics and photographs of the cryostat sample holder . . . .

49

2.9

Measurement circuits used for resistance measurements . . . . . .

50

2.10 Measurement circuit for pulse injection and consecutive resistance measurement . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

2.11 Measurement circuit for investigation of Joule heating due to pulses 52 2.12 Schematics of the pulse injection setup for PEEM . . . . . . . . . .

56

2.13 Standard Elmitec PEEM sample holder . . . . . . . . . . . . . . .

57

2.14 Elmitec PEEM sample holder modified for current injection . . .

58

2.15 PEEM sample holder for current injection (own design) . . . . . .

58

2.16 Ray diagram of the TEM used for off-axis electron holography . .

60

LIST OF FIGURES

ix

2.17 Schematics of a scanning electron microscope . . . . . . . . . . . .

61

3.1

Schematics of the MBE system used for growing NiFe and Co . .

65

3.2

Photographs of the MBE system used for growing Fe 3 O4 . . . . .

66

3.3

Schematic view of the CVD setup used for the preparation of CrO2 (100) films . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

3.4

Standard sample design for XMCD-PEEM studies of rings . . . .

68

3.5

SEM images of NiFe ring structures for CIDM experiments . . . .

69

3.6

Schematics of the prepatterned substrate process . . . . . . . . . .

71

3.7

XMCD-PEEM images of Fe3 O4 rings on prepatterned substrates .

71

3.8

Schematic representations of vortex and onion state . . . . . . . .

75

4.1

Schematics of a cross-tie domain wall . . . . . . . . . . . . . . . .

79

4.2

Zigzag domain walls in thin films . . . . . . . . . . . . . . . . . . .

80

4.3

Double vortex walls in thick ring elements . . . . . . . . . . . . .

81

4.4

PEEM images of rings with different geometries exhibiting transverse and vortex walls . . . . . . . . . . . . . . . . . . . . . . . . .

82

4.5

Domain wall type phase diagrams for NiFe and Co . . . . . . . .

83

4.6

Schematics of the domain wall type energy landscape . . . . . . .

84

4.7

Ultrathin Co rings on prepatterned Si substrates . . . . . . . . . .

86

4.8

Limiting cases of the structures described in the phase diagrams .

87

4.9

Spin structure transformations in NiFe rings due to heating . . . .

88

4.10 Images of a ring during a heating process showing the damage .

89

4.11 High-resolution PEEM images of domain walls . . . . . . . . . . .

91

4.12 Intensity profiles of domain walls . . . . . . . . . . . . . . . . . . .

92

4.13 Domain wall width as a function of the ring width . . . . . . . . .

93

4.14 PEEM images of interacting domain walls . . . . . . . . . . . . . .

96

4.15 Domain wall types in rings as function of edge-to-edge spacing .

97

4.16 Stray field of a domain wall . . . . . . . . . . . . . . . . . . . . . .

99

4.17 Distribution of energy barrier heights for vortex core nucleation . 100 4.18 PEEM images of nanostructures damaged by FIB patterning . . . 102 4.19 XAS and XMCD spectra of Fe3 O4

. . . . . . . . . . . . . . . . . . 103

4.20 XMCD-PEEM, MFM, and OOMF results of Fe 3 O4 rings . . . . . . 104 4.21 MFM and OOMMF results of rings magnetized along the hard axis 105 4.22 Fe3 O4 zigzag lines with different widths . . . . . . . . . . . . . . . 106 4.23 MFM contrast formation in a ring magnetized along the easy axis 107

LIST OF FIGURES

x

4.24 MFM and OOMMF results of rings magnetized along the easy axis 108 4.25 SEM image of a Fe3 O4 prototype structure for CIDM experiments 109 4.26 PEEM images of a NiFe capped CrO 2 wire . . . . . . . . . . . . . 110 4.27 PEEM images of a NiFe capped CrO2 film patterned with FIB . . 111 4.28 AFM and MFM images of domain patterns in CrO 2 nanostructures 112 5.1

SEM image of a NiFe ring with simulation and MR measurement

117

5.2

Domain wall motion as function of current, field, and temperature 119

5.3

Joule heating due to current pulses . . . . . . . . . . . . . . . . . . 121

5.4

Statistical distribution of the critical field . . . . . . . . . . . . . . 125

5.5

SEM and PEEM images of sample with the initial magnetization . 127

5.6

Domain wall velocities of different wall types . . . . . . . . . . . . 128

5.7

PEEM images of double vortex walls . . . . . . . . . . . . . . . . . 129

5.8

PEEM images of domain wall transformations after consecutive pulse injections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.9

Domain wall in a wide wire after consecutive pulse injections . . 134

5.10 Geometry dependent wall velocity as function of current density

135

5.11 Critical current density as function of the wire width . . . . . . . 137 5.12 Wall velocities as function of wire width and current density . . . 138 5.13 SEM images of a CrO2 wire with constriction . . . . . . . . . . . . 140 5.14 CrO2 hysteresis loops at 4.3 K . . . . . . . . . . . . . . . . . . . . . 141 5.15 Switching fields for the reversal of a CrO 2 wire . . . . . . . . . . . 142 5.16 Joule heating due to current in CrO 2 . . . . . . . . . . . . . . . . . 143 5.17 Resistance as function of temperature for a CrO 2 wire . . . . . . . 143 5.18 Critical field for domain wall depinning in a CrO 2 structure as function of temperature . . . . . . . . . . . . . . . . . . . . . . . . 145 A.1 Conductance of NiFe wires as a function of thickness . . . . . . . 154 A.2 Comparison of NiFe and Au conductance in Au capped NiFe wires 156 B.1 Layout of the µ-BLS experimental setup . . . . . . . . . . . . . . . 159 B.2 Schematic view of a magnetic memory element . . . . . . . . . . . 160 B.3 Schematics of the sample fabrication process . . . . . . . . . . . . 162 B.4 Spinwave spectra in the CoFe film surrounding the spin valve . . 163 B.5 Experimental and theoretical spinwave radiation patterns in CoFe 165

List of Acronyms AC

Alternating current

AMR

Anisotropic magnetoresistance

AFM

Atomic force microscopy / microscope

BLS

Brillouin light scattering

BMR

Ballistic magnetoresistance

BNC

British naval connector

CIDM

Current-induced domain wall motion

CIP

Current in-plane

CPP

Current perpendicular-to-plane

CMR

Colossal magnetoresistance

CVD

Chemical vapor deposition

DC

Direct current

DOS

Density of states

DWMR

Domain wall magnetoresistance

fcc

face-centered cubic (crystal structure)

GMR

Giant magnetoresistance

GPIB

General purpose interface bus

hcp

hexagonal close packed (crystal structure)

HV

High voltage

ITMR

Intergrain tunneling magnetoresistance

LAN

Local area network

LEED

Low energy electron diffraction

LEEM

Low energy electron microscopy

LHe

Liquid helium

LIA

Lock-in amplifier

LLG

Landau-Lifshitz-Gilbert (equation)

LIST OF ACRONYMS LN2

Liquid nitrogen

MBE

Molecular beam epitaxy (system)

MFM

Magnetic force microscopy / microscope

MOKE

Magnetic-optical Kerr effect

MR

Magnetoresistance

MRAM

Magnetic random access memory

µ-BLS

Micro-focus Brillouin light scattering

PEEM

Photoemission electron microscopy / microscope

PMMA

Polymethyl methacrylate

RHEED

Reflection high energy electron diffraction

SEM

Scanning electron microscopy / microscope

SEMPA

Scanning electron microscopy / microscope with polarization analysis

SLS

Swiss Light Source

SQUID

Superconducting quantum interference device

STM

Scanning tunneling microscopy / microscope

TEM

Transmission electron microscopy / microscope

TMR

Tunnel magnetoresistance

UHV

Ultra high vacuum

XAS

X-ray absorption spectroscopy

XMCD

X-ray magnetic circular dichroism

XMCD-PEEM

X-ray magnetic circular dichroism photoemission electron microscopy / microscope

XMR

Entirety of all magnetoresistance effects

X-PEEM

X-ray photoemission electron microscopy / microscope

XPS

X-ray photoemission spectroscopy

XRD

X-ray diffraction

xii

Introduction Nanotechnology is a fast developing and growing field that covers parts of many disciplines in natural sciences and engineering. It deals with materials, structures, and processes on the nanometer scale. The impact of nanotechnology on society, for example in the fields of nanoelectronics or health care, are enormous and often unknown to many people being in contact with the achievements of this technology in their daily life [Sch04]. Nanomagnetism is the part of the nanotechnology that deals with magnetism on the nanometer scale and has a well known application in storage disc drives. Less known but as important for technological progress are sensors based on effects which stem from the field of nanomagnetism. Disc drives store information by defining a certain direction of magnetization as a logical "1" and the opposite direction as a logical "0". Information is commonly written by a magnetic field that changes the magnetization direction of the bit. The readout process is realized by measuring the stray field with a field sensor. However, the permanent call for higher storage densities and faster data rates is pushing this technological approach to its fundamental limits. The limits in miniaturization of the bits as well as of the read-and-write head pose limits to the storage density. The time consuming mechanical positioning of the head and the rotation speed of the disc limit the data rates. These limits can be partially overcome by magnetic random access memory (MRAM), which combines the advantages of the fast charge-based stateof-the-art DRAM with the non-volatility of magnetic information storage. Single storage cells are written by a magnetic field and read out by a simple resistance measurement. These storage cells consist of magnetic multilayer systems, so-called spin valves or tunnel junctions [Pri99, ERJ + 02]. A new approach for writing information to such storage cells is the current-induced magnetization switching. Making use of the so-called spin transfer torque effect, magnetic

Introduction

2

layers can be switched by a current flowing through the element. The design of a possible memory device is significantly simplified, because field generating striplines are not needed any more. The spin transfer torque switching in magnetic multilayers has been studied intensively and was successfully demonstrated [MRK+ 99, HAN+ 04, CSK+ 04, Sun06]. Initiated by the research on spin torque effects in multilayers, also the current-induced manipulation of single domain walls in nanostructures has received rapidly increasing interest both due to fundamental interest in the physics involved and due to the application background. A prominent example for a domain wall based storage device is the recently proposed racetrack memory [Par04].

The phenomenon of current-induced domain wall

motion has been long known theoretically [Slo96, Ber84] as well as experimentally [FB85], but only recently controlled current-induced motion of single domain walls in magnetic nanostructures has been achieved (see for example [GBC+ 03, VAA+ 04, YON+ 04, RLK+ 05, KVB+ 05, KJA+ 05]). In particular, the observation of domain wall spin structure transformations due to current [KJA+ 05] points to the importance of comprehensive studies of domain wall spin structures. Furthermore, critical current densities for domain wall motion and wall velocities have been predicted [WNU04, HLZ06] and observed [NTM05, KJA+ 05] to depend on the wall spin structure. The ongoing discussion within theory about the correct model for the description of spin transfer torque effects (see for example [TK04, BM05, Bar06, TK06]) calls for indepth studies of current-induced domain wall motion with a special focus on wall spin structure transformations in different geometries and materials. Since theory predominantly uses model systems at constant (mostly zero) temperature so far, the experiments have to be performed at constant temperatures to allow for direct comparison. Therefore, the inevitable Joule heating [YNT + 05] has to be taken into account in order to separate thermal and intrinsic spin torque effects [YCM+ 06]. This thesis contributes from the experimental side to a deeper understanding of the domain wall spin structures in NiFe, Co, Fe 3 O4 , and CrO2 nanostructures and contains a comprehensive study of current- and field-induced domain wall motion at variable sample temperatures in NiFe. It is organized as follows: In chapter 1, an introduction to the relevant theory is given with the main focus on the spin transfer torque theory, its development and present state, and

Introduction

3

particular predictions of experimental results. After that, the experimental techniques used are discussed in chapter 2. The X-ray magnetic circular dichroism photoemission electron microscopy (XMCDPEEM) as the main magnetic imaging technique used is discussed including the developed setup for current pulse injection. Secondly, the bath cryostat setup for magnetoresistance measurements between 2 K and 300 K developed in the frame of this thesis is described in detail. Then the fabrication processes and the relevant general properties (magnetic and structural) of the investigated samples are briefly discussed in chapter 3. Chapter 4 presents the results obtained on domain wall spin structures in NiFe, Co, Fe3 O4 , and CrO2 , mainly by XMCD-PEEM. Comprehensive domain wall type phase diagrams for 180◦ head-to-head domain walls in NiFe and Co are obtained and explained, thermally induced wall type transformations are studied, the wall width is determined as a function of the element width, and the dipolar coupling between adjacent walls is investigated. Furthermore, the domain wall spin structures and their dependence on the magnetocrystalline anisotropy in Fe3 O4 and CrO2 structures are explored. Chapter 5 contains the results on the interaction between domain walls and current. In particular, the current- and field-induced domain wall motion in NiFe structures is studied at constant temperatures using measurements of the anisotropic magnetoresistance contribution of a domain wall. The Joule heating due to the current is determined and the heating effects are discriminated from intrinsic spin torque effects. The wall velocity in current-induced domain wall motion and current-induced transformations of the domain wall spin structures are studied using XMCD-PEEM. Additionally, the magnetoresistance contributions in CrO2 are probed, the Joule heating is measured, and current-assisted domain wall motion is studied in CrO 2 at low temperatures. Finally, the results are concluded and a brief outlook to possible future experiments is given. Parts of this thesis have been published [LBB + 06a, LBE+06, KLH+ 06, LKB+ 06, LBB+ 06b]. Reference will be made to this work where appropriate.

Chapter 1

Theory 1.1 Overview This chapter presents the theoretical background relevant for the physics and results presented in this thesis. First, the microscopic origins of magnetism are briefly discussed, including the exchange interaction and localized as well as delocalized electron contributions to ferromagnetism. These microscopic approaches are then complemented by a phenomenological view using thermodynamic potentials and macroscopic variables like magnetization and magnetic fields. This allows for establishing a straightforward relation to experiments, where only these macroscopic quantities are available. The micromagnetic simulations, which are frequently used nowadays in magnetism research and which base on this thermodynamic approach, are briefly described. Then the spin transfer torque theory is discussed in detail, since it is the main theoretical background for most of the results presented in this work. This theory includes the interaction of current and magnetization into the micromagnetic description developed in the preceding section. Different recent approaches are presented, in particular the possible roles of an adiabatic and a non-adiabatic spin-torque are described. Magnetoresistance effects in magnetic materials, which constitute a complete family of effects, are treated in the next section with the focus on the anisotropic magnetoresistance, the intergrain tunneling magnetoresistance, and the domain wall contributions to the magnetoresistance. Finally, the material class of halfmetallic ferromagnets with the two prominent members Fe 3 O4 and CrO2 is introduced and the striking feature of theoretically 100% spin polarization in these systems is discussed.

Theory

5

1.2 Microscopic Origins of Ferromagnetism Two starting points exist for the microscopic description of ferromagnetism: In a localized model, the electrons responsible for the ferromagnetism are localized at an atom. In the band model, the relevant electrons are delocalized and can be described by the interaction with an effective field of the other electrons and atoms in the solid. Usually both descriptions will be necessary to fully understand a ferromagnetic system. However, the band model is particularly relevant for the 3d-metals such as Fe, Co, Ni, and their alloys where delocalized 3d-electrons are responsible for the ferromagnetism, while in rare earth metals (with Sm, Eu, and Gd being prominent examples in magnetism) a localized electron theory is more suitable to describe the 4f -electrons, which cause the magnetic behavior.

1.2.1 Exchange Interaction The exchange interaction between single electrons can be regarded as the fundamental quantum mechanical effect that causes ferromagnetism. Exchange favors a parallel alignment of neighboring spins. Due to the Pauli exclusion principle, which does not allow fermions like electrons to have the same quantum mechanical state (identical spin and location), the distance between two electrons with the same spin is increased, which in turn reduces the Coulomb repulsion and therefore leads to a reduced energy of the system even though the reduction of the Coulomb energy is related to an increase of the kinetic energy. The phenomenon can be described for two spins by an exchange Hamiltonian that takes the form ˆ = −2J σ H ˆ1 · σ ˆ2 ,

(1.1)

where J is the exchange constant, i.e. the energy difference between parallel and antiparallel configuration, and σ ˆi are the Pauli spin matrices.

1.2.2 Localized Model and Mean Field Approximation The Hamiltonian introduced above can be generalized to describe a spin lattice of localized electron spins: ˆ=− H

X i,j

Jij σi · σj ,

(1.2)

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6

Since this Heisenberg operator is non-linear, a solution of the problem can be often obtained only by linearization. The mean-field approximation is such a linearization which reduces the problem to the interaction of one spin with a so-called mean field generated by all other spins [IL99]. The operator product in eqn. 1.2 is replaced by the product of the spin operator σi and the expectation value hσj i of the spin operator of the interacting P neighbors. The according mean-field can be written as B MF = gµ1B j Jij hˆ σj i. Assuming an external magnetic field B 0 , the Heisenberg Hamiltonian in meanfield approximation is obtained in the form [IL99] X ˆ MF = −gµB H σ ˆi · (BMF + B0 ).

(1.3)

i

1.2.3 Band Model of Ferromagnetism The band model assumes that each electron moves in an effective potential V (r) created by the other electrons and ions of the crystal and that the eigenstates depend only on the spin. The eigenstates are solutions of the Schrödinger equation   ~2 2 − ∇ + Vσ (r) φkσ (r) = Ekσ φkσ (r), (1.4) 2me with me , k and σ denoting the electron mass, the wave vector, and the electron

spin, respectively. Taking into account the energy reduction due to the exchange interaction by renormalizing the one-electron energies, one obtains [IL99] N↑ N N↓ E↓ (k) = E(k) − I . N

E↑ (k) = E(k) − I

(1.5) (1.6)

Here, E(k) are the energy values of a non-magnetic one-electron band structure, N↑ and N↓ are the numbers of electrons in the two spin states, and N the total number of electrons. The so-called Stoner parameter I describes the energy reduction due to the mentioned electron correlations. By defining the normalized excess of spin up electrons as R=

N↑ − N ↓ , N

(1.7)

which is proportional to the magnetization, and by introducing N↑ + N ↓ ˜ E(k) = E(k) − I 2N

(1.8)

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7

for convenience, we obtain 1 ˜ E↑ (k) = E(k) − IR 2 1 ˜ E↓ (k) = E(k) + IR. 2

(1.9) (1.10)

The energy splitting depends on R or in other words on the relative occupation of the sub-bands for the two spin orientations. Since this occupation is in turn given by the Fermi-Dirac distribution 1

,

(1.11)

1 X fk↑ (R) − fk↓ (R) N

(1.12)

f (Ekσ ) = exp the self-consistency condition R=



Ekσ −µ kB T



+1

k

must be fulfilled. By inserting the above equations, this can be written as R=

1 1 X 1 − .   ˜ ˜ 1 1 E(k)− 2 IR−EF E(k)+ 2 IR−EF N + 1 + 1 exp k exp kB T kB T

(1.13)

This equation can be resolved to R under certain conditions, under which a magnetic moment and thus ferromagnetism can exist. The term has to be expanded in powers of R. By restricting the treatment to T = 0 K, which is the temperature where ferromagnetism should occur most probably, and by introducing the ˜ F ) = V D(EF ), the so-called density of states per atom and spin orientation D(E 2N

Stoner criterion for the occurrence of ferromagnetism is finally obtained: ˜ F) > 1 I D(E

(1.14)

EF is the Fermi energy. The detailed proceeding for deriving the Stoner criterion from eqn. 1.13 can be found in [IL99]. The spin-dependent density of states in a 3d-ferromagnet is schematically shown in Fig. 1.1. The band splitting gives rise to the fact that electrons at the Fermi energy are spin polarized, which means that a current flowing in such a material is spin polarized, too. The so-called weak ferromagnetism occurs, when the majority density of states is not fully occupied (e. g. Fe), the strong ferromagnetism with a fully occupied density of states for the majority electrons is found for example in Co or Ni [Zel99].

Theory

8

Figure 1.1: (from [Har06]) Sketch of the band model. Non-ferromagnetic state, both subbands are equally occupied (left). Band splitting has occurred, the spin-up band is shifted, and therefore spin-down electrons have a higher density of states at the Fermi level.

1.3 Micromagnetic Systems Since the microscopic descriptions presented in section 1.2 do not provide parameters accessible to the experiment, a phenomenological approach with macroscopic variables such as the magnetization or an external field are often used to describe experimental findings and the behavior of magnetic systems. Different energy contributions like exchange, anisotropy, dipolar coupling, and Zeeman energy have to be taken into account when calculating the magnetization configuration. This can be done analytically in special cases using the Stoner-Wohlfarth model or by simulations as detailed in sections 1.3.3 and 1.4.2.

1.3.1 Thermodynamics in Magnetism The macroscopic starting point for the description of a magnetic system are the thermodynamic potentials. The magnetic configuration will change under the external conditions in order to minimize its energy or – more precisely – the according thermodynamic potential. The external conditions include magnetic fields and temperature. They may also contain the influence of a current, which will not be considered in the following however, but discussed later in section 1.5. The set of thermodynamic potentials suitable for description includes in general the internal energy, the enthalpy, the free energy, and the Gibbs free energy. Since each of these potentials remains constant if certain parameters are kept constant, the appropriate choice depends on the experimental conditions. The

Theory

9

Gibbs free energy [Ber98] G(H, T ) = U − T S − µ0 H · M

(1.15)

depending on the external field H and the temperature T is convenient in most situations. U denotes the internal energy and S the entropy. Since the magnetization M will be inhomogeneous over the sample in most practical cases, M ˆ ≡ M(r) so that the Gibbs free energy is has to be replaced by a vector field M

replaced by the Landau free energy [Ber98]

ˆ H, T ) = U (M) ˆ − T S − µ0 H · M. ˆ GL (M,

(1.16)

ˆ can be regarded as a continuum This assumes already that the magnetization M vector function in the sample instead of taking into account single magnetic moments or spins. This so-called micromagnetic approximation is justified if systems larger than interatomic distances are investigated. Its application is also limited to systems small enough so that an existing defect density does not dominate the magnetic behavior, since such defects are difficult to include into the above description. Both conditions are fulfilled in the frame of this thesis.

1.3.2 Energy Contributions 1.3.2.1

Exchange Energy

According to eqn. 1.2, a misalignment of magnetic moments leads to an increase of energy. This exchange energy is therefore inevitably present in systems with inhomogeneous magnetization and it is intuitively clear that large gradients are related to a large energy penalty. A Taylor expansion of the exchange energy contribution as a function of the magnetization gradient in the lowest-order term yields Z
A ˆ 2 dV. Eex = ∇M 2 ˆ |M|

(1.17)

The relation between the exchange stiffness A and the atomic scale parameter J ij in eqn. 1.2 can be understood like this: By limiting the sum to nearest neighbors and interpreting the σi as classical vectors one can find that A ∝ kJS 2 /a, where

J is the nearest neighbor exchange constant, S the spin magnitude, a the lattice constant, and k a numerical factor depending on the lattice symmetry [Ber98].

Theory 1.3.2.2

10 Anisotropy Energies

Anisotropy energy contributions arise due to the fact that certain magnetization directions in a system can be more favorable than others. The underlying symmetry breaking allows for classifying the anisotropies by their physical origin. The basic mechanism is the spin-orbit interaction with the prominent exception of the shape anisotropy, which is related to the stray field formation (see section 1.3.2.3). Since the magnetic anisotropy results from the coupling between the orbitals of the crystalline structure and the spin moments via spin-orbit coupling, the magnetic anisotropy will reflect the symmetry of the crystal or exhibit a higher symmetry itself. In a cubic lattice with the crystal axes being the x, y, and z coordinates, the anisotropy energy density can be written as [Ber98]   2 sin θ sin2 (2φ) sin2 (2φ) 2 +cos θ sin2 θ +K2 sin2 (2θ)+. . . (1.18) εani = K0 +K1 4 16 in spherical coordinates or as



εani = K0 + K1 m2x m2y + m2y m2z + m2z m2x + K2 m2x m2y m2z + . . .

(1.19)

in a cartesian system with the mi being the components of the magnetization direction m = M/|M| = (mx , my , mz ). The Ki , which can be positive or negative, define the easy and hard axes or planes of the system corresponding to minima and maxima of the anisotropy energy contribution. When a thin film is considered, in which only in-plane magnetization directions are possible, this is reduced to a fourfold or biaxial in-plane anisotropy: 1 εani = K0 + Kbiaxial sin2 (2φ) + . . . 4

(1.20)

Also twofold or uniaxial anisotropies are observed. All anisotropy energy densities εani can be directly transformed to anisotropy energies using Z
ˆ Eani = εani M(r) dr

(1.21)

V

Further magnetocrystalline anisotropy contributions exist, which do not play

a significant role in this thesis and are therefore only briefly mentioned for completeness: • Anisotropy energy contributions can occur due to symmetry breaking at the surface or interface of films. Due to the scaling with the inverse thickness they can be dominating particularly in thin films and multilayers.

Theory

11

• The magnetoelastic anisotropy arises in crystals were strain is present in

the lattice. A typical situation for the occurrence is the epitaxial growth of multilayers with a lattice misfit that results in strain [COP + 93, Lau02, FHG+ 06].

• External stress gives rise to analog energy contributions like the internal strain, but due to a different origin.

1.3.2.3

Stray Field Energy / Dipolar Coupling Energy

In bulk ferromagnets, the magnetic dipolar interaction is responsible for the existence of magnetic domains because the lowest energy state is achieved with magnetic flux closure configurations. The total energy contribution per unit volume can be written as [Ber98, JBdBdV96] Z Z 1 1 Edip = µ0 H2d dV = − µ0 Hd · M dV, 2 2

(1.22)

where Hd is the magnetostatic or demagnetizing field of the sample. Neglecting the discrete nature of matter the shape effect of the dipolar interaction in a ferromagnetic ellipsoid can be described via the anisotropic demagnetizing field Hd = −N M with the shape-dependent demagnetizing tensor N . For a thin film

all tensor elements are zero except for the direction perpendicular to the layer for which N ⊥ = 1. Equation 1.22 gives in this case [JBdBdV96] 1 Edip = µ0 Ms2 cos2 θ, 2

(1.23)

where it is assumed that the magnetization is uniform with a magnitude equal to the saturation magnetization Ms . θ denotes the angle with the film normal. It can be directly seen, that an in-plane configuration of the magnetization is energetically favorable. 1.3.2.4

Zeeman Energy

The Zeeman energy is the potential of a magnetic dipole moment in a magnetic field. For a homogeneous external field H 0 , this energy contribution depends only on the average magnetization and not on the detailed spin structure of the system. The Zeeman energy can be written as Z Edip = −µ0 H0 · M dV.

(1.24)

Theory

12

1.3.3 Brown’s Equations and the Effective Field Using the energy terms discussed, the magnetization configuration for a given anisotropy and a given applied field can be calculated in principle. Assuming a uniform magnetization, this can be done analytically using the so-called StonerWohlfarth model. A detailed description how this can be performed is presented exemplarily for a system with a fourfold anisotropy in [Wer01, Klä03, TWK + 06]. For an inhomogeneous magnetization, as encountered experimentally in this thesis, the calculations have to be done numerically (which practically means computationally), in order to be able to compare experimental results with the predictions of theory. Adding all energy contributions discussed above yields the following expression for the Landau free energy 1 : Z   A  ˆ 2 ˆ ˆ − 1 µ0 Hd · M ˆ − µ 0 H0 · M ˆ dV GL (M, H) = ∇M + εani (M) ˆ 2 2 V |M|

(1.25)

In order to determine the (meta-)stable magnetization configurations for

given parameters such as the external field, a variational problem has to be solved. The local minima of the Landau free energy have to be determined by varying the magnetization configuration of the system and fulfilling the sufficient conditions for the existence of a minimum

∂ ˆ GL ∂M

= 0 and

∂2 ˆ 2 GL ∂M

> 0.

The difficulty lies in the fact that G L is a functional of the entire vector field ˆ and thus one has to consider the infinite-dimensional functional space of all M possible magnetization configurations. Calculation of the variation δGL of the Landau free energy and taking into account the extremal condition δGL = 0 yields a set of equations that must be fulfilled at equilibrium, known as Brown’s equations [Bro63, Ber98]: ˆ × Heff = 0 M ˆ ˆ × ∂M = 0 M ∂n with

∂ ∂n

(1.26) (1.27)

denoting the derivative in the outside direction normal to the surface.

The first condition must be fulfilled for every point inside the sample, the second is a boundary condition for the surface. The effective field H eff is given by Heff = 1

2 1 ∂εani ∇(A∇M) − + HM + H0 . 2 µ0 Ms µ0 ∂M

(1.28)

Temperature effects are not included in this equation. They are also not included in the

OOMMF code [OOM] used for micromagnetic simulations.

Theory

13

It contains the applied field H0 , the demagnetizing field HM , as well as the exchange and anisotropy contributions. The cross product in eqn. 1.26 shows, that the torque on the magnetization due to the effective field has to become zero in equilibrium. The boundary condition 1.27 can be written in terms of the magnetization unit vector as m(r) × condition

∂ ∂n m(r)

∂ ∂n m(r)

= 0, which is equivalent to the simpler

= 0. The material parameters like the exchange constant A,

the saturation magnetization Ms , all anisotropy constants determining ε ani , as well as the external fields and the shape of the system have to be provided as input information. Solving Brown’s equations then yields the equilibrium magˆ netization distributions M. However, the dynamical behavior of a system, e. g. the response to a change of the external field or the injection of a current, are not included so far, because Brown’s equations only describe the conditions to be fulfilled in the equilibrium state. The answer to this problem is given by the Landau-Lifshitz-Gilbert equation.

1.4 Magnetization Dynamics The well established Landau-Lifshitz-Gilbert (LLG) equation describes the magnetization dynamics in a material without the influence of a current in form of a time dependent differential equation. This basis is derived, before the micromagnetic simulations based on the LLG equation are discussed. The influence of a current is included into the description in frame of the spin transfer torque model, which is presented in the following section.

1.4.1 Landau-Lifshitz-Gilbert Equation The following description shows how the Landau-Lifshitz-Gilbert equation can be obtained from a quantum-mechanical starting point. It is based on the descriptions in [Wie02] and [Hin02]. The precession of an electron spin in an external magnetic field can be derived from the Heisenberg equation of motion i~

 ∂hˆ s(t)i  ˆ s(t)) , = ˆ s(t), H(ˆ ∂t

(1.29)

ˆ the hamilwhere ˆ s(t) is the time dependent spin operator of the electron and H tonian. The brackets h. . .i denote the expectation value of an operator. The com-

Theory

14

  ˆ s(t)) can be approximated to first order in ~ to mutator ˆ s(t), H(ˆ  ˆ s(t))    ∂ Hˆ ˆ ˆ s(t), H(ˆ s(t)) = i~ ˆ s(t) × + O(~2 ) ∂ˆ s(t)

(1.30)

by using the general commutation laws for angular momenta   sˆx , sˆy = i~ˆ sz and cyclically

and

  sˆα , sˆα = 0 with α ∈ {x, y, z}.

This results in the following equation of motion:  ˆ s(t))  ∂hˆ s(t)i ∂ H(ˆ i~ = i~ ˆ s(t) × + O(~2 ) ∂t ∂ˆ s(t)

(1.31)

(1.32)

The transition from quantum mechanics to classical mechanics in the limit ~ → 0

can be performed using the Ehrenfest theorem [Ehr27], which identifies the spin s with the expectation value of the spin operator ˆ s and the classical Hamilton ˆ We obtain function H with the Hamiltonian H. ∂s(t) ∂H(s(t)) = s(t) × . ∂t ∂s(t)

(1.33)

The next step is to replace the spin s by the normalized magnetic moment S or the magnetization being the magnetic moment per volume unit, respectively. Using s = µ/γ with the gyromagnetic ratio γ = gµ B /~ of the electron (g = Landé factor, µB = Bohr magneton) and by normalizing the moment S = µ/µ s , eqn. (1.33) transforms to ∂S γ = − (S × H0 eff ). ∂t µs

(1.34)

The effective field H0 eff is determined by the derivative of the Hamilton function H0 eff =

∂ ∂S H.

In the simplest case, where the Hamiltonian contains only the

Zeeman term (H = µs S · B), the Larmor precession of the electron in an external magnetic field is directly obtained:

∂S = −γ(S × B). ∂t

(1.35)

Already in 1935, Landau and Lifshitz [LL35] included a damping term into the description that takes into account the energy dissipation and the according relaxation of the magnetic moment towards the external field direction. This resulted in the equation ∂S(t) γ λ = − S × H0 eff − S × (S × H0 eff ), ∂t µs µs

(1.36)

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15

where λ is the damping constant introduced. However, investigations of the magnetization reversal time of a magnetic sphere as a function of the damping λ showed that infinite damping unreasonably leads to zero reversal times (1/λdependence) [Kik56]. Gilbert [Gil55] derived the so-called Gilbert equation of motion from the starting point of eqn. 1.33 using a Rayleigh dissipation function:   γ ∂S(t) ∂S(t) 0 = − S × H eff + α S × (1.37) ∂t µ ∂t | s {z } | {z } precession

damping

As in the Landau-Lifshitz equation 1.36, the first term describes the precession and the second the damping. The Gilbert equation 1.37 can be transformed to the general form of the Landau-Lifshitz equation as detailed in the following. Expanding eqn. 1.37 with "S×" on both sides and making use of a × (b × c) =

b(a · c) − c(a · b) leads to ∂S(t) S× ∂t

  γ ∂S(t) ∂S(t) 0 = − S × (S × H eff ) + αS S · −α (S · S) µs ∂t ∂t γ ∂S(t) = − S × (S × H0 eff ) − α . (1.38) µs ∂t

Equating this result with eqn. 1.37 resolved to S ×

∂S(t) ∂t

gives

∂S(t) γ γα =− S × H0 eff − S × (S × H0 eff ), 2 ∂t (1 + α )µs (1 + α2 )µs

(1.39)

which is usually referred to as the Landau-Lifshitz-Gilbert (LLG) equation of magnetization dynamics in the literature. Sometimes also the implicit form with time derivatives on both sides, the actual Gilbert equation 1.37, is referred to as LLG, which is correct in the sense that both equations can be transformed into each other as described. It should be mentioned, that both terms in eqn. 1.39 contain the damping constant α. Therefore, a separation between precession and damping contributions is not possible. It is important to discuss the units used in the equations above. In eqn. 1.34 the moment S is dimensionless with [S] = 1 and the effective field H 0 eff is actually an effective energy. This way of description is favorable for micromagnetic simulations and calculations. But one always has to take a very careful look at prefactors and the exact definition of variables introduced when comparing different publications and sources of information. When the effective field H eff is given in correct units of magnetic fields (A/m) instead of energies ([H 0 eff ] = J)

Theory

16

and the magnetization M is introduced instead of the dimensionless magnetic moment S, eqn. 1.34 can be written as ∂M(t) (1.40) = −µ0 γ(M × Heff ). ∂t This finally leads to an implicit LLG equation analogous to eqn. 1.37 of the form   ∂M(t) α ∂M(t) = −µ0 γ(M × Heff ) + , (1.41) M× ∂t Ms ∂t where Ms denotes the saturation magnetization.

1.4.2 Micromagnetic Simulations We now turn to the numerical treatment of the micromagnetic equations and the widely used solver named "Object Oriented Micromagnetic Framework" (OOMMF) [OOM, DP02]. The operating principle is the following: First, the problem (sample shape) to be solved is subdivided into a two-dimensional grid of square cells with three-dimensional classical spins situated at the center of each cell.2 The cell size has to be smaller (at least not larger) than the relevant length scales, on which the magnetization changes. This can be the exchange length or the Bloch wall width lex =

s

2µ0 A Ms2

(1.42)

r

A , (1.43) K where A are the exchange constant and K an anisotropy constant [HS98]. A cell lwall =

size of 5 nm is a reasonable compromise between computation time and memory consumption on the one hand and a correct modeling on the other hand in most cases under investigation here.3 Smaller cell sizes were sometimes used and found not to influence the results of the simulations [KVB + 04b]. 2

In general, other methods also exist to discretize the problem. OOMMF also provides a true

three-dimensional solver named OXS (OOMMF extensible solver), which is suitable for simulation of layered systems. Furthermore, besides finite difference solvers like OOMMF, which discretizes the problem in cubic cells with equidistant nodes, also finite element based algorithms exist, which subdivide the problem into polyhedral elements [CFK93]. The polyhedra can have a variable size and shape across the object to take into account small features, which require a refined discretization, as well as larger features, for which larger polyhedra help to save computation time [Her01]. A recent review can be found in [FS00]. 3 The particular cell sizes used are given together with the set of input parameters in the results chapter, where the individual simulations are discussed, as well as in table 3.1 on page 72.

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17

For each cell the effective field Heff as derived in section 1.3.3 must be calculated. The anisotropy and Zeeman energy terms are obtained assuming a constant magnetization in each cell. The exchange energy is then computed for the eight neighboring cells. The most time-consuming step is the calculation of the magnetostatic field energy, because it is necessary to sum over the energy contributions from all cells in the structure. It is computed as the convolution of the magnetization against a kernel that describes the cell-to-cell magnetostatic interaction by using fast Fourier transformation techniques, which reduces the number of operations to O(N log 2 N ) instead of O(N 2 ), where N is the number of cells [DP02].

Then a numerical integration of the Landau-Lifshitz-Gilbert equation in the form given in eqn. 1.39 is performed using a second order predictor-corrector technique of the Adams type [DP02]. The procedure is iterated yielding a step by step calculation of magnetization configurations with decreasing energy until ˆ × Heff (see eqn. 1.26) of the effective field on the magnetization is the torque M below a chosen threshold value at each point of the system.

1.5 Spin Transfer Torque Model The theoretical description of current-induced domain wall motion, or in other words the interaction of spin polarized charge carriers with the magnetization of the material, is a complicated issue which is still the subject of much debate as it will be detailed in this section. Starting from the Landau-Lifshitz-Gilbert equation, the relevant approaches to include interactions between current and magnetization into the description will be discussed. The main theoretical framework in this context is the spin transfer torque model.

1.5.1 Hydromagnetic Drag Force During the last three decades, many efforts were made to describe currentinduced effects on domain walls theoretically and different approaches were put forward. A comprehensive review of the development of the theory can be found in [Mar05]. In 1974 the concept of the hydromagnetic drag force was introduced [Ber74, Car74, Cha74]. Then the spin transfer torque theory was developed and different extensions of the Landau-Lifshitz-Gilbert equation for the

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Figure 1.2:

(from [Ber78]) The non-

uniform current distribution (a) in an uniaxial material with a wall can be decomposed into a uniform distribution (b) and an eddy current loop (c) around the wall.

description of interactions between current and magnetization were suggested as detailed in section 1.5.2. The basic principle of the hydromagnetic drag theory is the following: The tilted magnetization in the wall region gives rise to a Hall effect. The current path is therefore modified as visualized in Fig. 1.2(a) and can be regarded as a superposition of the undisturbed current flow (b) with an eddy current around the domain wall (c). This eddy current causes magnetic fields that exert forces on the domain wall so that the wall is displaced in the direction of the charge carrier drift. The force is proportional to the cross-section of the wall and therefore to the film thickness, and so this hydrodynamic drag effect will be generally a significant issue only for film thicknesses larger than approximately 100 nm [Mar05]. Furthermore, the model of Berger [Ber74] was developed with the view on Néel or Bloch walls (see section 4.2) as present in bulk material of films. In 180 ◦ head-to-head domain walls, an analogous geometrical argument as sketched in Fig. 1.2 for a Néel or Bloch wall shows that the hydromagnetic drag force is negligible in this geometry. In the frame of this thesis, nanostructures are fabricated from thin film samples and mainly 180◦ head-to-head domain walls are observed. Thus the hydromagnetic drag force does not play any significant role here.

1.5.2 s-d Exchange Force and Spin Transfer Torque Particularly relevant is the direct interaction between the spin of the charge carrier and the domain wall. This description was also pioneered by Berger [Ber84], who termed the phenomenon s–d exchange force (between the localized 3delectrons responsible for ferromagnetism and the delocalized 4s-electrons carrying the current), but it is referred to as spin transfer torque or spin transfer

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effect nowadays. Starting from the s–d exchange potential   Hsd , V (x) = gµB s · Hsd (x) + 2

(1.44)

where Hsd (x) = −2Jsd hS(x)i/(gµB ) is the exchange field with the s–d exchange integral Jsd and the coordinate x normal to the wall plane, the force applied to

the domain wall by the current is finally obtained as Fx =

2Ms (βve − vw ). µi

(1.45)

Here, ve are the drift velocity of the charge carriers, v w the wall velocity, µi the intrinsic wall mobility, and β a dimensionless constant. The additive constant

Hsd 2

ensuring V (±∞) = 0 consequently does not play any role in the expression of the force. The important underlying assumptions are the adiabatic approximation, which means that the angle between the spin s and the exchange field H sd must be sufficiently small, as well as the classical treatment using Ohm’s law of the diffusive electron motion, which is justified if the electron wavelength is small compared to the wall width. The first approach to integrate the spin transfer torque into the LandauLifshitz-Gilbert equation (eqn. 1.41) by adding additional terms was made by Slonczewski [Slo96]. He considered two ferromagnetic layers separated by a non-magnetic spacer with the macrospins S 1,2 = |S1,2 |ˆ s1,2 . The torque exerted by a charge current I on a macrospin was found to be g ∂S1,2 =I ˆ s1,2 × (ˆ s1 × ˆ s2 ) ∂t e

(1.46)

with the electron charge e and a prefactor g containing the spin polarization P of the current:



1 + P3 g = −4 + (3 + ˆ s1 · ˆ s2 ) 4P 3/2

−1

(1.47)

First we see that the torque is proportional to the current and changes its sign when the current is reversed.4 Secondly, it depends on the spin polarization P , and the direction of the torque is expressed by the product ˆ s 1,2 × (ˆ s1 ׈ s2 ). When including this torque term into the LLG equation 1.41, we obtain a description

of the system with a spin current. 4

Viret and coworkers [VVOJ05] have suggested a current-induced pressure onto a tilted do-

main wall, which is quadratic in the current and therefore independent of its sign, but it is predicted to be dominating only at high current densities and in materials with large resistivity like magnetic semiconductors.

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Also the experimental research in the field of interactions between current and magnetization in this multilayer or so-called pillar geometry has attracted much interest in the last years. One of the first observations of current-induced switching in multilayers was reported by Myers et al. [MRK + 99], current-driven microwave oscillations were observed by Kiselev et al. [KSK + 03], and different temperature dependent experiments can be found in [MAS + 02, TSR+ 04, KEG+ 04]. A time dependent study of current-driven magnetization dynamics is presented in [KES+ 05] and results on the magnetization reversal in systems with perpendicular anisotropy was recently published [MRK + 06].

1.5.3 Landau-Lifshitz-Gilbert Equation with Spin Transfer Torque A key issue for the comparison of theoretical predictions and experimental observations are micromagnetic simulations, which require the correct addition of the torque term(s) to the Landau-Lifshitz-Gilbert equation. Thiaville and coworkers [TNMV04, TNMS05] have suggested the following extension of the LLG equation, that incorporates a spin torque correction for local angular momentum transfer from current to magnetization: ∂M(t) α ∂M(t) = −γ0 M × Heff + M× − (u · ∇)M | {z } ∂t Ms ∂t

(1.48)

extension

γ0 = µ0 γ = µ0 gµB /~ is the gyromagnetic ratio and u is defined below in eqn. 1.54. They restrict themselves to adiabatic processes, i. e. a local equilibrium between the conduction electrons and the magnetization is assumed. This description can be reformulated to obtain what Li and Zhang have introduced [LZ04a]. In the low temperature regime the magnetization has a constant value and thus they obtain τ[LZ04a] = −

1 M × [M × (u · ∇)M]. Ms2

(1.49)

This form of the spin torque is identical with what Bazaliy et al. [BJZ98] have considered earlier for metal-ferromagnet interfaces in presence of a spinpolarized current τ[BJZ98] = −

a M × [M × m] Ms

(1.50)

with m being the unit vector of the magnetization in the pinned layer. This corresponds directly with the macrospin version of the torque suggested by Slon-

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czewski [Slo96] (see eqn. 1.46). If the torque τ [LZ04a] is integrated across the multilayers investigated in [BJZ98], assuming the free and the pinned layer being in single domain states, both torques τ [LZ04a] and τ[BJZ98] turn out to be equivalent. However, the velocity u depends on the spin polarization P of the bulk material, while in the multilayer situation the interfaces are important. Therefore a direct relation between u and a is not obvious. The torque term τ [LZ04a] or the version suggested by Thiaville et al. [TNMV04] in eqn. 1.48 can be regarded as the continuous limit of eqn. 1.46. In [LZ04a] it is shown that the spin transfer torque on a domain wall has many features in common with that at an interface as considered by Bazaliy et al. with the ratio τ[LZ04a] /τ[BJZ98] being given by the ratio tF /W of the thickness of the ferromagnetic layer tF to the width of the domain wall W , i.e. the torque is proportional to the volume of the material that experiences spin transfer effects. By implementing the modified LLG equation into micromagnetic code and applying the code to a 5 nm thick and 100 nm wide wire with a domain wall in the center, they find that the wall is moved by a current, but stops on a nanosecond timescale after a displacement in the sub-µm range. Thiaville et al. [TNMV04] have performed micromagnetic calculations with their torque ansatz as well and they obtain – after including edge roughness – the onset of current-induced wall motion under an applied field above the Walker threshold [SW74] (in contrast to the results in [LZ04a] mentioned before). The wall does not stop, but the wall velocities are two orders of magnitude higher than experimentally observed and also the critical current densities predicted are too high. These discrepancies between theory and experiment called for refined approaches in the theoretical description.

1.5.4 Adiabatic and Non-adiabatic Spin Torque Besides the adiabatic torque discussed so far [TNMV04, LZ04a, LZ04b] also nonadiabatic contributions were considered [TNMS05, ZL04]. The adiabatic processes refer to the situation where the spins of the conduction electrons can locally follow the magnetization, while in the case of non-adiabatic processes this is not possible and a mistracking between the conduction electron spins and the local magnetization occurs. Zhang and Li [ZL04] include a non-adiabatic torque into the description.

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Figure 1.3: (from [LZ04a] (left) and [TNMV04] (right)) First available results from micromagnetic simulations of current-induced domain wall motion obtained by including different spin torque formulations into the Landau-Lifshitz-Gilbert equation.

This is deduced by calculating the response of the non-equilibrium conduction electron spins to a spatially and temporarily changing magnetization and obtain four different torque contributions with two of them representing the adiabatic and the non-adiabatic processes. The other two torque contributions stem from the time dependent variation of the magnetization, are independent of the current density, and lead to corrections of the gyromagnetic ratio γ and the damping constant α, respectively. In other words, they slightly affect only the two terms of the established Landau-Lifshitz-Gilbert equation 1.41 and are therefore of minor interest in this context. The two torques of interest result from spatial variations of the magnetization as present in a domain wall and can be identified with the adiabatic and the non-adiabatic torque ∂M(t) ∂t

α ∂M(t) = −γ0 M × Heff + M× Ms ∂t   bJ ∂M cJ ∂M − 2M × M × − M× , Ms ∂x Ms ∂x {z } | {z } |

(1.51)

non-adiabatic

adiabatic

where the constants bJ and cJ are given by bJ = j

P µB eMs (1 + ξ 2 )

and

cJ = ξbJ .

(1.52)

ξ is defined as the ratio τex /τsf of an exchange time (see [ZL04] for details) and

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the spin-flip relaxation time. Its value is of the order of 10 −2 for typical 3dferromagnets [ZL04]. The second non-adiabatic term is new and can be related to the mistracking of the conduction electron spins. Also Thiaville and coworkers [TNMS05] included a non-adiabatic term into the Landau-Lifshitz-Gilbert equation. They phenomenologically introduced the additional term rather than Zhang and Li [ZL04], who physically derived their suggestion. The extended LLG equation then reads [TNMS05]   ∂M(t) α ∂M(t) β = −γ0 M × Heff + − (u · ∇)M + M× M × (u · ∇)M . | {z } Ms ∂t Ms ∂t {z } | adiabatic non-adiabatic

(1.53)

The generalized velocity

gP µB j (1.54) 2eMs with j being the current density and P its spin polarization, points along the u=

current direction. Assuming g = 2 for an electron, this is identical with the parameter bJ in eqn. 1.53. This phenomenological approach is then tested by micromagnetic simulations. The critical current density drops to zero, but values comparable with the experiment are only obtained when edge roughness is included. However, the domain wall velocities are still much too high compared with experiments. In order to compare the Thiaville approach [TNMS05] with the suggestion of Zhang and Li [ZL04] we can rewrite eqn. 1.51 in the form ∂M(t) ∂t

α ∂M(t) M× = −γ0 M × Heff + Ms ∂t   0    1 β − 2 M × M × (u · ∇)M − M × (u0 · ∇)M . (1.55) Ms Ms

We directly see that both approaches lead to similar extended Landau-LifshitzGilbert equations, but with slightly different expressions for the generalized ve-

locities u and u0 , respectively, which are equal except a factor of 1/(1 + ξ 2 ) ≈ 1. The parameter β, which was introduced phenomenologically first, can be identified with β = (λex /λsf )2 ,

(1.56)

where λex is the exchange length and λsf the spin-flip length [TNMS05]. These equations provide different quantities for the experimentalist to check the validity of the theoretical descriptions. First of all, β or the ratio ξ = c J /bJ ,

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respectively, determine the non-adiabaticity of the spin torque. The doping of 3d-ferromagnets like NiFe, Fe, and Co with rare earth metals might allow to modify the spin-flip length and therefore to modify the value of β as it was already demonstrated for the damping constant α [RCB03, WBHB05, TBBH05, DLBB06]. Different results in experiments due to the artificially modified ratio of adiabatic and non-adiabatic spin torque can reveal information on the roles and the strengths of the two torque contributions. Furthermore, changing the material will change the spin polarization P and the saturation magnetization Ms and therefore modify u. For example, halfmetallic ferromagnets with very high values of P like Fe3 O4 or CrO2 (see section 1.7) and reduced Ms can be expected to show more pronounced spin torque effects compared to typical 3dferromagnets [LZ04b]. Tatara and coworkers very recently suggested a further modification of the Landau-Lifshitz equation [TTK+ 06]. In addition to the adiabatic and the nonadiabatic terms discussed above, they introduce two other torques τ na and τpin due to non-adiabatic momentum transfer 5 and pinning, respectively. Both nonadiabatic contributions are summed to β 0 ≡ βP + βna , where P is the spin

polarization of the current and βna a dimensionless wall resistivity [TTK + 06]. Starting from the equations of motion for the domain wall in collective coordinates [TK04], they identify a weak, an intermediate, and a strong pinning regime. The critical current density is predicted to depend on β 0 in the weak pinning regime and on the damping parameter α in the strong pinning regime. However, existing experimental results of the critical current density in metals are not quantitatively explained by these findings [TTK + 06].

1.5.5 Domain Wall Spin Structure Modifications Additionally to what has been discussed so far also changes of the domain wall spin structure are predicted by theory. In a one-dimensional model Waintal and Viret [WV04] predicted a current-induced domain wall distortion due to a periodic (non-adiabatic) torque generated by the precession of electron spins inside the wall. They suggested that this periodic torque can significantly distort the wall spin structure and that it might support the depinning process and even be able to switch the wall between different types. Recently, a criticism to these 5

Note the difference between the existing β-term, that takes into account non-adiabatic torque,

and the additional term introduced by Tatara et al. due to a non-adiabatic force [TTK + 06].

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findings has been put forward by Xiao et al. [XZS06], who investigate analytically as well as numerically a similar one-dimensional model of a domain wall. They observe a perfectly adiabatic torque for an infinite spin spiral as a simple model for a domain wall and they obtain a different wall width dependence of the non-adiabatic torque for a realistic one-dimensional wall profile. The domain wall model used by Waintal and Viret [WV04] is a finite width spin spiral, which leads to an unphysical gap in the second derivative of the magnetization of the domain wall edges. Thiaville et al. [TNMS05] observed periodic changes between vortex and transverse walls in the results of their micromagnetic simulations of a wall under spin current in a NiFe wire. These predictions were qualitatively confirmed by experiments, where the transformation of a vortex wall to a transverse wall was directly observed with spin-SEM [KJA + 05]. In this thesis, detailed results on current-induced domain wall spin structure changes were obtained using XMCD-PEEM as detailed in section 5.3. Also He, Li, and Zhang [HLZ06] found from their micromagnetic calculations that vortex domain walls tend to transform to transverse walls during the current-induced motion. After the transformation, the transverse walls stop and exhibit a higher critical current density, above which the wall velocity is equal to that of a vortex wall. Shibata and coworkers [SNT+ 06] theoretically investigated a vortex core inside a nanodot under spin current and predict a spiral motion of the vortex core, where the rotation sense depends on the core polarization direction. The final displacement of the vortex core is in transverse direction and increases linearly with the current density. These results are compatible with domain wall type transformations from vortex to transverse walls [KJA + 05].

1.5.6 Critical Current Density and Domain Wall Velocity The critical current density at which a domain wall starts a current-induced motion and the domain wall velocity are important parameters to validate theoretical descriptions by comparing their predictions with experimental results. Furthermore, these two quantities are essential from an application point of view. Since one is obviously interested in low critical current densities and high and reproducible domain wall velocities, e. g. for application in the prominent racetrack memory [Par04], it is important to understand the dependence of these

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parameters on material properties, temperature, wall spin structure, etc. When domain wall motion sets in, the domain wall is depinned, i. e. a pinning potential is overcome. He et al. [HLZ05] have investigated a wire with a constriction by means of micromagnetic simulation and obtained a pinningdepinning phase boundary of critical fields and currents, that depends besides the wire geometry on the non-adiabaticity of the spin torque. In this thesis, such depinning "phase boundaries" are experimentally obtained at constant sample temperatures (see section 5.2). The critical current density is predicted to decrease with increasing non-adiabaticity [HLZ05]. In particular, they suggest the interpretation that the adiabatic torque helps to displace the domain wall center away from the constriction and thus away from the center of the pinning potential, so that the non-adiabatic torque finally depins the distorted wall from a reduced effective pinning potential. When a domain wall is depinned by the critical current it generally moves with a certain wall velocity depending on the current density. Different theoretical attempts were made to describe the domain wall velocity including in particular its dependence on the current density. Several theoretical results were already discussed above in the context of the question on the non-adiabaticity of the spin torque in section 1.5.4 [ZL04, LZ04b, LZ04a, TNMV04, TNMS05]. Furthermore, Tatara et al. [TK04] predicted that the velocity v is proportional to p (js )2 − (jscrit )2 , where js is the spin current and jscrit the critical current. In the case of an adiabatic (wide) wall with spin transfer torque dominating it turns

out that jscrit ∝ K⊥ for weak pinning and jscrit ∝ V0 α for strong pinning. K⊥ is

the transverse anisotropy constant, V 0 the pinning potential, and α the damping constant. For an abrupt wall, where the forces due to momentum transfer do-

minate, jscrit ∝ V0 . This topic has recently been elaborated further [TTK + 06]

as briefly discussed above in section 1.5.4. However, it was pointed out by

Berger [Ber06] that the dependence of the wall mobility µ on the sample geometry t/w obtained from [TK04] as well as from [ZL04] does not agree with available experimental data, which exhibit µ ∝ (t/w) −2.2 (see references in [Ber06]).

In contrast, his own earlier work [Ber84] is explained to be in approximate agreement with these experimental results.

An indication, that defects such as edge roughness play an important role for the domain wall velocity, was also found earlier in numerical simulations of field-induced domain wall motion in NiFe wires with edge roughness [NTM03].

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Domain walls turned out to move faster in rough wires with a velocity of several 100 m/s. Beside pinning effects due to sample defects such as edge roughness also the domain wall spin structure was suggested to influence the critical current as well as the domain wall velocity as already indicated above by the different critical current densities for abrupt and wide walls suggested by Tatara et al. [TK04, TTK+ 06]. Different authors [NTM05, TNMS05, HLZ06] looked at the domain wall velocities of transverse and vortex walls, which are the basic 180 ◦ head-to-head domain wall spin structures occurring in the magnetic nanostructures under investigation (see section 4.2). In particular, the critical current density was predicted to be one order lower for a vortex wall than for a transverse wall [HLZ06] which can be understood from the fact that a transverse wall seems to be more sensitive to pinning in particular at edge roughness defects. A vortex wall can be trapped by a defect located at its core while it remains hardly affected if the defect is located at the edge of the structure [KMS95]. The domain wall velocities at identical current densities are predicted to be the same and of the order of several 100 m/s (for j ∼ 10 12 A/m2 ) for both wall types according to He et al. [HLZ06]. Interestingly, a hysteretic behavior in the wall motion was

observed [HLZ06] meaning that a depinned wall keeps moving at reduced current densities, at which the wall is not yet depinned. This suggests that a higher current density is needed for depinning a wall than for the wall motion itself. Tatara et al. [TSIK05] studied the domain wall displacement driven by an AC current below the critical (DC) current density. They observe that a motion below the threshold can occur if the frequency of the AC current is tuned to the resonance frequency of the pinning potential and thus they confirm earlier experimental results [SMYT04]. Besides the theories discussed so far, which are based mainly on some extended version of the Landau-Lifshitz-Gilbert equation for the description of the magnetzation dynamics, three alternative approaches shall be briefly discussed. Recently, Ohe and Kramer [OK06] numerically studied a domain wall driven by spin-polarized current using the LLG equation, but without any of the extensions discussed. Instead they treat the conduction electrons quantum mechanically in a lattice model of a one-dimensional spin chain and explicitly describe the magnetization and the effective field, which includes the influence of the current, at each spin site. This allows one to take into account quantum interference,

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spin mixing, and spinwave generation. A different picture was suggested by Falloon et al. [FJWS04]. They considered a circuit model of a domain wall, which they regarded as a four terminal device. They predict a simple formula for the domain wall magnetoresistance and obtain a wall velocity comparable in size with e. g. [TK04], but also two orders of magnitude larger than available experimental data. Barnes and Maekawa present "a complete theory" of current-induced domain wall motion "based upon a specific model Hamiltonian and physically justified approximations" [BM05]. They suggest that due to a perfect transfer of angular momentum from the electrons to the domain wall the ground state of the system is a uniform motion of the wall in absence of extrinsic pinning. In contrast to [TK04] they find that intrinsic pinning cannot exist. 6 When extrinsic pinning is included their approach approximately describes the wall velocity dependence on the current density experimentally observed by Yamaguchi et al. [YON + 04].

1.5.7 Temperature Dependence of the Spin Torque and the Role of Spinwaves A very important aspect to discuss is the temperature dependence of the spin torque and the resulting experimental observations. No theoretical calculations or micromagnetic simulations are so far available that include thermal effects into the description of the spin transfer torque phenomena. Tatara et al. [TVF05] have investigated thermally assisted domain wall motion under spin torque in the regime below the critical current density and found that the resulting domain wall velocity has an exponential temperature dependence like the field-driven thermally assisted motion. The fact that experimental wall velocities do not reach theoretically predicted values was attributed to spinwaves [TK04]. The efficiency of spin transfer torque is believed to be reduced because angular momentum is dissipated instead of supporting the domain wall motion. The generation of spinwaves by spin polarized currents was experimentally observed for multilayer systems [TJB + 00, RdALA00]. A spatially resolved study of spinwaves, which are irradiated from a magnetic nanostructure traversed by a current into the surrounding material, can be found in [DDH+ 04, DDH+ 05]. 6

See also comment [Bar06] by Barnes to [TK04] and reply by Tatara and Kohno [TK06].

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Figure 1.4: (from [FBNM04]) Spinwave spectrum modified by current.

Another interesting fact predicted by theory is the so-called spinwave Doppler shift. Due to an applied current the spinwave spectrum is modified and shifted by an amount proportional to the current density of the form j · k as shown in Fig. 1.4. First, this has been suggested by Bazaliy et al. [BJZ98] and

later elaborated in more detail [FBNM04]. The spinwave instability that results from this modified spinwave spectrum should cause the homogeneously magnetized state not to be the ground state anymore [STK05]. Domain nucleation under sufficiently high current densities is predicted to occur and constitute the energetically favorable state. The critical current density was found to be temperature dependent in this thesis (see section 5.2) [LBB+ 06b] and the wall velocity was experimentally found to increase with increasing temperature in a ferromagnetic semiconductor [YCM+ 06]. Such experimental findings have to be related to the theory, in particular to the possible temperature dependence of the different terms of the LLG equation. Also from an application point of view, it is crucial to understand why the spin torque efficiency increases or decreases with temperature. It is suggested that the critical current density depends on the non-adiabaticity parameter ξ, where ξ ∝ 1/λ2spinflip [ZL04, TNMS05]. Thus a decreasing spin-flip length λspinflip with increasing temperature would lead to an increase of the spin torque efficiency. Furthermore the damping parameter α is predicted to have an influence on the wall velocity, though not on the threshold current density in the weak pinning regime examined here [ZL04, TK04]. In Cu/NiFe/Cu trilayer systems a decrease of the spin diffusion length and thus an increase of the damping by spin diffusion in the Cu layer was experimentally observed using

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ferromagnetic resonance experiments [YAMM05, YAMM06]. Finally, the inevitable Joule heating effect has to be mentioned briefly in this context. When discussing the temperature dependence of the spin torque effect it is important to exclude heating effects due to the current. Domain walls can be nucleated due to heating above the Curie temperature of the material [YON + 04]. Therefore, these heating effects have to be quantitatively determined [YON + 04] and taken into account in the interpretation of any experimental data on currentinduced domain wall motion.

1.6 Magnetotransport and Magnetoresistance Effects 1.6.1 The "XMR-Zoo" The general phenomenon that the resistance of a given magnetic system depends on a magnetic field and therefore its magnetization state is called magnetoresistance (MR) effect. Such effects are of high importance for applications in data storage because stored information can be read out by a simple resistance measurement and easily be written by modifying the spin structure with e.g. an external magnetic field. Applications in sensors are also very common nowadays, because the change of a magnetic field influences the magnetization of a sensor and therefore its readout signal. Many parameters of interest such as positions, angles, or velocities can be translated to a magnetic field change [GM04, CvdBR+ 97] and are thus available for measurement via a magnetoresistance effect. The number of reported magnetoresistance effects is large and still growing. The entirety of all effects is sometimes named XMR effect, where the "X" serves as a wildcard character. We will briefly discuss some of the most prominent effects and then look at the effects relevant for this thesis in more detail. 1.6.1.1

Giant Magnetoresistance (GMR)

The giant magnetoresistance (GMR) occurs in magnetic multilayer systems where two magnetic layers are separated by a non-magnetic but conducting spacer [BBF+ 88, BGSZ89]. The effect can be observed in two different geometries, either with the current flowing in the plane (current in-plane, CIP-GMR) or perpendicular to the plane (current perpendicular-to-plane, CPP-GMR) of the

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layers. The resistance depends on the relative orientation of the magnetic layers and is reduced in the case of a parallel magnetization configuration. 1.6.1.2

Tunnel Magnetoresistance (TMR)

The resistance of a stack of two magnetic layers separated by a thin nonmagnetic, insulating barrier depends on the relative orientation of the magnetic layers due to the different tunneling probabilities of charge carriers with opposite spin orientation through the tunnel barrier. The effect is therefore called the tunnel magnetoresistance (TMR) and in the simplifying model of Julliere [Jul75] the TMR ratio is given by TMR =

R − Rk 2P1 P2 = . Rk 1 − P 1 P2

(1.57)

Rk and R are the resistances of the tunnel element with parallel and antiparallel magnetization of the two magnetic layers, respectively. P 1 and P2 denote their spin polarizations. 1.6.1.3

Colossal Magnetoresistance (CMR)

The colossal magnetoresistance (CMR) is observed in manganite perovskites of the composition T1−x Dx MnO3 , where T is a trivalent lanthanide cation (e. g. La) and D a divalent e. g. alkaline-earth (e. g. Ca, Sr, Ba) cation. In such materials a field-induced so-called magnetic ordering phase transition from an insulating to a conducting state takes place [vHWH + 93, Ram97]. 1.6.1.4

Lorentz Magnetoresistance (LMR)

The Lorentz magnetoresistance, sometimes referred to as normal or ordinary MR, results from the Lorentz force of a magnetic induction on the charge carriers. The effect can be large at low temperatures and a low density of impurities and defects [Faw64], and it increases quadratically with the magnetic field. Accordingly, the Lorentz magnetoresistance is usually negligible at room temperature and at moderate fields, which is the case in the frame of this thesis. 1.6.1.5

Spin-disorder Magnetoresistance

The spin-disorder resistivity occurs due to the scattering of the conduction electrons with magnons. The decrease of the number of magnons under an applied

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field leads to a linear decrease of the electrical resistance with the field. This effect has been discussed by Mott [Mot36] in connection with the temperature dependence of the resistivity of ferromagnetic metals. It is more significant close to the critical temperature of the material and usually dominates over the LMR at room temperature.

1.6.2 Anisotropic Magnetoresistance (AMR) The anisotropic magnetoresistance (AMR) was observed for the first time by Thomson [Tho57] in 1857. Anisotropic scattering of the charge carriers caused by spin-orbit coupling leads to an anisotropy of the resistance. The resistivity tensor of a monodomain polycrystal with the magnetization direction chosen arbitrarily along the z-axis can be written as [CF82, FV99]   ρ⊥ −ρH 0   ρij =  0 ρH ρ⊥ , 0 0 ρk

(1.58)

where ρk and ρ⊥ are the longitudinal (along the current) and transverse (perpendicular to the current) components of the resistivity at zero field, respectively, and ρH is the extraordinary Hall resistivity. Taking into account the relation X Ei = ρik jk (1.59) k

between the electric field components E i and the current components jk , this corresponds to the following expression of the electric field E = ρ⊥ (B)j + [ρk (B) − ρ⊥ (B)][m · j]m + ρH (B)m × j

(1.60)

with the magnetic induction B and the unit vector of the magnetization m. With the definition ρ = E · j/|j|2 and θ being the angle between m and j we obtain ρ=

ρk + ρ ⊥ 1 + (ρk − ρ⊥ )(cos2 θ − ). 2 2

(1.61)

If we assume a random orientation of the magnetic domains in zero field, the mean value of cos2 θ is equal to

1 2

in a film with in-plane magnetization so that

the zero field resistivity is (ρk + ρ⊥ )/2, while the saturation values are ±(ρ k − ρ⊥ )/2 for longitudinal and transverse fields, respectively. We can see that the effect does not directly depend on the applied field, but on the spin structure of the sample via the angle θ between magnetization and current.

Theory

33

B

easy axis

remanence low resistance

B-field in easy axis lower resistance

B

B-field orthog. to easy axis higher resistance

Figure 1.5: (from [Büh05]) Schematics of the intergrain tunneling magnetoresistance.

Recently, efforts were made to calculate the AMR for NiFe quantitatively. A semiclassical approach was used [RCdJdJ95] based on a two-current model, which treats currents of electrons with majority and minority spins independently and therefore assumes a weak spin-flip scattering. Ab initio calculations of the AMR for bulk NiFe alloys [KPSW03] resulted in a very good agreement with experimental results [Smi51].

1.6.3 Intergrain Tunneling Magnetoresistance (ITMR) The intergrain tunneling magnetoresistance (ITMR) can be regarded as a member of the TMR family. In CrO2 powder samples, a MR effect was observed in the low temperature regime with a maximum resistance at the coercive field of the material [CBB+ 98]. This effect can be attributed to tunneling of spin polarized charge carriers across the non-conductive grain boundaries between adjacent grains with a slight misorientation (Fig. 1.5). Similar effects were observed in CrO2 films [HC97, ST98]. The MR values increased in powder as well as in film samples with an increased amount of non-conductive Cr 2 O3 . In CrO2 films with high quality and therefore a reduced influence of the ITMR compared to other possible effects, the Lorentz magnetoresistance (see section 1.6.1) gains importance in particular at high fields [GLX00, RRS + 01, RPS+ 02].

1.6.4 Domain Wall Contributions to the Magnetoresistance Magnetoresistance effects can be specific to particular materials (like AMR, CMR) or material systems (like TMR, GMR, ITMR). But also the sample spin

Theory

34

structure and in particular domain wall spin structures can lead to additional magnetoresistance contributions. However, it is important to distinguish, whether a magnetoresistance contribution of a domain wall is an intrinsic effect of the wall or not. The term of "domain wall magnetoresistance" (DWMR) is commonly used, but it is often unclear if the related effect is an intrinsic domain wall contribution – which would justify this term – or simply an extrinsic effect like the AMR contribution of the magnetization inside the wall.

1.6.4.1

Ballistic Magnetoresistance (BMR)

The difference in resistance between parallel and antiparallel orientation of the magnetic moments at point contacts on a ballistic scale is named the ballistic magnetoresistance (BMR) [GMZ99, TZMG99]. The dimensions of the point contact have to be of the order of the mean free path of electrons in the system. A large number of publications investigating MR effects in Ni point contacts and wires can be found in the literature, but the existence and the possible origins of the effect are the subject of much debate. As an example of the controversy, MR values larger than 100.000% were reported [HC03], and at the same time no BMR effects were observed by a second group [EGE + 04] in a similar experiment. Besides a resistance increase due to a domain wall also a decrease [TF97] was suggested and experimentally observed [RYZ + 98]. An oscillatory behavior with the domain wall width was recently suggested from theory [SR05].

1.6.4.2

AMR Contribution to the Domain Wall Magnetoresistance R

Imeas

R

Imeas

Figure 1.6: (from [Büh05]) Schematics of the AMR contribution of a domain wall and its measurement. The current flow is indicated. On the left, no wall is present and the resistance is high, on the right the presence of a domain wall (here a transverse wall) reduces the resistance.

Theory

35

Besides an intrinsic domain wall magnetoresistance also extrinsic contributions, e. g. from the AMR or the LMR, have to be taken into account in any experiment [Hea34, XVH+ 00, CYM+ 06]. In the mesoscopic NiFe structures used in this work, the extrinsic AMR contribution of the domain wall is dominating [KVB+ 02, KVR+ 03]. In the ring geometry with electrical contacts widely used in this thesis, the current flows along the ring perimeter. If no domain walls are present in the so-called vortex state of the ring, the magnetization is aligned parallel to a possible current flow everywhere in the ring (Fig. 1.6, left). But a domain wall represents an area in which the magnetization has a component perpendicular to the current flow as depicted in Fig. 1.6 on the right. This leads to a negative resistance contribution of the domain wall due to the AMR effect, which can be easily measured.

1.7 Fe3 O4 and CrO2 : Halfmetallic Ferromagnets Halfmetallic ferromagnets are characterized by the combination of ferromagnetic behavior and a particular electronic structure that leads to unusually high values of the spin polarization. Besides Heusler alloys also transition metals oxides such as Fe3 O4 , CrO2 , and manganites have been theoretically predicted to belong to the class of halfmetallic ferromagnets. In these materials the spin-dependent density of states (DOS) is asymmetric with respect to the spin orientation, so that for one orientation the electrons exhibit a metallic character due to occupied states at the Fermi level, while the second orientation exhibits a semiconducting behavior with an energy gap at E E N
(E)

N(E) d

d




s s d

N (E)

sf 

d



 a)





N (E)

s s

 b)

Figure 1.7: (from [Kön06]) Schematics of spin-dependent density of states for (a) 3d transition metals and (b, c) for halfmetallic ferromagnets.

Theory

36

the Fermi level as visualized in Figs. 1.7(b) and (c). This behavior was observed for the first time in 1983 in Heusler alloys [dGMvEB83]. The spin polarization in general can be written as P =

D↑ (EF ) − D↓ (EF ) , D↑ (EF ) + D↓ (EF )

(1.62)

where D↑,↓ (EF ) are the densities of states at the Fermi level for spin-up and spin-down electrons, respectively. 3d-metals, as shown in Fig. 1.7(a), exhibit completely spin polarized d-bands, but the non-polarized s-bands contribute to the DOS at the Fermi level yielding a total spin polarization of about 45% for NiFe [PAH+ 98]. In order to obtain a spin polarization of 100% in eqn. 1.62, the s- and d-bands have to be shifted due to hybridization such that the DOS at the Fermi level is non-zero only for one of the 3d-bands. Figures 1.7(b) and (c) visualize two scenarios fulfilling this condition. The bandstructure of CrO 2 belongs to the class shown in (b) with a positive spin polarization, while the Fe 3 O4 scenario with a negative spin polarization is in principle shown in (c). More details about the bandstructure of CrO2 and Fe3 O4 can be found in [Kön06] and [Har06], respectively, and in [Ded04] about both materials, as well as in the relevant references therein. Experimental methods for the determination of the spin polarization of a material are spin-resolved photoelectron spectroscopy [Hüf03], transport measurements in SC/I/FM junctions [TM71, TM73] (SC=superconductor, I=insulator, FM=ferromagnet), or point contact Andreev reflection at a SC/FM interface [UPLB98]. The first experimental evidence for the high spin polarization with a value of 95% was obtained in 1987 from polycrystalline CrO 2 films at room temperature using spin-polarized photoemission spectroscopy [KSG + 87]. Values of more than 90% were confirmed later using superconducting point-contact spectroscopy (e. g. [SBO+ 98]). A similarly high value of about 90% at E F has been also confirmed recently for epitaxial CrO 2 (100) films [DFK+ 02, FDK+ 03], which were the basis for the patterned samples investigated in this thesis. A high spin polarization of approximately -80% at E F of epitaxially grown Fe3 O4 (111) has been observed at room temperature using spin-polarized photoemission [DRG02, FDK+ 03] also on films of the type used in this thesis. Both Fe3 O4 and CrO2 are very well established materials. The first is maybe

Theory

37

the oldest known magnet named magnetite, the later is widely used as storage media on magnetic bands [Cha67]. The high spin polarization values theoretically predicted and experimentally confirmed as detailed above, have attracted renewed interest to these materials as possible candidates in spintronic applications, where the increased spin polarization might lead to more pronounced effects such as a higher tunnel magnetoresistance in tunnel junctions or faster a domain wall displacement at lower critical currents in current-induced domain wall motion or switching experiments.

Chapter 2

Experimental Techniques 2.1 X-ray Magnetic Circular Dichroism Photoemission Electron Microscopy (XMCD-PEEM) In the investigation of spin structures in layered or nanopatterned magnetic samples, magnetic imaging techniques are essential tools for gaining insight into the physics. Magnetic force microscopy is among the prominent and widely used ones (see section 2.6), because it can be made available easily in any laboratory. The method mainly applied in this thesis is XMCD-PEEM with synchrotron radiation, which has the main advantages of being non-intrusive and element-specific. Using synchrotron radiation for investigation of magnetic materials and nanostructures is a fast developing field of research, because more and more synchrotron radiation facilities are available around the world [KAS+ 99, Kuc05], which allow novel experiments giving additional insight into magnetism. Beamlines at synchrotron sources provide monochromatic X-rays with high brightness and tunable energy, which are vast advantages compared to "lab-compatible" X-ray sources. 7

2.1.1 Photoelectron Emission Microscopy (PEEM) The name of photoelectron emission microscopy is misleading, because for the high photon energies used in XMCD-PEEM low energy secondary electrons are 7

The discussion of synchrotron X-ray sources is beyond the scope of this thesis. Physical and

technical details about synchrotron radiation sources can be found for example in a textbook by Wiedemann [Wie03].

Experimental Techniques

39

Figure 2.1: (from [Loc]) X-PEEM and LEEM imaging modes.

dominant for imaging, so that "secondary electron emission microscopy" would be a more precise term [Kuc05]. PEEM is a well established technique for the investigation of surfaces [Sla60]. Monochromatic synchrotron radiation sources have opened a new field of applications for PEEM [TH88], where resonant X-ray absorption at core levels is used to obtain a chemical mapping of the sample surface. The incorporation of an electron beam splitter allows the excitation by low energy electrons instead of Xrays [Bau94] (Low energy electron microscopy, LEEM) and the combination in one instrument provides the advantages of a fast switching between LEEM and PEEM mode. Since in PEEM, the emitted electrons do not have a well-defined energy and momentum, the accelerated electrons are passed through a contrast aperture. Therefore, increased lateral resolution can be only achieved at the expense of intensity and vice versa. Figure 2.1 schematically shows the combined LEEM-XPEEM-instrument installed at the "Nanospectroscopy" beamline of Elettra (see also section 2.1.3). The sample is illuminated by X-rays under an angle of 16 ◦ . The emitted electrons are

Experimental Techniques

40

accelerated by typically 18 kV (Elettra) or 20 kV (SLS) from the grounded sample to the objective lens. A possible sample tilt can be corrected and the lateral position of the sample can be adjusted to chose the desired field of view, which has typical diameters between 5 µm and 100 µm. Astigmatism and small misalignments can be corrected by stigmator lenses. The electron beam is energy-filtered and magnified in the imaging column and then projected onto an electron multichannel multiplier with a phosphorous screen. This screen is imaged with a CCD camera which then provides real-time images of the sample.

2.1.2 Magnetic Circular Dichroism The described PEEM technique becomes particularly useful for magnetic investigations by combination with X-ray magnetic circular dichroism (XMCD). The concept of XMCD spectroscopy, visualized in Fig. 2.2, was pioneered in 1987 [SWW+ 87]. This short description with a view to the application of the concept in XMCD-PEEM follows a brief introduction by Kuch [Kuc05]. The X-ray absorption in a one electron description can be understood as shown in Fig. 2.2(a). Electrons from the occupied 2p core level states 8 are excited to empty states above the Fermi level. Spin orbit interaction splits the 2p level into the 2p3/2 and 2p1/2 levels and the according transitions to the empty 3d states result in the L3 and the L2 peaks, respectively. The transitions into s and p states cause the signal background. When 2p to 3d transitions are induced by circularly polarized X-rays, a different number of electrons is excited for the two X-ray helicities. In a ferromagnet, the density of states (in particular the 3d states at the Fermi level) is spin dependent and therefore the X-ray absorption intensity is different for different polarizations. A dichroism spectrum is obtained as the difference of two spectra acquired with opposite helicities of the incident X-rays. The role of angular momentum becomes particulary relevant, if the XMCD technique is used to determine spin and orbital momenta using the so-called sum rules [TCSvdL92, CTAW93, SK95]. A review on XMCD spectroscopy as an investigation method for the magnetic properties of transition metals can be found in [SN98]. Therein, the sum rules are reviewed: the charge sum rule, the spin sum rule, and the orbital sum rule. Simply spoken, these sum rules link the XMCD line intensity to an electronic or magnetic ground-state property, in 8

To simplify matters here, we restrict ourselves to the L2,3 absorption edges of 3d transition

metals such as Fe, Ni and Co.

Experimental Techniques

41

Figure 2.2: (from [SN98]) (a) Electronic transitions in conventional L-edge X-ray absorption and (b, c) X-ray magnetic circular dichroism, illustrated in a one-electron model. The transitions occur from the spin-orbit split 2p core shell to empty conduction band states. In conventional X-ray absorption, the total transition intensity of the two peaks is proportional to the number of d-holes (first sum rule / charge sum rule). By use of circularly polarized X-rays the spin moment (b) and orbital moment (c) can be determined from linear combinations of the dichroic difference intensities A and B, according to other sum rules (spin and orbital sum rule).

particular spin and orbital moments can be obtained from the XMCD spectra using the sum rules. A detailed discussion is beyond the scope of this thesis, because XMCD is used here as contrast mechanism in photoemission electron microscopy rather than for the determination of magnetic moments with spectroscopy methods.

2.1.3 XMCD-PEEM with Synchrotron Light X-ray magnetic circular dichroism photoemission electron microscopy (XMCDPEEM), sometimes referred to as "PEEM" in this thesis, constitutes the "unification" of the powerful techniques of XMCD and PEEM. It was demonstrated for the first time by Stöhr and coworkers [SWH + 93], who have combined magnetic

Experimental Techniques

42

Figure 2.3: (from [CIL+95]) XMCD spectra of (a) Fe and (b) Co. In the upper parts of the images, the X-ray absorption spectra are displayed for the two helicities, in the lower parts the resulting XMCD spectra are shown.

dichroism with photoemission microscopy and obtained an element-specific, surface-sensitive (5 to 10 nm deep) and non-intrusive technique for mapping the spin structure of films, multilayers, and nanostructures. The typical resolution obtained nowadays is about 30 nm. Topical reviews can be found in [SPA + 98] and [SA00]. According to the above explanation of XMCD the XMCD-PEEM technique can be regarded as a spatially resolved mapping of the XMCD signal, in other words the contrast in the XMCD image results from subtraction of two images taken with different X-ray helicities. This requires to determine the correct energy of the desired absorption edge depending on the material investigated. Example spectra for Fe (NiFe was routinely measured at the Fe edge) 9 and for Co are shown in Fig. 2.3, the spectrum for Fe 3 O4 is presented in section 4.7.2. The image intensity in XMCD-PEEM is proportional to the dot product of the polarization P and the magnetization M of the sample. This means that only one magnetization component can be directly imaged at a time. Information on the complete in-plane magnetization distribution can be obtained together with a second image taken after rotating the sample by 90 ◦ . The PEEM work presented in this thesis was performed at the "Surface and Interface Microscopy" beamline of the Swiss Light Source (SLS) in Villigen / Switzerland and at the "Nanospectroscopy" beamline of the Sincrotrone Trieste (Elettra) in Basovizza / Italy. At both facilities identical versions of the 9

The XMCD signal of Ni80 Fe20 at the Fe edge is stronger than at the Ni edge, which roughly

compensates the effect of stoichiometry [Nol].

Experimental Techniques

43

Figure 2.4: Photographs of the Elmitec PEEM attached to the Nanospectroscopy beamline of Elettra. Top: General view. Bottom: Detailed view showing (1) the PEEM main chamber, (2) the incoming beamline, (3) the electron microscope, (4) the detector, and (5) the camera for image acquisition.

Experimental Techniques

44

commercial Elmitec SPELEEM instrument are installed [LCH + 02] making the distribution of work to both facilities feasible. Figure 2.4 shows two photographs of the Elettra endstation. The instrument is described in section 2.1.1. The standard sample cartridge used for imaging is explained in section 2.3.2, where also our own modifications necessary for pulse injection experiments are presented.

2.2 Magnetoresistance Measurements All magnetoresistance measurements presented in this thesis were performed in a bath cryostat setup developed early in the work. The setup was then improved and tested in the frame of the diploma thesis of W. Bührer, in particular the control software was rewritten and the details of the experimental procedures were elaborated [Büh05]. An overview of the experimental setup is given here.

2.2.1 General Experimental Setup 2.2.1.1

Cryogenic System

A bath cryostat setup from CryoVac was used to perform electrical measurements at temperatures in the range between 1.6 K and 320 K. Figure 2.5 shows a schematic cross-section of the cryostat. The sample holder is inserted from the top so that the sample is positioned in the very bottom of the inner cylinder (number 11 in Fig. 2.5). A built-in temperature sensor is situated directly below the sample. The sample space is isolated with a liquid nitrogen shield and a vacuum shield, that can be pumped down to about 2×10 −6 mbar. About 3.25 liters of liquid helium (LHe) can be stored in the helium reservoir, which is connected via a needle valve with the sample space. The sample space can be pumped with a helium pump so that LHe is drawn into the sample space for cooling. The LHe reservoir exhaust and the He pump are connected to the inhouse He recovery system. Both lines can be connected or disconnected using a valve, called "bypass valve" in the following. The complete cooling system is schematically shown in Fig. 2.6. Essentially, three operating modes of the cryostat exist, depending on the desired temperature [Cry]: • Cooling by flowing gas (T > 4.3 K): The needle valve is opened and LHe is drawn into the sample space by the He pump. The throttle valve and

Experimental Techniques

45

Figure 2.5: (from [Cry]) Schematic cross section (left) and top view (right) of the CryoVac cryostat. 1 – probe space flange, 2 – He pumping flange, 3 – LHe reservoir inlet, 4 – flange for pumping / rinsing the He reservoir, 5 – LHe flux control needle valve, 6 – LN2 inlet and outlet, 7 – flange for connection of He reservoir to He recovery system, 8 – electrical feedthrough for connecting built-in temperature sensor and heating, 9 – isolation vacuum valve, 10 – isolation vacuum flange, 11 – sample space, 12 – LHe flux control needle valve.

Experimental Techniques to He recovery

46

Bypass valve

LHe-reservoir Manometer

Pressure control valve Throttle valve

He-control valve

to He recovery He-pump Sample

Figure 2.6: (from [Büh05]) Schematics of the cooling system.

the needle valve are adjusted for a pressure of about 900 mbar inside the system. The desired temperature is set at the front panel of the temperature controller (see section 2.2.1.3). The heater inside the sample holder is closed-loop controlled by the temperature controller. • Cooling by LHe (T = 4.3 K): For initial cooling, the needle valve is opened and LHe is drawn into the sample space by the He pump. When 4.3 K is

reached the pump is switched off, the needle valve is wide opened and the bypass valve is also opened. In this mode, a complete filling of the LHe reservoir can be used for 5 to 6 h of measurements at a constant temperature of 4.3 K. • Cooling by LHe at low pressure (1.6 K < T < 4.3 K): The system is cooled to 4.3 K as described before. The needle valve is closed and the throttle valve

is fully opened so that the sample space is pumped with the maximum available power. A pressure of about 200 mbar and a temperature of about 1.6 K can be reached. Intermediate temperatures can be obtained by either opening the needle valve slightly (4.3 K "warm" LHe will flow into the

Experimental Techniques

47

small solenoid

Bhorizontal

Bvertical double solenoid

Figure 2.7: (from [Büh05]) Photograph (left) and schematics (right) of the vector field system. The sample is positioned exactly in the center of the two homogenous magnetic fields so that a field along any desired in-plane direction can be created with the setup. Sample rotation allows also out-of-plane fields.

sample space) or by heating the sample very moderately. One LHe filling of the sample space is sufficient for about 30 min, alternatively a slightly opened needle valve allows stabilizing 2.0 K for 2 to 3 h. Since the cryostat temperature remains at about 110 K for about 24 h (depending on the quality of the isolating vacuum) when the system is cooled with LN2 only, temperatures above this value can be stabilized also without LHe by making use of the cooling of the LN2 shield. 2.2.1.2

Vector Field Setup

A photograph of the vector field setup is shown together with a schematics in Fig. 2.7. Two magnet systems, one double solenoid from Bruker and a single solenoid driven by a Kepco power supply, are placed such that they generate orthogonal fields and therefore allow the application of an in-plane field in any desired direction. The horizontal field is generated by a water-cooled Bruker BE-10 double solenoid with a Bruker B-MN ±45/60 C5 power supply, which is

actively controlled via a planar hall probe attached to a bipolar Bruker B-H 15 field controller. Approximately 520 mT can be applied in this direction and stabi-

lized with an accuracy of about 0.01 mT. 10 The small water-cooled solenoid gen10

Problems related to the stability and accuracy of this system and their solutions are discussed

in [Büh05].

Experimental Techniques

48

erates a field in the vertical direction up to about 130 mT. A bipolar Kepco-BOP 36 power supply provides up to 12 A at 36 V flowing through the solenoid with a resistance of approximately 2.8 Ω. Due to massive and still unsolved problems with the GPIB IEEE-488.2 interface card of the Kepco power supply, one of the programmable analog outputs of the lock-in amplifier (see section 2.2.2) is used to control the power supply via an analog signal ranging from -10 V to +10 V corresponding to the full range of ±12 A of the Kepco. 11

Both solenoid systems were calibrated using a longitudinal or a planar hall

probe, respectively, inserted directly into the sample space. While for the small solenoid the necessity of such a calibration is obvious, the Bruker magnet had to be calibrated, because the hall probe of the feedback-control system cannot be placed on the symmetry axis of the field, since the space is completely occupied by the small solenoid and the cryostat. Thus the field measured by the field controller is not identical with that applied to the sample giving rise to a constant correction factor, which depends on the exact mounting position of the hall probe and has to be measured. 2.2.1.3

Sample Holder

An existing sample holder was modified for the particular requirements of the experiments conducted in this thesis. At the end of an approximately 150 cm long metal tube schematically shown in Fig. 2.8 (left), a copper block was attached that hosts a chip carrier with 32 contacts (Fig. 2.8 (right)). 16 shielded twisted pair constantan cables connect the chip carrier with a 32-pin electrical feedthrough at the top end of the tube, which is in turn connected to a switch box with 32 corresponding BNC jacks. A chip carrier as shown in Fig. 2.8 (right) hosts the sample with a maximum size of about 5 mm × 10 mm, which is wire-

bonded to the carrier. This system allows a very fast and reliable sample exchange. Contact problems due to thermal stress were never observed.

Above and below the chip socket, two heating coils with opposite rotation sense can be seen, which allow for a direct heating of the sample without generating any unwanted fields at the sample position. A calibrated Cernox TM temperature sensor is situated above the upper heating coil and is fixed with thermally conductive paste in a hole in the copper block. The 32 signal connections 11

Problems related to the Kepco solenoid setup and their solutions are discussed in [Büh05].

Experimental Techniques

49

connector 32pin 4pin angular disc flange

temperature sensor

heating solenoids

chip carrier holder

Figure 2.8: (partly from [Büh05]) Left: Schematic drawing of the sample holder. Right: Bottom end of the sample holder with the empty chip socket and with a chip carrier mounted. A sample is glued onto the chip carrier and wire-bonded.

as well as the connections of the temperature sensor and of the heating coils are fixed with a black cryo-compatible glue for strain relief (Fig. 2.8 (right)). The sample handling turned out to be a highly critical aspect for conducting experiments successfully, because static electricity as well as other perturbing influences can destroy the highly sensitive samples. The necessary actions taken to protect the samples are described in [Büh05].

2.2.2 Electrical Measurement Circuits Most of the (magneto-)resistance measurements were performed as AC measurements using the RH7280 lock-in amplifier (LIA) from Signal Recovery. Relevant resistance changes to be resolved were partly below 0.05% and therefore, a low-noise setup had to be used. In a lock-in measurement, the frequency of the AC current can be adjusted for an optimized signal-to-noise ratio. The frequency-selective measurement principle rules out any noise except that with the chosen measurement frequency. Here, the LIA was used to generate an AC voltage of the chosen frequency, which serves as a constant AC current source

Experimental Techniques

Lock-In Osc Outp

Rcurr

50

Rwire

sample structure

Lock-In Osc Outp

Rcurr

Rwire

sample structure

Rwire Inp A Inp B

Inp A Inp B Rwire Rwire

Ground

(a) Two-point measurement

Ground

Rwire

(b) Four-point measurement

Figure 2.9: (from [Büh05]) Measurement circuits used for resistance measurements.

when connected across a sufficiently high series resistor to the sample. The LIA inputs A and B were used for a differential voltage measurement between two contacts of the sample. In the following, the different measurement circuits are explained in detail.

2.2.2.1

AC Resistance Measurements

Two-point AC resistance measurements were mainly used to characterize a new sample and cross-check whether all contact leads and the connected nanostructures itself are intact. The circuit is shown in Fig. 2.9(a). Since a typical twopoint sample resistance including the wiring is 300 Ω for the NiFe samples investigated, Rcurr was usually chosen to be 100 kΩ. In this case, the LIA output amplitude allows measurement currents of up to 10 µA. For measurements on CrO2 , a lower Rcurr was used to obtain a better signal-to-noise ratio due to the higher measurement current. The four-point resistance measurement setup is shown in Fig. 2.9(b). The four-point method allows a direct measurement of the sample resistance without additional contact or wire resistances, which are typically larger than the sample resistance, because the constantan wires inside the sample holder contribute each with about 100 Ω. The firmware of the lock-in amplifier had to be modified by the manufacturer in order to read out the measured signal with the full available precision [Büh05], so that even smallest resistance changes due to the applied magnetic fields or current pulses could be detected with a sufficiently small discretization of the measurement signal.

Experimental Techniques

51

sample structure

Pulse-Generator Rwire Lock-In

Rcurr

Rwire

Osc Outp Rwire Inp A Inp B

Rwire Rwire

Ground

Figure 2.10: (from [Büh05]) Measurement circuit for pulse injection and consecutive resistance measurement.

2.2.2.2

Pulse Injection

In order to study current-induced domain wall motion, current pulses have to be injected under applied fields followed by a resistance measurement, that is used to detect the spin structure changes via the AMR effect as described in section 1.6.4.2.12 The pulse injection with a wiring as shown in Fig. 2.10 was performed with the 33220A function generator from Agilent Technologies. The internal output resistance of 50 Ω of the pulse generator is connected in parallel to the sample, when its output is switched on. This causes the LIA to measure completely different values, because a significant amount of the measurement current is then flowing through the pulse generator. Thus the pulse generator output had to be switched off during any resistance measurement. 2.2.2.3

Joule Heating Measurements

As described in section 5.2.3 it is crucial to quantitatively measure the Joule heating effect of the current pulses in order to separate thermal and spin transfer torque effects. Yamaguchi and coworkers have suggested an experimental method [YNT+ 05, Yam04], which we have adopted successfully. First, the resistance dependence on temperature is measured independently using the four-point resistance measurement described above over the complete temperature range available in the cryostat. A small current of 5 µA is used which is expected to cause no significant Joule heating. In a second step, a storage oscilloscope is integrated into the circuit as shown in Fig. 2.11. While the 12

The detailed experimental procedure is explained in section 5.2.2 on page 118.

Experimental Techniques

52 Rcurr

Pulse generator

Rwire

sample structure

Rwire

Storage Oscilloscope Rwire Rwire

Figure 2.11: (from [Büh05]) Measurement circuit for investigation of Joule heating due to pulses.

pulse is injected across the sample and a series resistor R 0 , the voltage drop across either the sample (Usample ) or the series resistor (U0 ) is measured using a Tektronix TDS 620B storage oscilloscope. 13 The temperature independent resistance R0 and the voltage drop U0 allow the calculation of the pulse current I 0 , which in turn provides the sample resistance R sample using Rsample =

Usample Usample = R0 I0 U0

(2.1)

The timescale needed to reach thermal equilibrium has to be much shorter than the typical pulse length of 10 to 20 µs, which is the case here as discussed in [Büh05]. 2.2.2.4

DC Resistance Measurements

In particular for CrO2 , for which the contacts turned out to be non-ohmic, I-Ucurves had to be measured. For this purpose a Keithley 6430 sourcemeter was used as a programmable DC current source, while the voltage drop across the sample was measured with a Keithley 2000 or 2001 multimeter. The sourcemeter was not used directly for the resistance measurement, because the multimeters offered a more precise voltage measurement. Resistances were measured in twopoint as well as in four-point configuration as described above for the AC case.

2.2.3 Software "TransportLab" The whole setup is fully controlled over a PC equipped with a GPIB interface card, a serial bus, and with the LabView TM software installed. The lock-in amplifier, the pulse generator, the Bruker field controller, the sourcemeter, and the 13

In contrast to Yamaguchi et al. [YNT+ 05], two separate measurements must be performed,

since the available oscilloscope does not allow for a parallel measurement. This should not influence the results, since the pulse injection and the resulting heating are expected to be reproducible.

Experimental Techniques

53

multimeter are connected via the GPIB bus. The temperature controller is addressed via the serial interface and the Kepco power supply is controlled using one of the two analog outputs of the lock-in amplifier. For the special purpose of gauging the applied magnetic fields a gaussmeter with a hall probe was used. The gaussmeter was also connected via the GPIB bus for a convenient readout. Using LabViewTM a user interface called "TransportLab" was developed which allows to drive the experiment flexibly, adjust all relevant parameters, as well as to display and save the experimental data. The main measurement modes implemented and frequently used are briefly explained in the following: • Rotation Sweep:

The field amplitude is kept constant but rotated within defined angular

ranges with chosen stepsizes. The resistance is measured after each field step. • "Mode Étoile":

The "mode étoile"14 is a modification of the rotation sweep. A saturation field is applied in every direction and then reduced to any desired value (preferably zero), before the resistance is measured and the procedure re-

peated for the next rotational field step. • Amplitude Sweep:

This is an extension of a standard hysteresis curve measurement. For a defined angle, any desired series of field amplitude sweeps can be executed.

• Rotation Amplitude Sweep:

The rotation amplitude sweep is a combination of the rotation and the amplitude sweep. It allows to execute the amplitude sweep mode for any

desired series of angles instead of only one fixed angle. It should be mentioned that the same measurement as performed with the mode étoile can be done using the rotation amplitude sweep mode and reorganizing the sequence of data points. 14

The term "mode étoile" (French for "star mode") is derived from the star-like field history

applied to the sample in this mode. The French version originates from similar MR measurements of M. Kläui performed in collaboration with W. Wernsdorfer in Grenoble [KVR + 03], where this Francophonic term was "born".

Experimental Techniques

54

• I-U-curves:

Current voltage curves can be automatically recorded using the devices

described in section 2.2.2.4. Minimum and maximum current to be applied and the current step size can be chosen. • CIDM for NiFe:

This mode conducts the complete measurement for current-induced do-

main wall motion experiments on NiFe samples. By saturating the field in a desired direction and releasing it back to zero, a domain wall is created and positioned. The resistance is measured to confirm this. Then an amplitude scan is performed during which pulses are injected after each field step. Optionally, the saturation can be repeated for each field step before the pulse injection in order to prevent, that a first current pulse transforms the spin structure of the domain wall, so that the critical current for wall motion is reduced or increased for the following pulse injection. • CIDM for CrO2 :

Since resistance levels were not entirely reproducible for CrO 2 samples, i.e.

the domain wall configuration was obviously not ideally reproducible, this measurement mode was implemented in addition to the existing CIDM mode for NiFe. The domain wall preparation is performed by applying a certain field (usually maximum field) in a given direction along the CrO 2 stripe, then a lower field is applied in the opposite direction. Thus, the magnetization in the stripe is saturated first and afterwards one part of the stripe is reversed. The relevant switching fields have to a determined before. Then an amplitude sweep is acquired (see above). A list of field strengths can be defined at which a pulse is injected. The field sweep is interrupted at these field steps and continued again after the pulse injection. The resulting data set allows to compare the resistance levels before and after the pulse injection individually. All measurements can be executed directly from the software interface or saved as a script file. Saving as a file allows arbitrary combinations of measurements to be executed without user attendance. The measurement data is saved and a live plot provides direct information about the running measurement. A detailed description of the software "TransportLab", the underlying script concept and the programm modules can be found in the appendix A of [Büh05].

Experimental Techniques

55

2.3 PEEM with In-situ Current Pulse Injection Implementing the possibility of current pulse injection into the PEEM instruments at Elettra and SLS allows for studying current-induced effects on the spin structure of nanostructures, and in particular of domain walls, by direct imaging. Advantageous compared to MR based measurements is the direct proof of any observation by an image rather than a resistance change. It is also possible to investigate materials which show no or no significant suitable MR effects. In contrast to magnetic force microscopy (MFM), XMCD-PEEM is a non-intrusive technique that does not influence the spin structure of the sample during imaging, as the MFM tip can do. Furthermore, the in-plane magnetization is mapped directly, while the MFM is sensitive to the stray field components which are parallel to the tip magnetization.

2.3.1 Pulse Injection Unit However, in order to combine the possibility of current pulse injection with the powerful imaging technique of XMCD-PEEM, significant technical difficulties have to be solved. Since a high voltage of 20 kV is applied between sample and microscope during imaging, all attached electronics has to be installed inside the HV rack of the instrument or the complete PEEM has to be switched off for each single pulse injection. The latter method served well for demonstrating that the experiment is feasible in general, but for an efficient use of beamtime the necessary equipment has to be installed inside the HV rack and driven from an externally connected computer. In the following, the final version of the setup, which has been improved during the course of several beamtimes, is described. A brief outlook on the near future version is given. Figure 2.12 schematically shows the present version of the setup together with planned extensions (hatched). The pulse generator is remotely controlled via a laptop, which is connected using a commercial fiberoptic LAN cable and two media converters that transform the electrical to optical signals and vice versa. This way of connecting equipment allows to bridge the high voltage of the rack and to externally drive the pulse generator using a user-friendly web application running on the instrument directly. A single pulse with desired amplitude, duration, polarity, and shape can be injected into the sample by a simple mouse click. The pulse generator output with a maximum of ±10 V is ampli-

fied by a self-constructed pulse amplifier that allows generation of pulses up to

Experimental Techniques

Fiberoptic LAN PC or Laptop

56

Figure 2.12: Schematics of the pulse in-

HV rack (20kV) Transformer Pulse Generator

Pulse Amplifier

jection setup installed in the HV rack of the PEEM. The existing components – the

LIA

transformer, the pulse generator, the pulse amplifier, and a laptop connected via a fiberoptic LAN cable – are shown in white.

PEEM

Switch Box

Planned extensions of the setup including a lock-in amplifier for MR measurements and a switch box are shown hatched. The fiber

sample

LAN connections (existing and planned) are indicated as dotted lines.

±310 V, which can be applied to the sample. An isolating transformer is used

to keep the complete pulse equipment floating with respect to the 230 V power supply inside the HV rack. This is necessary in order to ensure that all instru-

ment grounds have the same potential like the ground of the attached sample. The sample ground potential can vary due to the applied start voltage of the PEEM as well as unintentionally during eventually occurring discharges on the sample. Furthermore, a "security switch" is incorporated in the setup (not shown in Fig. 2.12). Manually switched by an isolating stick from the front of the HV rack, it either connects the sample to the pulse amplifier and the generator or disconnects the instruments for additional protection during imaging. This setup allows a very efficient way of flexible pulse injection into the sample so that the limiting time factor remains the PEEM operation itself (mainly time for image acquisition and sample remagnetization). A further improved setup is planned. This will include a lock-in amplifier for in-situ magnetoresistance measurements, which will allow for investigations of current-induced effects on the spin structure (domain wall motion and transformations) together with inverse effects (current changes due to resistance modifications induced by a modified spin structure). In order to variably connect the pulse generator or the lock-in amplifier to the four possible sample contacts (see section 2.3.2) or disconnect the equipment for protection during imaging, a remotely controlled switch system will be implemented. This complexity calls for a dedicated control software, for example based on LabView TM , to drive the complete experiment via the existing fiber LAN connection.

Experimental Techniques

57

Figure 2.13: (from [Loc]) Photos in top view of the standard Elmitec PEEM sample holder with the cap mounted (left) and dismounted (right). The holder is fixed in a frame for mounting purposes. The sample is shown in blue.

2.3.2 Sample Cartridge For current pulse injections, four spring connectors are available on the commercial PEEM cartridges from Elmitec. Two are normally used for the thermocouple and two for the filament, that allow for heating the sample and measuring the temperature. These four contacts are used to simultaneously connect four different structures on the sample for current pulse injections. The cartridge potential (start voltage potential) serves as a common "ground" for all structures. However, the sample itself has to be connected to the contacts on the sample holder without shortcuts to the cartridge. A cap on top of the sample with a circular hole in the center provides a flat surface, which is a necessary precondition for applying high voltages. In particular this cap should not shortcut the structures on the sample. At present, two working sample cartridge versions exist. The first is a modified Elmitec cartridge, the second is an own development based on an existing design of J. Raabe.15 Images of the original Elmitec sample holder with and without the cap mounted are shown in Fig. 2.13. Our own modification of this holder is presented in Fig. 2.14. The inner part is replaced by an isolating macor socket. The sample is fixed with silver glue on R coated wires connect the contact springs on the bottom side with top. Kapton

small pieces of Au foil, which are fixed at the edges of the macor cylinder using 15

We gratefully acknowledge the transfer of knowhow from J. Raabe, who had successfully

performed experiments using a self-constructed sample cartridge with current pulse contacts before [RQB+ 05].

Experimental Techniques

58

Figure 2.14: Elmitec PEEM sample holder modified for current injection with the cap mounted (left) and dismounted (right), where sample and Au foil pads can be seen.

Figure 2.15: PEEM sample holder for current injection (own design), top view (left) and crosssectional view (right). The cap is dismounted, so that the circuit board base plate can be seen, where the sample can be mounted on top.

Experimental Techniques

59

also silver glue. A wire bonder with Au or Al wire is then used to connect the Au foil pads with the structured contact pads on the sample. The cap is partly isoR foil to prevent electrical contact between lated on the inner side with Kapton

the cap and the sample or the Au foil. Furthermore, the cap is supported by washers so that the screws do not press the cap onto the sample surface, which

might physically destroy the bonds as well as shortcut the patterned contacts on the sample. A maximum distance of about 1 mm between sample surface and cap still allows for imaging of features that are located sufficiently close to the center of the sample. The second approach consists of a cartridge with a larger cap, that covers the complete holder as shown in Fig. 2.15. On the bottom side of the cap, a circular countersink provides additional space for the bonding wires. The sample is glued with PMMA resist onto a specific base plate. This plate is made from a Cu plated high frequency circuit board material, 16 on which structures are patterned using standard optical lithography and an etching process. The sample is wire-bonded to this plate. The leads allow attaching the sample in different orientations, because two sets of bond pads are available. This base plate is fixed on the cartridge with screws and connected to the contact springs via R coated wires, which are soldered onto the contacts. Kapton

2.4 Electron Holography Electron holography is an electron microscope imaging technique for quantitative measurements of the magnetic induction and the magnetization with a sub-10 nm resolution. Reviews on the technique and the presentation of state-ofthe-art results obtained on magnetic nanostructures can be found in [MDBS05] and [DBMK+ 00]. The technique is based on the interference of coherent electron waves that produces an interferogram or "hologram". This interference pattern must be processed to retrieve the complex electron wavefunction, which contains the phase and the amplitude information about the sample. In off-axis electron holography, which is illustrated schematically in Fig. 2.16, an electrostatic biprism is used to interfere the electron wave scattered by the sample with a reference wave 16

The circuit board material is "RT duroid 3003", a spare board of which was available in the

electronic workshop.

Experimental Techniques

60

Figure 2.16: (from [MDBS05]) Schematic ray diagram of the transmission electron microscope used for off-axis electron holography. The field emission gun (FEG) provides the coherent illumination of the sample and the biprism.

that has traveled through vacuum. The relative phase shift of the scattered electron wave contains information on the mean inner potential of the sample as well as the in-plane component of the magnetic field integrated along the incident beam. The phase shift φ is given for one dimension by [MDBS05] Z ZZ e φ(x) = c V (x, z)dz − By (x, z)dxdz ~

(2.2)

with a universal constant c, V being the inner potential and B y the in-plane component of the magnetic induction perpendicular to the x- and z-directions. The z-axis is chosen to be the direction of the incident electron beam. This equation, which correlates the phase shift with the magnetic induction, is the basis for reconstructing the in-plane structure of the magnetization in the sample and of the stray field. However, from this description it becomes clear that the technique is limited to thin samples with a maximum thickness of about 500 nm because the electron wave has to be transmitted without too many unwanted multiple scattering events. The electron holography experiments reported in this thesis were performed by H. Ehrke at the University of Cambridge in the group of R.-E. Dunin-Borkowski.

2.5 Scanning Electron Microscopy (SEM) Since the structures investigated in this thesis have typical dimensions in the micrometer and feature sizes in the nanometer range, optical microscopy cannot be

Experimental Techniques

61

Figure 2.17: (from [Klä03]) Schematics of a scanning electron microscope.

applied to image the samples and check for quality and possible damages. Scanning electron microscopy (SEM) is a suitable technique, because the de-Broglie wavelength of the electron is h λB = √ 2me eU

(2.3)

with me and e being the electron mass and charge, respectively. It has a value of about 1 pm for typical acceleration voltages U . In the SEM, an electron gun generates a beam that is collimated by electromagnetic lenses, focused by an objective lens, and scanned across the sample surface by electromagnetic deflection coils. Secondary electrons emitted from the sample are collected and used to form the image. A schematic of a SEM is shown in Fig. 2.17. Besides the main requirement of a conductive sample surface the SEM technique is easy to handle and therefore widespread and commonly used nowadays [Rei98].

Experimental Techniques

62

2.6 Atomic and Magnetic Force Microscopy (AFM / MFM) Atomic and magnetic force microscopy belong to the class of the scanning probe microscopy techniques [Wie94]. The scanning tunneling microscopy uses the quantum tunneling probability between a tip and the sample as basic information for imaging, while atomic force microscopy (AFM) [BQG86] uses forces between tip and sample in order to acquire the topography. In AFM the tip is mounted on a cantilever, of which the displacement is measured using a reflected laser beam. The tip is scanned across the sample and the interaction force is measured via the laser beam spot displacement. In the static operation mode or so-called contact mode, tip and sample are in contact and a feedback loop maintains a constant (zero) flight height of the tip. A topographic image of the surface with a constant force is obtained. In the dynamic mode or so-called non-contact mode, the cantilever oscillates with a frequency close to its eigenfrequency. The resonance frequency, the frequency shift, and the oscillation amplitude allow to obtain information on the forces and thus on the surface. Magnetic force microscopy (MFM) is based on the same principles like AFM, but it is sensitive to magnetic forces by using a ferromagnetic tip that interacts with stray fields of the sample. It is important to notice that the MFM data contain both the topographical information of the corresponding AFM image together with the magnetic information. Assumed that the tip magnetization is fixed, the components of the force are given by [TMG05] ZZ Z ZZZ ∂Hsample ∂Htip Fi = µ 0 Mtip · = µ0 Msample · , ∂xi ∂xi Vtip Vsample

(2.4)

where V denotes the respective volumes of tip and sample, M the magnetization and H the stray field. This means that different components of the stray field can be measured with different tip magnetizations in principle. However, the common way of operation is using a tip magnetized perpendicular to the sample surface along its main axis (which is more stable due to its shape anisotropy) and measuring the out-of-plane components of the stray field as done here.

Chapter 3

Magnetic Nanostructures – Fabrication and Properties 3.1 Introduction and Overview The sample fabrication is a crucial step on the way to successful experiments in the entire field of nanomagnetism. 17 The nanostructures investigated in this thesis were fabricated using a set of techniques, which will be discussed in this chapter. First the material deposition is described, which was performed either by molecular beam epitaxy or chemical vapor deposition. Then the lithography and pattern transfer are discussed. Finally the relevant general structural and magnetic properties of the samples will be discussed. In order to fabricate magnetic nanostructures, besides material deposition the nanoscopic shape has to be defined, which is done in many cases using lithography techniques, and the pattern has to be transferred into the continuous magnetic film.18 This pattern transfer is often performed using an etching 17

After gaining own experience in sample fabrication using optical lithography, ion beam de-

position, and ion milling (see appendix B), I gratefully acknowledge the support of many people, who were involved in the preparation of excellent samples, which were the basis for interesting experiments. In particular these are: D. Backes and L. J. Heyderman at the Laboratory for Microand Nanotechnology at the PSI in Villigen (CH), C. A. F. Vaz at the Cavendish Laboratory in Cambridge (UK), L. Vila and E. Cambril at the Laboratoire de Photonique et de Nanostructures - CNRS in Marcoussis (F), C. König at the RWTH Aachen as well as C. Hartung, M. Fonin, and M. Kläui in Konstanz. 18 This description is restricted to the so-called top-down approach, which means that a continuous sample (film) is patterned in the desired way. The alternative is the bottom-up approach,

Magnetic Nanostructures – Fabrication and Properties

64

step, which can be a chemical wet or dry etch process, or using an ion milling step, which is a "mechanical" way of pattern transfer. A special case is the focused ion beam milling (FIB), where a focused beam of ions is scanned across the sample surface and thus the pattern definition and transfer are executed in the same process step. The pattern transfer can be performed before or after the film deposition. In the case of prepatterned substrates, the desired pattern is first transferred to the substrate e. g. by lithography and subsequent etching and the structures are directly obtained during deposition. When the pattern transfer is performed using a so-called lift-off, first a mask is defined lithographically, then the material is deposited and finally the unwanted material is removed by lifting off the mask together with the material on top. The third possibility is to start with the film deposition, lithographically define an etching mask afterwards and then perform an etching or milling process for the pattern transfer. This very brief overview of nanopatterning does not lay claim to being complete in any way, but has introduced all relevant techniques which are used in this thesis and are therefore described in more detail in the following sections of this chapter.

3.2 Material Deposition For the deposition of magnetic materials, two techniques are relevant for the samples investigated in this thesis. The first is the molecular beam epitaxy (MBE) 19 [HRS04], during which a beam of atoms or molecules is evaporated from a material source onto a substrate, where the atoms (or molecules) condense in a crystalline lattice. Ultra high vacuum (UHV) conditions are necessary to ensure a clean surface and an undisturbed film growth. The lattice mismatch of the materials involved, resulting strain, the possible presence of any process gas such as e. g. O 2 , as well as temperature and pressure during growth can influence the process critically. The which consists of building the desired nanostructures from an atomic or molecular starting point e. g. by self-assembly techniques [SLB04]. However, well-defined particular shapes and sample designs can often be obtained only using top-down methods, since they allow the definition of any desired pattern within the general limits and resolutions of the techniques used. 19 The abbreviation is also used for the apparatus itself.

Magnetic Nanostructures – Fabrication and Properties

65

MBE technique was used for the preparation of all NiFe, Co, and Fe 3 O4 samples investigated. The second technique is chemical vapor deposition [HRS04], which means the deposition of a film from a precursor in the gas phase, used here for the preparation of the CrO2 films.

3.2.1 Molecular Beam Epitaxy of NiFe and Co Layers The samples are grown in an UHV chamber with a base pressure of typically ≈ 2×10−10 mbar as described in more detail in [Klä03, HDK + 03]. The growth

chamber is equipped with an Auger electron spectroscopy system to check the sample composition and purity and a reflection high energy electron diffraction (RHEED) system to determine the quality of the surface crystallinity. The thickness of the deposited films is estimated using a quartz crystal monitor. The system has four sources for the evaporation of metals. A diagram of the growth chamber is given in Fig. 3.1. The samples investigated in this thesis were grown on naturally oxidized Si substrate. This yields polycrystalline films, while for the ideal epitaxial growth of a single crystal film the SiO layer would have to be removed and a Cu seed layer deposited onto the substrate. The ferromagnetic

P2 P1

Figure 3.1: (from [Klä03]) Schematic

V 1

view of the UHV system used for MBE growth of NiFe and Co.

W1

to P4: vacuum pumps; V1 to V6:

V 6 V 2

RH EED

AES

G1

P 4

valves; W1 to W3: glass windows; G1: ion gauge.

W3

W2

P1

Evap.

Magnetic Nanostructures – Fabrication and Properties

66

layer was capped with typically 2 nm Au or about 5 Å Al in order to prevent oxidation of the samples.20

3.2.2 Molecular Beam Epitaxy of Fe3 O4 Layers Epitaxial Fe3 O4 (100) thin films with thicknesses between 30 nm and 50 nm were grown by MBE on MgO substrates as described in [Har06] and discussed in more detail in [Fon04]. The very small lattice mismatch of only 0.31% between the unit cell size of Fe3 O4 (8.396 Å) and twice the cell size of MgO (4.212 Å) makes MgO a very suitable substrate for epitaxial growth of high quality Fe 3 O4 films [KGC97]. Here MgO(100) single crystal substrates of rectangular or square shape (5 mm×10 mm or 10 mm×10 mm) were used. The Omicron Surface Science System shown in Fig. 3.2 with its main components indicated was used for the growth of epitaxial Fe 3 O4 films and subsequent structural characterization as described in section 3.4.2. Before deposition, the 20

The choice between Au and Al partly depended on the availability of the material in the

growth chamber. The thicker Au layer has to be removed by in-situ sputtering before imaging with XMCD-PEEM, while the Al, exhibiting a wetting growth mode, sufficiently prevents the oxidation at a film thickness below 1 nm. Thus the Al capping can remain on the sample surface during XMCD-PEEM imaging.

Figure 3.2: (from [Har06]) Photographs of the UHV system used for MBE growth of Fe3 O4 . (1) manipulator for sample positioning and heating, (2) Omicron EFM 3 evaporators with integral flux monitor, (3) four-pocket electron beam evaporator, (4) RHEED system, (5) analysis chamber, (6) X-ray source, (7) UV source, (8) hemispherical electron energy analyzer, (9) LEED system, (10) sputter ion source, (11) loadlock.

Magnetic Nanostructures – Fabrication and Properties

67

substrates were annealed in-situ in an oxygen atmosphere of 5×10 −6 mbar for 1 h at about 600◦ C and for further 10 minutes at about 700 ◦ C. The Fe3 O4 (100) films were prepared by evaporation of Fe in an O 2 atmosphere of 5×10−6 mbar with a deposition rate of approximately 2 Å/min. The substrate temperature was initially set to 500◦ C and then reduced to ≈ 310◦ C. For protection during the following ex-situ processing and in order to prevent oxidation before and

during the experiments, a 3 nm thick Au capping layer was deposited on top.

3.2.3 Chemical Vapor Deposition of CrO2 Layers CrO2 films with high epitaxial quality are usually grown by thermally induced decomposition of a solid or gaseous precursor as initially suggested by Ishibashi et al. [INS79]. Typical precursors are CrO 3 , available in the solid state, and CrO2 Cl2 , initially available in liquid form. The process gas is transported using convection, diffusion, or a defined gas flow to the substrate surface, where the atoms are adsorbed first, form growth centers by diffusion, and finally contribute to a continuous film growth. For the samples investigated here, TiO 2 (100) substrates were used with a lattice mismatch of 3.7% along the in-plane a-axis and of 1.5% along the caxis [Kön06]. CrO3 was used as precursor material in the chemical vapor deposition (CVD) process. A schematic view of the setup is shown in Fig. 3.3. Details of the necessary substrate pretreatment, the complete film deposition process, and the setup can be found in [Kön06].




O2 

 



 

O2 Figure 3.3: (from [Kön06]) Schematic view of the CVD setup used for the preparation of CrO2 (100) films with CrO3 as solid precursor material. (1) quartz glass tube; (2) single zone furnace; (3) precursor material CrO3 ; (4) TiO2 substrate; (5) heating unit; (6) thermocouple.

Magnetic Nanostructures – Fabrication and Properties

68

3.3 Lithography and Pattern Transfer 3.3.1 Electron Beam Lithography and Lift-off The largest number of samples investigated in this thesis was fabricated by electron beam lithography followed by the material deposition (see section 3.2) and a lift-off process. This general procedure was used for all NiFe and Co samples investigated with XMCD-PEEM (see chapter 4) as well as for all electrically connected NiFe samples investigated with either magnetotransport measurements or XMCD-PEEM (see chapter 5). However, the fabrication process differed for the different sets of samples as detailed in the following. 3.3.1.1

Samples for XMCD-PEEM Studies of the Domain Wall Spin Structure

All details of this meanwhile well-established lithography process can be found in [HDK+ 03]. The typical sample design including different rings and wavy lines with different widths, diameters, and edge-to-edge spacings is shown in Fig. 3.4. Main aspects of the lithography process performed are the unusually low electron beam energy of 2.5 keV reducing the proximity effect and the fact that the sample stage is moved rather than the incident electron beam. The rings are written in form of a single circular line and the line width is adjusted via the electron dose as suggested earlier [DH99]. Most of the results presented in sections 4.3, 4.4, 4.5, and 4.6 were obtained with such and similar samples.

Figure 3.4: Standard sample design for XMCD-PEEM studies of ring spin structures.

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69

Figure 3.5: SEM images of NiFe ring structures (D = 2 µm, W = 200 nm, t = 34 nm) for CIDM experiments using MR with two notches (left) and without notches (right).

3.3.1.2

Ring Structures for CIDM Experiments Using MR

For the electrically connected nanostructures used for the study of currentmagnetization interactions, an additional fabrication step is necessary. In an overlay procedure, Au contacts are defined using electron beam lithography and subsequent lift-off. The main challenge is a sufficiently good sample positioning which is crucial to avoid a shift between the ring structure and the contact wires. This is done using alignment marks patterned together with the ring structures. These samples were patterned at the Laboratoire de Photonique et de Nanostructures – CNRS (France) as detailed in [KVB + 02]. SEM images are exemplarily shown in Fig. 3.5. The results on these samples are mainly presented in section 5.2. 3.3.1.3

Zigzag Wires for CIDM Experiments Using XMCD-PEEM

For fabrication of these samples, an overlay process was necessary, too. These samples were fabricated at the Laboratory for Micro- and Nanotechnology at the PSI (Switzerland) as detailed in [HKN + 04] using a two-step lithography process and lift-off as well. The results on these samples are mainly presented in section 5.3. 3.3.1.4

CrO2 Wires with Notches for CIDM Experiments Using MR

The CrO2 nanostructures were fabricated using electron beam lithography for the definition of an etch mask on top of the CrO 2 film followed by an Ar ion

Magnetic Nanostructures – Fabrication and Properties

70

milling step for pattern transfer into the film. These samples were completely fabricated at the II. Physikalisches Institut of RWTH Aachen. Details about the patterning process can be found in [Kön06].

3.3.2 Nanostructures Patterned with Ion Milling Since Fe3 O4 films cannot be patterned using lift-off, because the growth is not possible on substrates carrying a resist mask already, pattern definition and transfer have to be performed after the film growth. This was done by definition of an Al/Cr mask on top of the Au capped Fe 3 O4 layer using standard electron beam lithography, lift-off, and subsequent plasma etching of the Cr. This mask is used for pattern transfer into the Fe 3 O4 layer by Ar ion milling before the mask is removed in a second plasma etching step. The processing in form of a step-by-step description can be found in [Har06].

3.3.3 Focused Ion Beam Milling (FIB) Besides the pattern transfer with ion milling using a Cr mask as described above, also focused ion beam (FIB) patterning of Fe 3 O4 and partially CrO2 samples was performed by M. Kläui at IBM Rüschlikon (Switzerland). This method is advantageous, because only one process step is involved, no further material deposition is necessary, and a surface contamination with e. g. electron beam resist is excluded. However, the FIB process can lead to implantation of ions and / or the modification of the magnetic properties of the sample [FRS04]. This effect is inherent to the technique of FIB, at least in the exposed areas and the adjacent parts of the sample the influence of the ions is inevitable. The size of the influenced area depends in the ion energy and the spot size of the ion beam, however reduced ion energy means an increased writing time.

3.3.4 Prepatterned Substrates Fe3 O4 was also grown on prepatterned TiO2 substrates to check for the general suitability of this method. The prepatterning was performed in the same way like the etching of the Fe3 O4 films described above. Fig. 3.6 schematically visualizes the process sequence for sample fabrication using prepatterned substrates. The advantage is, that the film and in particular its surface cannot be damaged by the patterning process. The first results have shown, that epitaxial

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71

Figure 3.6: (from [Klä03]) Schematics of the prepatterned substrate process. (i) electron beam exposure, (ii) removing the exposed resist, (iii) etching of the substrate, (iv) removing of the unexposed resist, (v) growth of the metallic film.

growth of films on prepatterned substrates is possible and that a magnetic decoupling of the film and the background material is obtained. An example image taken with XMCD-PEEM is shown in Fig. 3.7. For more details on the technique, see section 2.1. It remains to be shown, that this fabrication method is also suitable for electrically connected structures, where the patterned leads and the background have to be electrically disconnected on a millimeter length scale, which is expected to be difficult.

Figure 3.7: XMCD-PEEM images of Fe3O4 rings on prepatterned substrates. The image contrast formation is explained in section 2.1.

3.4 Properties of Films and Nanostructures After the film deposition, the general properties of the films have to be studied, partly they are already monitored during the fabrication process – for example using electron diffraction techniques during MBE growth. The relevant

Magnetic Nanostructures – Fabrication and Properties

72

NiFe

Co

Fe3 O4

800 × 103

1424 × 103

480 × 103

0

0

damping parameter α

0.01

0.01

-1.1 × 104

0.1

cell size

2–5 nm

2–5 nm

5–10 nm

saturation magnetization Ms (A/m) exchange constant A (J/m) anisotropy constant K1 (J/m3 )

1.3 × 10−11

3.3 × 10−11

1.2 × 10−11

Table 3.1: Parameters of polycrystalline NiFe, polycrystalline Co, and epitaxial Fe3 O4 (100) used for the micromagnetic simulations.

properties, mainly referring to the crystalline structure and the general magnetic properties, are briefly discussed in the following for the different materials investigated.

3.4.1 NiFe and Co Samples The NiFe and Co samples have a polycrystalline structure. Since the NiFe fcc crystallites exhibit a weak magnetocrystalline anisotropy, the spin structure of the NiFe nanostructures investigated is primarily governed by the shape anisotropy. The Co nanostructures also exhibit a negligible over-all anisotropy, but a relatively stronger crystalline anisotropy of the single hcp grains. Some differences in the experimental results can be related to this difference in the magnetocrystalline anisotropy as detailed in sections 4.3 and 4.6 in the context of the particular results. Especially advantageous for measurements are the high saturation magnetization of Co and the large anisotropic magnetoresistance ratio for NiFe. For the micromagnetic simulations, the material parameters listed in table 3.1 were used. In [Klä03] more details about the crystalline and magnetic properties of such NiFe and Co films can be found and differences between polycrystalline and fully epitaxial films are discussed.

3.4.2 Fe3 O4 Samples The growth of the Fe3 O4 films and the related structural and magnetic analysis was performed by C. Hartung in the frame of her diploma thesis [Har06]. After the growth, the films were investigated in-situ using low energy electron diffraction (LEED), X-ray photoelectron spectroscopy (XPS), and scanning tun-

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neling microscopy (STM). A well ordered Fe 3 O4 (100) surface was observed with LEED and the absence of other possible iron oxide phases such as α-Fe 2 O3 was confirmed from XPS spectra. The magnetic properties were studied using a superconducting quantum interference device (SQUID). In-plane hysteresis loops along different crystal axes and the magnetization as function of the temperature M (T ) were measured. At the so-called Verwey transition [Ver39] at 120 K, a structural change from the high-temperature cubic phase with the easy axis along the [100] cubic axis to a low-temperature monoclinic phase with the easy axis aligned along the c-axis takes place, which leads to a step in the M (T )-dependence. A very sharp Verwey transition at 120 K was clearly observed for the samples investigated here. This sharp transition and the fact that the transition temperature is not reduced for thinner films indicate a Fe3 O4 film with high stoichiometric quality. Hysteresis loop measurements for different in-plane directions yielded identical curves for the [010] and the [001] direction as well as for the [011] and the [011] direction. The comparison confirms that the in-plane easy axes are the latter ones as expected. The anisotropy constant obtained from the hysteresis loops is consistent with the literature value of K1 = -1.1×104 J/m3 within the error bars. The same applies for the saturation magnetization, for which the error is large however. For the micromagnetic simulations performed for Fe 3 O4 structures, the parameters listed in table 3.1 were used.

3.4.3 CrO2 Samples The growth of the CrO2 films on TiO2 substrates and the related structural and magnetic analysis was performed by C. König [Kön06]. The films were structurally characterized using X-ray diffraction (XRD) and the surface was investigated using scanning tunneling microscopy (STM) as well as atomic force microscopy (AFM). The XRD measurements revealed good epitaxial growth of a (100)-oriented film indicated by the pronounced (200)- and (400)-peaks of CrO 2 . HF pretreatment of the substrates yielded films with an improved surface quality: an averaged peak-to-peak roughness of about 5 nm in a 2 µm × 2 µm area

and a rms-roughness of 7 Å was obtained from AFM measurements [Kön06].

The magnetic characterization was performed using a magneto-optical Kerr (MOKE) magnetometer, a superconducting quantum interference device

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(SQUID), and spin-resolved photoemission spectroscopy. MOKE hysteresis loops taken with the field applied along the in-plane [001] c-axis and the [010] a-axis, respectively, revealed a strong in-plane anisotropy with the [001] easy axis and the [010] hard axis. From SQUID loops, the saturation magnetization and the switching fields at different temperatures and film thicknesses were determined as detailed in [Kön06]. A Curie temperature of 385 K was obtained from M(T ) curves, which is in very good agreement with a literature value of 386.5 K [YCL+ 01]. The photoemission spectroscopy revealed the expected high values for the spin polarization of up to P = (90 ± 10)% as already discussed in section 1.7 and to be found in [DFK+ 02, FDK+ 03, Ded04].

3.5 Magnetic States and Switching of Ring Structures After discussing the general crystalline and magnetic properties of the samples in the previous sections, this section is particulary devoted to the magnetic states and the switching behavior of rings, because the ring shape is the main geometry used in this thesis for the investigation of domain wall spin structures. It is very suitable for such experiments, since domain walls can be formed simply by saturating and subsequently releasing a homogeneous external magnetic field. While the domain wall spin structures in rings (and in other geometries with comparable thickness and line width) are generally discussed in the overview in section 4.2, here the magnetic states in rings and their switching will be introduced briefly. The ring geometry has been proposed for the use in magnetic random access memory (MRAM) [ZZP00] or in sensors [MPCB02]. The energetically most favorable state of a ring is the flux closure vortex state with the magnetization completely aligned along the ring perimeter. This configuration is free of any strayfield and avoids the necessity to form a vortex core at a high cost of exchange energy in contrast to the disc shape. Another stable configuration is the so-called onion state of the ring with one head-to-head and one tail-to-tail 180 ◦ domain wall [KRLD+ 01]. In Fig. 3.8 both states are schematically shown together with the vortex state with a vortex core in a disc for comparison. Besides these two basic states, other configurations can exist in special cases like the vortex-core state [KVB+ 03a] in very wide rings or a triangular state in disc-like elements [KRV+ 06].

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Figure 3.8: (from [Klä03]) Schematic representations of the vortex state in a ring (a), in a disc (b) and the onion state in a ring (c).

Such rings can exhibit different switching mechanisms when exposed to an external magnetic field sweep resulting in different shapes of the corresponding hysteresis loops [KVB+ 03a, KVB+ 04a, Klä03]. Three main switching mechanisms are observed in rings: • Single switching occurs in form of a single transition from the onion state to the reversed onion state in thin rings.

• The double switching process involves a transition from the onion to the vortex state and then to the reversed onion state.

• Triple switching occurs for wide and very thick rings and leads from the

onion via the vortex state and the so-called vortex-core state to the reversed onion state. The term vortex-core state describes the configuration with one vortex in the very wide ring.

The occurrence of the different switching processes can be understood if the single transitions are investigated. The main difference lies in the fact that two different processes are involved in the switching. The first is a domain wall depinning and annihilation process, which e. g. leads to the onion to vortex transition. One of the existing two walls is depinned and moves towards the second, and both walls annihilate. The second is a domain wall nucleation process, which induces e. g. the vortex to reversed onion transition. These two processes are more or less favored depending on the exact geometry of the rings. The switching of rings is reviewed in [Klä04], detailed information can also be found in [Klä03].

Chapter 4

Domain Wall Spin Structures 4.1 Overview This chapter presents the domain wall spin structures observed in NiFe, Co, Fe3 O4 , and CrO2 nanostructures. For experiments in the field of current induced domain wall motion, a detailed knowledge of the domain wall spin structures is crucial, because these effects are known to critically depend on the spin structure as well as to influence the spin structure [KJA + 05]. This influence was also clearly confirmed within the frame of this thesis. Therefore, the set of studies presented in this chapter can be understood as the essential basis for the experiments on current-induced effects on domain walls in the following chapter. The main experimental technique used for the investigation of spin structures is XMCD-PEEM (see section 2.1), which is a non-intrusive and elementspecific imaging technique with a maximum lateral resolution of about 30 nm. A complementary technique used is electron holography (see section 2.4), which has a sub-10 nm resolution. An electron wave travelling through the transparent sample on a thin membrane collects a phase shift due to the interaction with electric and magnetic fields. This wave is interfered with a reference wave and the resulting interference pattern allows to obtain the distribution of magnetic induction in the sample. First, a brief introduction into domain walls in bulk materials, thin films, and nanostructures is given in section 4.2. Then, the following topics are discussed: • The spin structure of domain walls in NiFe and Co rings or wires de-

pends on the element width and thickness. Head-to-head 180 ◦ domain

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walls with vortex or transverse spin structure were already observed in Co [KVB+ 04b] depending on the geometry. Similar results were now obtained for NiFe. The comprehensive domain wall type phase diagrams for NiFe and Co rings are presented and discussed in section 4.3. The experimental results are compared with available calculations [MD97] as well as micromagnetic simulations and the observed differences can be understood taking into account thermally activated domain wall type transformations as discussed in section 4.4. These results have been published in [KVB+ 04b, LBB+ 06a, LKB+ 06]. The experimental observations of Kläui et al. [KVB+ 04b] were not obtained within this thesis, but the comprehensive picture, which has been gained now together with the results on NiFe including thermally activated wall type transitions [LBB + 06a], allow now to give a description of the entire topic as reviewed in [LKB + 06]. • Vortex and transverse domain wall spin structures constitute local energy minima and the difference between experiment and calculations in the domain wall type phase diagrams have been suggested to be due to the energy barrier in between [KVB+ 04b]. Therefore, a thermally activated transformation from the energetically less to the more favorable configuration can be expected. Temperature dependent XMCD-PEEM studies of domain walls in rings confirmed this suggestion. From the transition temperature, at which transverse walls are transformed into vortex walls, the energy barrier between these two configurations was obtained. These results are presented in section 4.4 and published in [LBB + 06a, LKB+ 06]. • Besides the internal domain wall spin structure, the wall width depending on the geometry of the nanostructure was investigated. Imaging domain

walls in rings with different geometries allowed to obtain the dependence of the domain wall width on the width of the structure (see section 4.5). • When nanostructures with domain walls are situated next to each other the stray field of a wall can influence the spin structure of the adjacent wall.

This effect was studied by investigating rings with different edge-to-edge spacings. Combining the results with a direct quantitative measurement of the stray field of a domain wall using electron holography, the energy barrier distribution for vortex core nucleation was obtained (section 4.6). These results have been published in [LBE + 06].

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• In the view of experiments on current-induced domain wall motion in the

halfmetallic ferromagnets Fe3 O4 and CrO2 , it is essential to investigate the spin structure of domain walls in these materials in general as well as to identify suitable sample geometries for experiments. This is of particular importance because in-plane anisotropies in these materials are expected to influence the domain wall formation significantly. The results are presented in sections 4.7 and 4.8. Besides XMCD-PEEM data, this includes

results from atomic and magnetic force microscopy as well as micromagnetic simulations.

4.2 Introduction to Domain Walls 4.2.1 Domain Wall Spin Structures In ferromagnetic materials, magnetic domains are observed, which can be described as areas with homogeneous magnetization. These areas are confined by transition regions, called domain walls, where the magnetization direction changes. The formation of such domains occurs due to the energy minimization of the system. In particular in mesoscopic structures, a homogenous magnetization (a mono-domain state) can be energetically less favorable than a multidomain state with domain walls. A comprehensive overview on domain walls can be found in the textbook by Hubert and Schäfer [HS98], which parts of this section 4.2 are based on. 4.2.1.1

Bulk Material

In ferromagnetic materials, a domain wall between two domains with opposite magnetization directions can be a Néel wall (named after Louis Néel), in which the magnetization rotates in-plane, or a Bloch wall, where it rotates out-of-plane. The Bloch wall, proposed by Landau and Lifshitz [LL35], was named after Felix Bloch [Blo32]. 4.2.1.2

Thin Films

Néel realized that Bloch’s description of a domain wall is not valid anymore in thin films as soon as film thickness and domain wall width (see section 4.2.2) are comparable. In general, the detailed domain wall spin structure is influenced

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Figure 4.1:

(from [HS98], p. 240) "Domain"

model of a cross-tie wall. Dashed lines symbolize a continuous reorientation of the magnetization. The filled circles in the center, where the magnetization directions "cross", are so-called "cross Bloch lines".

strongly by local material properties in systems with less than three dimensions. The spin configuration with the (local) minimum energy can critically depend on local defects, roughness, and magnetocrystalline anisotropies. Besides 180◦ Néel walls, also 90◦ Néel walls are observed. Two 90◦ walls can be energetically more favorable than one 180 ◦ wall, which leads to a replacement of a 180◦ wall by the more complicated cross-tie wall structure [HSG58], which is schematically shown in Fig. 4.1. In thin films, zigzag domain walls can form perpendicular to the easy axis (Fig. 4.2), which are metastable configurations existing when a global rearrangement of the magnetization is not possible. The dipolar energy of the wall is reduced because a flux closure between adjacent saw teeth of the wall is possible via out-of-plane stray fields. On the other hand, the exchange energy is increased due to the increased wall length. Therefore, the formation of zigzag lines is enhanced in materials with relatively weak exchange coupling and relatively strong dipolar coupling. The actual domain wall within this zigzag pattern can be a regular 180◦ wall as well as a cross-tie wall [HS98] as shown in Fig. 4.2(b). 4.2.1.3

Mesoscopic Structures

In quasi one-dimensional systems, such as the patterned mesoscopic structures investigated in this thesis, 180◦ head-to-head or tail-to-tail domain walls can be observed. In particular, ring structures have been studied intensively and it was found that the rings can either exhibit the flux closure vortex state or the onion state [KRLD+ 01] with two domain walls as detailed in section 3.5. Due to the high symmetry of the ring structure, a domain wall can be easily formed and positioned at any desired angle by the application and subsequent relaxation of an external magnetic field. This procedure is not applicable to the straight line geometry, where the introduction of domain walls by differently shaped wire

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Figure 4.2: (from [HS98], p. 452) Zigzag walls separating antiparallel domains. (a) 60 nm thick Co film (b) High-resolution image of a 42 nm thick Co film displaying a cross-tie pattern on the individual walls. (c) Equilibrium zigzag wall generated by a gradient field acting on a 50 nm thick NiFe film.

ends (nucleation pad and needle shaped end) is a commonly used method. The domain walls in such elements are 180 ◦ head-to-head or tail-to-tail domain walls, respectively, with either a transverse or a vortex structure predicted by theoretical calculations [MD97] to depend on thickness and width. These particular calculations were confirmed experimentally for polycrystalline hcp cobalt recently [KVB+ 04b] and for NiFe in this thesis. Details can be found in section 4.3, where details of the energetics involved are discussed. Micromagnetic simulations of the two basic domain wall spin structures are shown in Fig. 4.4(a) and (b) on page 82. Besides these two basic types, different but related domain wall spin structures are reported. Nakatani et al. [NTM05] have established a refined phase diagram by numerical calculations and found an asymmetric transverse wall to be energetically favorable for certain element widths and thicknesses. The triangular domain (Fig. 4.4(b)), that forms the transverse wall, is tilted so that exchange and stray field energy contribute with slightly different amounts to the wall energy. In very thick ring elements double vortex walls were reported recently [PHC+ 06] as shown in Fig. 4.3. The occurrence of this additional wall type is attributed to the large thickness where the cost of exchange energy due the formation of a second vortex is overcompensated by the gain of magnetostatic energy. These energy contributions were quantitatively determined from micromagnetic simulations. It should be mentioned that current-induced formation of double- and multi-vortex walls in thinner elements was observed in this thesis

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Figure 4.3: (from [PHC+ 06]) Micromagnetic simulations (top) showing magnetic spin configurations of NiFe ring elements with 2 µm diameter obtained at remanent states after saturation along the perpendicular direction for 40 nm thickness (left) and 65 nm thickness (right). The blue and the red color indicate the divergence of the magnetization along the +z and the -z out-of-plane directions, respectively. The lower part shows the corresponding MFM images.

(see section 5.3), while the experiments reported by Park et al. [PHC + 06] refer to remanent onion states of rings prepared by a homogeneous external magnetic field.

4.2.2 Domain Wall Widths Hubert and Schäfer [HS98] state that there cannot exist "a unique definition of a domain wall width", since "domain walls form a continuous transition between two domains" (p. 219 in [HS98]). This already expresses the general difficulty in measuring a domain wall width. One should always bear in mind how the domain wall width is measured in a given context. There are different definitions related to the slope of the magnetization angle or one of its components like first proposed by Lilley [Lil50]. This type of definition is useful when there is a direct transition between two adjacent domains like in a Néel wall or a Bloch wall. However, here we want to determine the widths of entire "objects" such as

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transverse or vortex domain walls with a distinct substructure [Kun06]. Therefore, characteristic intensity profiles of the walls are extracted from the images and used to determine the wall width as detailed in section 4.5. The widths obtained cannot be directly compared to typical values for Néel or Bloch walls in films or bulk material because they characterize a complete transition structure.

4.3 Domain Wall Type Phase Diagrams for NiFe and Co The spin structure of head-to-head domain walls in NiFe and Co was systematically studied by direct imaging with XMCD-PEEM and the domain wall type phase diagrams determined from the images. Therefore, arrays of polycrystalline NiFe and Co rings with thickness t between 2.5 and 38 nm, width W between 110 and 1800 nm, and outer diameter D between 1.64 and 10 µm were fabricated as described in chapter 3. The edge-to-edge spacing between adjacent rings was more than twice the diameter to prevent dipolar interactions that would otherwise influence the domain wall type (see section 4.6).

4.3.1 Phase Diagrams In Fig. 4.4, we present PEEM images of (c) a thick and wide NiFe ring, (t = 30 nm, W = 530 nm, D = 2.7 µm), (d) a thin and narrow ring, (t = 10 nm, W = 260 nm, D = 1.64 µm), and (e) an ultrathin ring (t = 3 nm, W = 730 nm, D = 10 µm) mea-

Figure 4.4: Spin structure of (a) a vortex wall and (b) a transverse wall simulated using the OOMMF code [OOM]. PEEM images of (c) 30 nm thick and 530 nm wide (D = 2.7 µm), (d) 10 nm thick and 260 nm wide (D = 1.64 µm), and (e) 3 nm thick and 730 nm wide (D = 10 µm) NiFe rings. The gray scale shows the direction of magnetic contrast.

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Figure 4.5: (partly from [KVB+ 04b]) Experimental phase diagrams for head-to-head domain walls in (a) NiFe and (c) Co rings at room temperature. Black squares indicate vortex walls and red circles transverse walls. The phase boundaries are shown as solid lines. (b, d) Comparison of the upper experimental phase boundary (solid lines) with results from calculations (dotted lines) and micromagnetic simulations (dashed lines). Close to the phase boundaries, both wall types can be observed in nominally identical samples due to slight geometrical variations. The thermally activated wall transitions shown were observed for the ring geometry marked with a red cross in (a) (W = 730 nm, t = 7 nm).

sured at room temperature. The domain wall type was systematically determined from PEEM images for more than 50 combinations of ring thickness and width for both NiFe and Co and the quantitative phase diagrams shown in Figs. 4.5(a) and (c) were extracted. The phase diagrams exhibit two phase boundaries indicated by solid lines between vortex walls (thick and wide rings, squares), transverse walls (thin and narrow rings, circles), and again vortex walls for ultrathin rings. Now we first discuss the upper boundary shown in Figs. 4.5(a, c). The-

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Thermal activation TW

VW

Figure 4.6: Schematics of the domain wall energy landscape. Transverse and vortex walls constitute local energy minima separated by a barrier, which can be overcome by thermal activation.

oretically this phase boundary was investigated by McMichael and Donahue [MD97]. They calculated the energies for a vortex and a transverse wall and determined the phase boundary by equating these two energies. The calculated phase boundary (dotted lines in Figs. 4.5(b, d)) is of the form t · W = C · δ 2

where δ is the exchange length and C a universal constant. 21 It is shifted to lower thickness and smaller width compared to the experimental boundary (solid lines in Figs. 4.5(b, d)). This discrepancy can be understood by taking into account the following: The calculations [MD97] compare total energies and therefore determine the wall type with the absolute minimum energy as being favorable. In the experiment, the wall type was investigated after saturation of the ring in a magnetic field and relaxing the field to zero. During relaxation, first a transverse wall is formed reversibly [KVW+ 04]. For the formation of a vortex wall, an energy barrier has to be overcome to nucleate the vortex core. So the observed spin structure does not necessarily constitute the absolute minimum energy, but transverse walls can be observed for combinations of thickness and width where they constitute local energy minima even if a vortex wall has a lower energy for this geometry. This situation is visualized in Fig. 4.6. To shed further light onto this, we have simulated the experiment by 21

The relation t · W = C · δ 2 is obtained by first calculating the exchange energy of a vortex (as

a measure of the main energy contribution of a vortex wall) and the magnetostatic energy of the

magnetization inside a transverse wall pointing perpendicular to the wire. Then, the difference between these two energies is set to zero and the phase boundary is obtained. In other words, only the dominating energy contributions (exchange energy of the vortex wall and only the magnetostatic energy of the transverse wall) are taken into account and other contributions like e. g. magnetocrystalline anisotropies are completely neglected.

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calculating the domain wall spin structure after reducing an externally applied field using the OOMMF code [OOM] (for NiFe: M s = 800 × 103 A/m,

A = 1.3 × 10−11 J/m; for Co: Ms = 1424 × 103 A/m, A = 3.3 × 10−11 J/m; for both:

damping constant α = 0.01, cell size 2–5 nm). The simulated boundary is shifted to higher thickness and larger width compared to the experiment. This we attribute to the fact that thermal excitations help to overcome the energy barrier

between transverse and vortex walls in case of the room temperature experiments, while they are not taken into account in the 0 K simulation. So we can expect that for temperatures above room temperature the upper phase boundary is shifted to lower thickness, in other words, that transverse walls formed at room temperature change to vortex walls with rising temperature. This means that with rising temperature the experimental phase boundary approaches the calculated one since the walls attain the energetically lower spin structure. In order to check this aspect, we have performed temperature-dependent XMCD-PEEM studies. The results are presented in section 4.4. These experiments directly show that the position of the upper experimental phase boundary is temperature dependent and is shifted to lower thickness and width with increasing temperature. The results thus confirm the hypothesis about the discrepancy between experiment and theory put forward in [KVB + 04b]: Both domain wall types constitute local energy minima, with the transverse wall attained due to the magnetization process, even if a vortex wall has a lower energy. It can be seen by comparing the boundaries for NiFe and Co in Fig. 4.5, that for NiFe the calculations [MD97] fit the experiment better than the simulations while for Co the opposite is true. The energy barrier between a transverse and a vortex wall can be overcome more easily in the case of NiFe rather than Co, so that transverse walls created are more likely to be retained at a certain temperature in a Co ring than in a NiFe ring with analogous dimensions. This is consistent with the observation that in NiFe there is a more abrupt change between transverse and vortex walls with varying geometry than in Co (see section 4.6 and [LBE+06]). The reason for this difference is thought to be the smaller number of pinning sites in the soft NiFe fcc crystallites with weak anisotropy compared to the strongly anisotropic hcp Co crystallites that lead to more pinning sites.

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Figure 4.7: Ultrathin Co rings on prepatterned Si substrates subsequently taken during the growth process. (a) No magnetic contrast is visible, but the shadows (A) of the rings (B) due to the grazing incidence growth after 20 min. (b, c) Domain pattern on and besides the rings indicate an uniaxial anisotropy with the easy axis in the vertical direction after 30 min.

4.3.2 Walls in Thin and Wide Structures – Limits of the Description We turn now to the discussion of the low thickness regime of the phase diagrams shown in Fig. 4.5, where a second phase boundary between 3 and 4 nm is found for both NiFe and Co. Since vortex walls had been surprisingly observed in thin NiFe rings, this was experimentally checked also for Co. The thinnest Co samples prepared (nominally 1 nm Co with about 5 Å Al capping), did not show any magnetic contrast in XMCD-PEEM. Therefore, Co was evaporated in-situ onto a prepatterned Si substrate (see section 3.3.4) during imaging in order to obtain information in this ultra-low thickness regime. The existing setup allowed deposition only under grazing incidence. It turned out that the deposition under grazing incidence induced an additional uniaxial anisotropy perpendicular to the direction of incidence as known from the deposition on Cu(001) surfaces [vDSP00]. Figure 4.7 shows three PEEM images taken during the growth process. In (a) after 20 min, the shadows (A) of the rings (B) indicate the incidence direction (horizontal in the images), in (b) and (c) a clear magnetic contrast is observed after 30 min, which gives evidence for an uniaxial growthinduced magnetic anisotropy.22 Since this anisotropy influences the domain wall formation and therefore does not allow the comparison with the structures fabricated using ex-situ MBE growth, electron beam lithography, and lift-off, this approach was not explored further. In terms of energetics, the lower phase boundary in Fig. 4.5 is not expected 22

According to [Che], the growth rate is approximately 0.5 ML/min.

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Figure 4.8: Limiting cases of the structures investigated: 3 nm thick and 1.8 µm wide (a) NiFe and (b) Co rings showing ripple domain formation, (c) 6 nm thick and 3 µm wide ring with distorted transverse walls, and (d) 10 nm thick and 2.1 µm wide disc-like NiFe ring with 700 nm inner diameter in the triangle state (for detailed explanations of the contrast see [VKH+ 05, VKB+ 06, KRV+ 06]). The gray scale indicates the direction of magnetic contrast.

because the calculations [MD97] show that a transverse wall has a lower energy than a vortex wall in this thickness regime. But these calculations assume a perfect microstructure and do not take into account morphological defects such as the surface roughness. Holes, which might serve as nucleation centers for the vortex wall formation, were not observed in atomic force microscopy (see section 2.6) images. However, this does not exclude a spatial modulation of magnetic properties [HJA94] such as the exchange or the saturation magnetization, which could locally allow for a stronger twisting of adjacent spins. Thus a vortex wall would be energetically more favorable in this thickness regime due to imperfections of the microstructure or the morphology. In the thin samples investigated, a ripple domain formation [HS98] is observed as shown in Figs. 4.8(a, b) (see also Fig. 4.4(e)). This can be attributed to statistical variations of the anisotropy of individual grains. Consequently, this phenomenon is more pronounced in the polycrystalline Co structures, in which individual grains exhibit a non-negligible anisotropy compared to the weak anisotropy in NiFe. The description in the frame of these phase diagrams is however limited by the width and thickness of the structure. In rings wider than ≈ 1.5 µm, we ob-

serve more complicated domain wall spin structures like distorted transverse

walls (Fig. 4.8(c)). With increasing width, the influence of the shape anisotropy decreases in favor of the exchange interaction as recently observed in zigzag lines [UU06]. Wide rings with a hole in the center exhibit a disc-like behavior with a triangle state as shown in Fig. 4.8(d). This type of structure is discussed in more detail in [VKH+ 05, VKB+ 06, KRV+ 06]. In very thick elements double

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vortex walls were reported recently [PHC + 06] (see section 4.2.1.3 for details), which can also constitute (meta-)stable configurations in the thickness regime investigated here, as it turned out from experiments on current-induced domain wall transformations [KLH+ 06] (see section 5.3). Recent theoretical calculations [NTM05] propose to distinguish between symmetric and asymmetric transverse walls which is not done here, because both types are difficult to distinguish experimentally and sample irregularities can influence the detailed wall spin structure. Also the annular geometry used here makes a detailed comparison to the calculations [NTM05] difficult, which were performed for a wire geometry.

4.4 Temperature Effects on Domain Wall Spin Structures In order to corroborate the explanation for the difference between the experimental phase boundaries on the one hand and calculations and simulations on

Figure 4.9: (a–d) PEEM images of a 7 nm thick and 730 nm wide ring imaged during a heating cycle at temperatures of (a, d) T = 20◦ C (before and after heating, respectively), (b) T = 260◦C, and (c) T = 310◦ C (estimated errors are ± 10 K). The two transverse walls (a) are not visibly influenced

by heating (b) until the transition temperature is reached (c), at which a thermally activated tran-

sition to a vortex type occurs in both walls. (d) confirms that the vortex walls are retained after cooling down. Due to heating, rings (here (e–h): 7 nm thick, 1135 nm wide) with two vortex walls can attain either (g) a vortex state with one 360◦ domain wall or (h) the vortex state. The intermediate state, where one wall is displaced, is shown in (f). The gray scale indicates the direction of magnetic contrast.

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the other hand as detailed in section 4.3, we have performed temperature dependent XMCD-PEEM studies. Figure 4.9(a–d) shows an image series of a 7 nm thick and 730 nm wide NiFe ring (geometry marked by a cross in Fig. 4.5(a)) for different temperatures of (a, d) T = 20◦ C (before and after heating), (b) T = 260 ◦ C, and (c) T = 310◦ C. Transverse walls are formed (a) during saturation in a magnetic field and relaxation before imaging. At first, heating does not influence the spin structure of the domain walls as shown in (b), only the image contrast becomes weaker because imaging is more difficult at higher temperatures due to drift problems and decreasing magnetization. At a transition temperature between T = 260 ◦ C and T = 310◦ C corresponding to a thermal energy between 6.7 × 10 −21 J and 8.0 × 10−21 J, the transverse walls change to vortex walls (c), so that a domain

wall spin structure was created which is not accessible for the same ring geometry by only applying uniform magnetic fields. When the heating is continued to

higher temperatures the magnetization disappears at the Curie temperature, and it can also happen that the structures are physically destroyed. Figure 4.10(a–g) shows a series of PEEM images at one helicity taken with increasing heating currents. The dark parts of the ring indicate damaged areas of increasing size. The low energy electron microscope (LEEM) image in (h) shows the topographical

Figure 4.10: (a–g) PEEM images of a 9 nm thick and 530 nm wide NiFe ring with 5 µm outer diameter for one helicity showing dark areas of increasing size, which correspond to the enlarging damaged areas of the ring during the heating process. (h) LEEM image of the topography that shows the existence of a grainy structure in the damaged areas.

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contrast and confirms the damage, which can be seen from the grainy structure in parts of the ring. The investigation of a larger number of domain walls showed that the transition temperature slightly varies between different domain walls in rings of the same size. This can be expected because the change of the domain wall spin structure with temperature from transverse to vortex – related with overcoming the energy barrier between the two wall configurations – is a stochastic thermally activated switching process with a distribution of energy barriers, which leads to a variation in the transition temperature. Imperfections of the microstructure may also cause a variation of the transition temperature for nominally identical rings since defects can assist as well as impede the change of the spin structure from transverse to vortex. Figure 4.9(d) confirms that the vortex wall is stable during cooling down. This means that both domain wall types are (meta-)stable spin configurations and therefore constitute local energy minima at room temperature for this geometry. These PEEM experiments directly show that the position of the upper experimental phase boundary is temperature dependent and is shifted to lower thickness and width with increasing temperature. These results thus confirm the hypothesis about the discrepancy between experiment and theory put forward in section 4.3: Both domain wall types constitute local energy minima, with the transverse wall attained due to the magnetization process, even if a vortex wall has a lower energy. Experimentally, we directly observe thermally activated crossing of the energy barrier between high energy transverse and low energy vortex walls (cf. Fig. 4.6 on page 84). It should be mentioned however, that the flux closure vortex state of the ring without any domain walls and with the magnetization aligned everywhere along the ring perimeter is the energetically most favorable state. Many rings attain this state when the temperature is increased as shown in Figs. 4.9(e–h). In order to observe the wall type transformations shown in Figs. 4.9(a–d), it is therefore necessary, that the energy barrier between transverse and vortex walls is lower than the barrier for the transition to the vortex state of the ring. This critically depends on imperfections of the ring microstructure which can serve as pinning centers and stabilize a domain wall.

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Figure 4.11: High-resolution XMCD-PEEM images of three NiFe rings in the onion state. The grayscale shows the magnetization direction. (a) shows a t = 10 nm thick ring with width W = 260 nm and diameter D = 1.64 µm exhibiting two transverse walls, (b) a ring (t = 30 nm, W = 530 nm, D = 2.7 µm) with two vortex walls, and (c) a ring (t = 10 nm, W = 1135 nm, D = 5 µm) that exhibits one transverse and one vortex wall. The angular scale used for the intensity profiles in Fig. 4.12 is indicated in (a). An area of the type, in which the profiles were taken, is highlighted in light grey in (a).

4.5 Domain Wall Widths Besides the general types of possible domain wall spin structures, it is also important to investigate the wall widths and the width dependence on the element geometry, in particular on the element width. For example, the domain wall magnetoresistance contribution of the anisotropic magnetoresistance (see section 1.6.4.2) will depend on the wall width, i. e. on the amount of magnetization pointing perpendicular to the current flow. A detailed understanding of the domain wall magnetoresistance therefore requires a quantitative knowledge of the domain wall width as function of the element geometry. The large amount of XMCD-PEEM images acquired in order to determine the domain wall type phase diagrams (see section 4.3) also allows to obtain the domain wall width as a function of the element geometry. However, before presenting the results, it is important to define the term "domain wall width" in this particular context (see section 4.2.2 for details). In the NiFe and polycrystalline Co samples discussed 180 ◦ head-to-head or tailto-tail domain walls are observed, respectively. Here, the term "domain wall width" refers to the whole wall spin structure rather than a single transition as in a Néel or Bloch wall. We now turn to the details of the measurement of the domain wall widths

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from PEEM images as presented in Fig. 4.11. Images (a) and (b) show rings with dimensions far away from the phase boundary (see Fig. 4.5 on page 83) so that either transverse or vortex walls can be observed in each ring. The 10 nm thick and 1135 nm wide ring in (c) has dimensions close to the phase boundary and therefore exhibits two domain walls of different types. Intensity profiles taken along the ring perimeter and summed over the width of the ring are presented in Fig. 4.12. In (a), a clear dip can be seen which is due to the part of the transverse wall exhibiting black contrast. The positions of the maxima are taken and from their difference the width of the domain wall is calculated using the ring circumference. The characteristic profile of a vortex wall in Fig. 4.12(b) looks different because of the more complicated contrast inside the vortex. The first minimum is due to the gray part of the tilted spins directly above the vortex wall. The second minimum is caused by the black part of the vortex. The exact shape of such a profile taken from a vortex wall depends on the exact spin structure of the wall which can be slightly elongated like shown in Fig. 4.11(c). The positions of the inflection points as indicated by circles in Fig. 4.12(b) are used for calculating the domain wall width as before for the transverse wall. These inflection points indicate the left and right edges of the vortex wall structure, respectively, averaged over the ring width. From such intensity profiles, the width of the domain walls in rings as a function of the line width are obtained and displayed in Fig. 4.13. The average widths are indicated by blue circles and can be fitted very well using a linear fit. The ratio of the wall width and the ring width obtained from this fit is 2.25 ± 0.15.

Figure 4.12: Intensity profiles of (a) the right wall in Fig. 4.11(a) and (b) the right wall in Fig. 4.11(b).

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Figure 4.13: Domain wall width as a function of the ring width in NiFe obtained from intensity profiles of the type shown in Fig. 4.12. Red triangles represent vortex walls, black squares transverse walls, and blue circles the average values. The blue line is a linear fit to the average values.

A dependence on the ring curvature was not observed, the dependence on the ring thickness not systematically studied. Recently, micromagnetic simulations reproduced this linear dependence of the wall width on the line width [Kun06]. Vortex and transverse walls are indicated by different symbols in Fig. 4.13, but a systematic difference in width between both types cannot be derived from the data. However, it is difficult to define the way of measuring the exact wall width for both wall types in a way that allows a quantitative comparison of the values. For example as can be seen from Fig. 4.11, vortex walls show no significant difference between the wall widths measured at the inner and the outer ring circumference, respectively, while the triangular spin structure of the transverse wall has a small non-zero width at the inner circumference and its maximum width at the outer one. Furthermore, depending on the width and the thickness of the ring, it is impossible to observe both wall types as the wall type phase diagram shows (see Fig. 4.5(a) on page 83). Therefore, no distinction was made between the wall spin structures here, but it was averaged over both types. As already stated in section 4.3.2 and shown in Figs. 4.8(c) and (d) on page 87, the domain wall spin structure is distorted in elements wider than approximately 2 µm due to a reduced influence of the shape anisotropy so that a robust measure for the wall width cannot be defined anymore. The resolution of the XMCD-PEEM technique is not sufficient to resolve domain wall spin struc-

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tures in elements narrower than approximately 100 nm in a way that their width can be measured with a reasonable relative error. Therefore, domain walls in structures with notches as narrow as 30 nm were imaged using electron holography (see section 2.4). However, the combined analysis of both XMCD-PEEM and holography data is not a matter of this thesis and will be published in future [BLKR]. In this context, also micromagnetic simulations with the OOMMF code [OOM] of the particular geometries investigated here are in progress. In conclusion, the domain wall width in NiFe was found to depend linearly on the ring width, while no significant dependence on the element thickness and the ring diameter or curvature was observed. The definition of the term "domain wall width" must be taken into account when comparing these results with other sources. Domain walls widths of walls in elements wider than approximately 2 µm, cannot be compared with results from narrower structures because the domain wall spin structure is strongly distorted. The lower width limit for investigation is set by the resolution of the XMCD-PEEM technique and is approximately 100 nm.

4.6 Interacting Domain Walls and Wall Stray Fields Besides studying the spin structure of isolated domain walls as presented in the previous sections, also the dipolar coupling between adjacent walls is of interest. A strong influence of domain wall interaction on the switching of magnetic elements such as rings was found recently, when interactioninduced collective switching of adjacent elements was observed for small spacings [ZGM+ 03, KVBH05]. Such switching is dominated by domain wall motion and can only be understood with a detailed knowledge of the interacting domain wall spin structures and a quantitative determination of the domain wall stray field. In this section, both the spin structure of interacting walls for different edge-to-edge spacings and the stray field of an isolated wall are experimentally determined and the energy barrier height distribution for vortex nucleation is obtained from the data. While the results presented in this section had been in the review process for publication [LBE+ 06], interesting data on the energy barrier to magnetic vortex nucleation were published elsewhere [LBBZ06]. In that work, the energy barrier height for the nucleation of a vortex core in NiFe squares was studied at dif-

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ferent temperatures and under external fields by means of Lorentz microscopy. The macroscopically observed loss of net magnetization with time could be correlated with nucleation events.

4.6.1 Sample Fabrication and Experimental Techniques After saturating with a magnetic field and relaxing the field, rings attain the onion state characterized by two head-to-head domain walls as discussed in the sections before (see also Fig. 4.14(a)). An array of 25 rings in the onion state exhibits 50 walls in total. The domain walls inside the array interact with adjacent walls via their stray fields. Only 10 walls, which are located at the two opposite edges (top and bottom edges in Figs. 4.14(b) and (c)) of the array and therefore have no neighboring rings, are not influenced by stray fields of an adjacent wall. For all experiments, ring thickness and width were chosen such that isolated rings of this geometry exhibit vortex walls according to the phase diagram presented in section 4.3 [KVB+ 04b, LBB+06a]. Arrays of 5 × 5 NiFe and Co rings, each of outer diameter of 1.64 µm and

width of 350 nm, were fabricated as described in [HDK + 03] and [YKV+ 03] (see also chapter 3). Edge-to-edge spacings between rings down to 10 nm were used to investigate different dipolar coupling strengths between domain walls in adjacent rings. For the transmission off-axis electron holography experiments, 3/4-rings were patterned from 27 nm thick Co films on 50 nm thick SiN membranes [HKS+ 05]. Open rings rather than full rings were grown on the fragile membranes in order to facilitate the lift-off process which cannot be assisted by ultrasound, in contrast to the PEEM samples grown on naturally oxidized Si substrates. The thickest sample for which the lift-off was still possible without damage has a thickness of 27 nm. PEEM images of domain walls in 3/4-rings and full rings with the same dimensions showed no difference in the domain wall spin structure. XMCD-PEEM was used to image the magnetization states of the rings. In order to obtain quantitative information about stray fields, which are not accessible by XMCD-PEEM, Co samples were investigated by off-axis electron holography. Co was chosen rather than NiFe for this investigation due to its higher saturation magnetization and therefore higher stray field. From this combined study, the energy barrier height distribution for vortex core nucleation is finally determined. In order to obtain this distribution, the

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Figure 4.14: (a) A high resolution XMCD-PEEM image of two rings in the onion state, after saturation with an external field in the vertical direction and relaxation. White and black contrasts correspond to the magnetization pointing up and down, respectively. A non-interacting vortex wall (top) and three interacting transverse walls are visible. Overview images of an array of 27 nm thick and 350 nm wide NiFe rings with an edge-to-edge spacing of (b) 40 nm and (c) 500 nm, respectively. The transition from 100 % transverse walls inside the array for narrow spacings (b) to close to 0 % for large spacings (c) can be clearly seen. Since domain walls at the top and bottom edges of the array do not interact with adjacent walls, they are vortex walls for all spacings investigated.

following single steps are described in the consecutive subsections: • The transition from transverse to vortex walls in the remanent state as

function of the edge-to-edge spacing between adjacent rings is measured in ring arrays using XMCD-PEEM.

• The stray field of an isolated domain wall is quantitatively determined using electron holography.

• Using this stray field decay, the spacing dependent distribution is rescaled

to a field dependent distribution, which can be fitted by the error function.

• The derivative of this error function gives the energy barrier height distribution as a function of the field strength.

4.6.2 XMCD-PEEM Imaging of Interacting Domain Walls Figure 4.14 shows XMCD-PEEM images of arrays of 27 nm thick NiFe rings with (b) 40 nm and (c) 500 nm edge-to-edge spacing, respectively, as well as a high resolution image (a) showing both wall types. Vortex walls can be easily identified by black and white contrast which occurs because all magnetization directions

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Figure 4.15: Percentage of transverse walls inside a ring array as function of edge-to-edge spacing. Black squares are for 27 nm NiFe, and red triangles for 30 nm Co, respectively. The error bars √ represent the absolute statistical error 1/ n due to the finite number n of domain walls investigated. The horizontal lines show the 10-90 %-levels of the transition from a transverse to a vortex domain wall from which the width w and the center rc can be extracted as described in the text.

corresponding to the full grey scale are present in a vortex. In contrast, transverse walls exhibit the characteristic grey-white-grey contrast with the triangular spin structure in their center. In Fig. 4.15, we show the percentage of transverse walls inside the array as function of the edge-to-edge spacing for 27 nm thick NiFe rings (black squares) extracted from images of the type shown in Fig. 4.14. A decreasing number of transverse walls is found with increasing spacing. Domain walls at the edges of the arrays are vortex walls irrespective of the spacing due to the absence of dipolar coupling with adjacent walls. 23 The data points for infinite spacings in Fig. 4.15 result from these domain walls. The 10%- and 90%-levels of the transitions as shown in the figure were obtained from the saturation levels for small and large spacings. The intersections of linear fits for the data points in between with the 10%- and 90%-levels define the transition widths. The transverse to vortex transition for 27 nm thick NiFe is characterized by a (10-90 %)-width of the switching distribution of w = (65 ± 9) nm and a center at r c = (77 ± 5) nm. In Fig. 4.15, red triangles show a similar transition for 30 nm thick Co rings with w = (328 ± 130) nm and rc = (224 ± 65) nm. 23

There is still a weak dipolar coupling between domain walls in horizontally neighboring

rings, but it is assumed to be negligible here.

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In order to explain these results, we first consider the process of domain wall formation in an isolated ring. When relaxing the applied external field from saturation, transverse walls are initially formed. In order to create a vortex wall, a vortex core has to be nucleated. This hysteretic transition from one wall type to the other involves overcoming a local energy barrier [KVW + 04], since the nucleation of the vortex core is associated with a strong twisting of the spins in the core region [CKA+ 99]. In arrays of interacting rings, the edge-to-edge spacing dependent stray field stabilizes transverse walls so that for small spacings (corresponding to a strong stray field from the adjacent domain wall) transverse walls are favored (Fig. 4.14(b)). For increasing spacing, the influence of the stray field from an adjacent wall is reduced, until vortex walls are formed in the rings with the lowest energy barrier for the vortex core nucleation. The further the spacing increases the more rings nucleate vortex walls (Fig. 4.14(c)). Thus the spacing at which a wall switches from transverse to vortex is related to the nucleation barrier, which depends on local imperfections such as the edge roughness. Therefore the number of domain walls that has switched from transverse to vortex as a function of the edge-to-edge spacing is a measure of the distribution of energy barriers for the vortex core nucleation. For NiFe, a relatively sharp transition occurs from all walls being transverse to all walls being vortex walls. This corresponds to a narrow energy barrier distribution, while the domain walls in Co rings exhibit a much wider transition. This difference is believed to result from the different polycrystalline microstructures of the NiFe (magnetically soft fcc crystallites with negligible anisotropy) and the Co (hcp crystallites with strong uniaxial anisotropy leading to a larger number of pinning sites). Furthermore, this results in the presence of transverse walls in our Co sample even at infinite spacings. Thus Co had to be chosen for the electron holography measurements rather than NiFe in order to be able to observe a transverse wall and its stray field in an isolated structure at all.

4.6.3 Stray Field Mapping Using Electron Holography This spacing-dependent distribution for the vortex core nucleation needs to be transformed to a distribution as a function of the stray field strength, which is as a first approximation proportional to the energy. To do this, the stray field as well as the magnetization of the domain wall was imaged using high-resolution off-

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Figure 4.16: The inset shows a high resolution off-axis electron holography image of a transverse wall in a 27 nm thick Co 3/4-ring. The color code indicates the direction of the in-plane magnetization and the black lines represent directly the stray field. The stray field strength was measured at several distances inside the marked area. The data points show the stray field normalized to the saturation magnetization as a function of the distance r from the ring edge for the wall shown in the inset. The line is a 1/r-fit.

axis electron holography. The inset of Fig. 4.16 shows an image of the in-plane magnetic induction integrated in the electron beam direction, obtained from a transverse wall in a 27 nm thick isolated Co 3/4-ring designed with the same width as that of the rings imaged by XMCD-PEEM. No significant difference between the functional dependence of the stray field on the spacing is expected for a 27 nm and a 30 nm thick sample. The stray field was measured along the length of the region indicated in the image, and is shown as a function of the distance r from the ring edge in Fig. 4.16, normalized to the saturation magnetization of Co. The line is a 1/r-fit which can be expected for the distance dependence of the stray field created by an area of magnetic poles for small r [McC77]. This dependence also confirms earlier results from indirect Kerr effect measurements [KVBH05]. In order to obtain the stray field of one single domain wall acting on an adjacent wall, the stray field of an isolated wall was imaged.

4.6.4 Energy Barrier Height Distribution for Vortex Nucleation The spacing-dependent energy barrier height distribution is now rescaled to a field-dependent distribution using the measured stray field decay of Fig. 4.16

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Figure 4.17: (a) Black squares represent the same data points as shown in Fig. 4.15 for the 30 nm thick Co sample, but as a function of the normalized field strength. The black dashed line shows a fit with the error function. The corresponding Gaussian distribution of the energy barriers is shown as a full red line. (b) Corresponding data for the 27 nm thick NiFe sample rescaled using the stray field measurement of a domain wall in 30 nm thick Co.

and presented in Fig. 4.17(a). The rescaled data can be fitted with the error function erf(x), which is the integral of a Gaussian distribution. The error function is not the only possible fit covered by the error bars in Fig. 4.17(a), but it is consistent with our data. Assuming a similar dependence of the stray field for NiFe like measured for Co (1/r-dependence, but normalized to the saturation magnetization of NiFe instead of Co), a Gaussian distribution is also obtained for the energy barrier height distribution for NiFe as presented in Fig. 4.17(b). Thus a Gaussian distribution for the energy barriers is found, which is in agreement with the presence of independent local pinning centers at the particular wall position that determine the nucleation barrier. The position of the maximum of the distribution is Hmax /Ms = 0.21 ± 0.10 and the full width at half

maximum w/Ms = 0.16 ± 0.05, where Ms is the saturation magnetization. Using

Emax =

1 2 µ0 Ms Hmax ,

an energy density of Emax = (8.4 ± 4.0) × 104 J/m3 equiva-

lent to the field Hmax can be obtained for the 30 nm thick Co sample.

Fig. 4.15 shows that the transition for the Co sample saturates at a finite value for large spacings. In terms of the model described above, which explains how vortex walls are formed during relaxation from saturation, this means that an additional effective field would be needed to overcome the pinning of the remaining transverse walls at structural imperfections and to allow the vortex core nucleation and formation of an energetically favorable vortex wall. Since the pinning is much stronger in our Co sample than in the NiFe sample, this occurs here only for Co.

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4.7 Spin Structure of Fe3 O4 Nanostructures The spin structure of different Fe3 O4 nanostructures were investigated by means of XMCD-PEEM in combination with magnetic force microscopy and corresponding micromagnetic simulations using OOMMF [OOM]. The MFM experiments and most of the simulations were performed by C. Hartung in the frame of her diploma thesis [Har06]. The complete set of results on rings from XMCDPEEM, MFM, and OOMMF is shown below, because a comprehensive understanding of the spin structure of Fe 3 O4 elements can be obtained by the combination of these techniques. The influence of the in-plane anisotropy is clearly observed. Other geometries than rings are discussed with a view to intended experiments on current-induced domain wall motion. A more detailed description and further results are omitted here and can be found in [Har06].

4.7.1 Experimental Difficulties Encountered For patterning and imaging the halfmetallic ferromagnets Fe 3 O4 and CrO2 with XMCD-PEEM, several experimental difficulties had to be solved. For highquality epitaxial growth of Fe3 O4 (100) films, the appropriate MgO(100) substrates have to be used (see section 3.2.2). This does not allow a lift-off process as performed for the 3d metal samples investigated (see section 3.3.1), because the epitaxial growth of Fe3 O4 is not possible on substrates carrying a resist mask due to the necessary high annealing temperatures during the process (see section 3.2.2). Therefore, either focused ion beam milling (see section 3.3.3) or wet etching techniques were used. It is important to keep the MgO substrate covered with conductive material as far as possible, because the MgO surface is non-conductive so that the sample will charge in the PEEM microscope in a way that prevents performing any experiments. A further problem is that patterning using FIB might damage the material and modify the ferromagnetic properties of the sample as briefly discussed in section 3.3.3. Ions have destroyed the magnetic contrast in some of the samples investigated as exemplarily shown in Fig. 4.18 for rings as well as for zigzag lines. Also the samples patterned with an etch process, sometimes did not show any magnetic contrast. This can be attributed to problems with the process itself. In conclusion it is important to see, that it is very difficult to establish a fabrication process that reliably yields well-defined Fe 3 O4 nanostructures exhibiting

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Figure 4.18: (partly from [Har06]) (a) Array of rings with different widths patterned using FIB. The narrowest rings (bottom of the image) exhibit no magnetic contrast due to damage. MFM images of such rings also show no magnetic contrast, but a good topographical definition is confirmed by AFM [Har06]. (b) The zigzag line in the middle is damaged and shows no magnetic contrast.

magnetic contrast in XMCD-PEEM. Recently, a first test of Fe 3 O4 deposition on prepatterned MgO substrates showed promising results with PEEM as briefly discussed in section 3.3.4. Magnetic contrast was observed and the structures were magnetically decoupled from the background. In the following, we focus on the results obtained despite these difficulties on FIB patterned as well as etched samples.

4.7.2 XAS and XMCD Spectra For XMCD-PEEM imaging, the appropriate beam energy has to chosen at which maximum XMCD contrast is obtained for the particular material under investigation. In general, the energy of the relevant absorption edge can be obtained from tables. However, the energy value to be set at the synchrotron beamline usually exhibits an offset of the order of a few electronvolts. X-ray absorption (XAS) spectra are acquired for each photon helicity and the XMCD spectrum is obtained by subtraction.24 Fig. 4.19 shows XAS spectra at the L2,3 absorption edges for an unpatterned as well as a patterned area and a XMCD spectrum of a ≈ 35 nm thick Fe 3 O4

film. The data agrees very well with reference spectra for bulk Fe 3 O4 (solid lines in the spectra shown in the insets [KPV00]) over the entire energy range. In 24

For NiFe and Co, these spectra are shown in Fig. 2.3 on page 42.

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Figure 4.19: (partly from [Har06]) (a) XAS spectra at the L2,3 absorption edges and (b) XMCD spectrum of a Fe3 O4 film. The XAS spectrum is shown for an unpatterned sample area (filled symbols) and for an micropatterned area (open symbols). The XMCD spectrum is acquired in an unpatterned region. For comparison, reference spectra from [KPV00] are shown in the insets, where the solid lines correspond to bulk Fe3 O4 .

the XMCD spectrum, two peaks with photon energies 708.0 eV and 709.8 eV are marked with arrows. The XMCD-PEEM images shown here were obtained at these X-ray energies.25

4.7.3 Spin Structure of Fe3 O4 Rings Since ring structures have been already comprehensively studied in NiFe and Co and since the spin structures of complete rings as well as of domain walls in such elements are very well understood, it is advantageous to investigate the same shape for Fe3 O4 in order to encounter possible differences. Such differences can be expected, since Fe3 O4 samples exhibit a fourfold in-plane anisotropy with two hard axes perpendicular to each other ([001] and [010]) and two easy axes in between ([011] and [011]) as discussed in section 3.4.2 [Har06]. Besides XMCD-PEEM imaging, magnetic force microscopy and micromagnetic simulations were performed as discussed above. MFM is sensitive to the perpendicular component of the stray field and is therefore a complementary 25

Due to an inevitable energy drift, the absolute values to be set at the monochromator of the

beamline can vary slightly between beamtimes and to some extent also during beamtimes. The fact that the relevant XMCD line shapes for Fe3 O4 are sharper than for NiFe or Co, makes the image contrast for Fe3 O4 particularly sensitive to energy instabilities. This energy drift is in general smaller at SLS than at Elettra, where a shift of nearly 1 eV during 24 h has occurred during experiments performed. Such a shift leads to a complete loss of the image contrast, if the energy is not adjusted accordingly.

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Figure 4.20: (from [Har06]) Comparison of an XMCD-PEEM image (a) of a magnetite ring (D = 10 µm, W = 1135 nm) with the results of OOMMF simulations (b) and MFM measurements (c) (both for a ring with D = 5 µm, W = 1135 nm). The samples were initially magnetized along a hard axis, as indicated by the arrow denoted by "H" in each image. The crystallographic directions are indicated in the center of the figure. The MFM contrast formation is illustrated in (d). In the PEEM image, the tail-to-tail zigzag domain wall and the left 90◦ spin reorientation are marked with "A" and "B", respectively.

method to XMCD-PEEM which images one component of the in-plane magnetization directly. OOMMF is used (saturation magnetization M s = 4.8 × 105 A/m, exchange constant A = 12 × 10−12 J/m, anisotropy K1 = -1.1 × 104 J/m3 , damping parameter α = 0.1, cell size 10 nm, [Har06]) to check the results for consistency. A

comparison of images obtained with XMCD-PEEM, MFM, and OOMMF is presented in Figs. 4.20(a–c). The contrast formation in the MFM image is visualized in (d). The PEEM and the MFM images clearly show what is confirmed by the simulation: The magnetization direction is mainly determined by the easy in-plane

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Figure 4.21: (from [Har06]) MFM (left) and OOMMF (right) results for rings with D = 5 µm and different widths (350 nm, 530 nm, 730 nm, top to bottom), initially magnetized along the hard axis.

axes of the film as already observed for epitaxial fcc Co [VLDK + 03, VKB+ 04], in contrast to the polycrystalline NiFe and Co samples investigated (see section 4.3), where the shape anisotropy causes the magnetization to be aligned along the ring perimeter. Also here the shape anisotropy of the ring leads to the formation of the onion state with tail-to-tail and head-to-head walls (indicated by "A" in Fig. 4.20(a)) at the top and the bottom of the ring, respectively.

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Figure 4.22: (from [Har06]) PEEM image of Fe3 O4 zigzag lines with different widths. The main axes of the zigzag lines are aligned with a hard axis, i.e. with the [010] direction. The lines were initially magnetized along the second hard axis perpendicular to their main axes. The magnetization directions are marked by black and white arrows.

The internal spin structure of these walls is different from what is known from NiFe and Co. Instead of transverse or vortex walls, a zigzag domain wall is observed. The formation of the zigzag structure (see section 4.2) can be attributed to a stronger dipolar and a weaker exchange coupling in this material. This allows the stray field to be reduced at the exchange energy cost of a longer domain wall. It should be noted, that due to the influence of the anisotropy these walls are no 180◦ head-to-head walls as observed in NiFe and Co. The zigzag walls separate two domains with an angle of only 90 ◦ . Accordingly, two 90◦ changes of the magnetization direction at the left and the right of the ring occur (indicated by "B" in Fig. 4.20(a)). Fig. 4.21 shows the results from a more systematic combined MFM and OOMMF study of rings initially magnetized along the hard axis with different widths. The results are qualitatively the same like shown in Fig. 4.20, but the simulations show that the occurrence of the zigzag structure depends on the ring width. For example, it disappears for 350 nm width (top) and is pronounced for 730 nm width (bottom). A higher number of saw teeth in a wider structure is also observed with PEEM as shown in Fig. 4.22. Another interesting aspect is comparing the spin structures of rings initially magnetized along hard and easy axes, respectively. The MFM contrast formation in a ring initially magnetized along an easy axis is depicted in Fig. 4.23 and rep-

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Figure 4.23: (from [Har06]) MFM contrast formation in a ring initially magnetized along easy axis.

resentative results are shown in Fig. 4.24, which directly correspond the images presented in Fig. 4.21 for an initial magnetization along a hard axis. In addition to the domain walls, four instead of two 90 ◦ magnetization reorientations can be observed. The head-to-head and tail-to-tail domain walls are true 180 ◦ walls now as known from NiFe and Co. The magnetization direction is mainly determined by the magnetocrystalline anisotropy like before, the element shape has a minor influence. The contrast of the MFM images seems to be complicated at first glance, but can be understood with the help of the schematics shown in Fig. 4.23 and correspond well with the results of the simulations. XMCD-PEEM images for this particular magnetization configuration and ring geometry are not yet available.

4.7.4 Spin Structure of Zigzag Wires for CIDM Experiments In view of the intended current-induced domain wall motion experiments with Fe3 O4 , an appropriate nanostructure has to be identified taking into account the influence of the anisotropy. The results on rings show that 180 ◦ head-to-head (or tail-to-tail) transverse or vortex domain walls can be formed by magnetization along an easy axis. The magnetization reorientations however, should be avoided. For magnetoresistance measurements, they can give rise to additional MR contributions like a domain wall would do. It is also not clear, how such configurations behave under current flow. Therefore, an appropriate sample design is a wire with a large-angle kink

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Figure 4.24: (from [Har06]) MFM (left) and OOMMF (right) results for rings with D = 5 µm and different widths (350 nm, 530 nm, 730 nm, top to bottom), initially magnetized along an easy axis.

as shown in Fig. 4.25. The main axis of the wire is one of the easy axes, which supports the formation of 180◦ walls with spin structures of the type shown in Fig. 4.24. The initial magnetization direction is the second easy axis perpendicular to the wire. The kink leads to the formation of one wall at this particular position and the large kink angle of close to 180 ◦ allows the assumption that a domain wall inside and outside the kink (after a possible current-induced motion) have very similar spin structures. XMCD-PEEM imaging of such structures was not successful so far due to the fabrication difficulties described above.

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Figure 4.25: (from [Har06]) SEM image of a 750 nm wide Fe3 O4 wire with an angle close to 180◦ between the segments. The main axis of the wire is aligned with the easy axis. Dark contrast indicates Fe3 O4 , bright contrast the MgO substrate.

4.7.5 Fe3 O4 Structures Capped with NiFe During the initial phase of XMCD-PEEM experiments on Fe 3 O4 also samples capped with NiFe were studied. Comparing with the results obtained on uncapped samples26 , we can conclude that the NiFe is ferromagnetically coupled to the Fe3 O4 and therefore reflects its spin structure directly. Similar structures with and without NiFe capping revealed a similar contrast. Therefore, the results obtained on the capped Fe3 O4 samples are not discussed in further detail.

4.8 Spin Structure of CrO2 Nanostructures In the frame of this thesis, the spin structure of CrO 2 was investigated using XMCD-PEEM. As detailed in the following, the experiments did not yield informations on the spin structures of CrO 2 elements as intended. However, magnetic force microscopy carried out on CrO 2 structures revealed the expected domain patterns, which depend the on magnetization direction with respect to the anisotropy axes and the shape anisotropy. For investigations with XMCD-PEEM CrO 2 samples were capped with Al and NiFe. On the Al capped samples, no magnetic contrast was obtained. In retrospective this can be attributed to the fact that the aluminium might have reduced the metastable ferromagnetic CrO 2 to the more stable isolating and antiferromagnetic phase Cr2 O3 [Kön06]. Sputtering of the sample did not yield 26

The Fe3 O4 samples are initially capped with Au, which is removed by sputtering prior to

imaging.

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Figure 4.26: PEEM images of a NiFe capped CrO2 wire magnetized approximately along the directions indicated by the arrows which point both roughly along the hard axis of the CrO2 film. The non-homogeneous contrast and the contrast inversion from (a) to (b) indicates antiferromagnetic coupling between CrO2 and NiFe.

any magnetic contrast either, possibly because the sputtering process destroys the ferromagnetic phase CrO2 . As performed for Fe3 O4 (see section 4.7.5), also CrO2 samples were capped with NiFe. We expected that this soft magnetic overlayer is exchange coupled to the CrO2 layer and therefore reflects the CrO 2 spin structure, which would allow for indirectly imaging the CrO2 at the energies of the Ni or Fe edges. However, the coupling turned out to be not as simple as hoped for. In Fig. 4.26, magnetization fields were applied along the directions indicated by the arrows, which both point approximately along the hard axis of the CrO 2 film. In remanence the magnetization is obviously aligned parallel or antiparallel to the easy axis. The direction critically depends on the direction of the applied field, which is slightly misaligned with the hard axis in anticlockwise direction in (a) and in clockwise direction in (b). However, it is expected that the CrO 2 wire magnetization is completely aligned along the easy axis in remanence, which is even supported by the shape anisotropy of the wire in this case. This means that either a monodomain state or a bidomain state with a domain wall at the kink (encircled areas in Fig. 4.26) can be expected in the CrO 2 wire. However, the encircled pattern exhibiting bright contrast in Fig. 4.26(a) is reversed in (b) as well as the contrast of the surrounding area. This points to a partly ferromagnetic and partly antiferromagnetic coupling between the CrO 2 film and the NiFe capping. A possible explanation of this antiferromagnetic coupling can be CrO 2 that was reduced to Cr, which causes this coupling due to interlayer exchange. However,

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Figure 4.27: PEEM images of a NiFe capped CrO2 film patterned with FIB. (a) Zigzag line and (b) FIB focussing area as detailed in the text.

. no direct experimental evidence for this explanation is available so far. Such a coupling was found to oscillate with Cr film thickness in a NiFe/Cr multilayer [WDFH93]. Since the thickness of the Cr cannot be expected to be uniform in our case due to the non-uniform reduction of the CrO 2 to Cr, parts of the NiFe capping might be coupled ferromagnetically and parts antiferromagnetically. Furthermore, the focused ion beam patterning can influence the exchange coupling [FRS04]. We observe indications that the FIB patterning process has influenced our samples as well. Figure 4.27(a) shows two parallel zigzag paths (homogeneous grey contrast) overlapping in the lower left part of the image, which are ion milled and thus non-magnetic. Interestingly, the dark contrast of the continuous film at the edges of the image is modified in the area influenced by the ion beam. In Fig. 4.27(b) a sample area is shown, where the ion beam was focussed before writing the structures. The focussing area is the approximately quadratic area with bright contrast, the patterned line in the upper part of the image exhibits a homogeneous grey contrast again. While this complicated coupling, which might be influenced in addition by the FIB patterning process, is an interesting side-effect, it complicates the interpretation of the data with a view to the CrO2 spin structure of interest. Therefore, this topic was not investigated in more detail during the limited beamtime. In parallel, the spin structure of CrO 2 nanostructures was investigated with

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Figure 4.28: AFM (a,c) and MFM images (b,d) of 2 µm wide CrO2 wires oriented along (a,b) the easy axis and (c,d) the hard axis of the film. The wires were magnetized (b) parallel and (d) perpendicular to the wire axis, respectively.

atomic and magnetic force microscopy (see section 2.6). Some representative results are shown in Fig. 4.28. On the left, AFM and MFM pictures of the 2 µm wide stripe oriented along the easy axis with a constriction and magnetized along the stripe is presented. As expected, the stripe is in a monodomain state and only at the constriction, significant stray fields are visible as can be seen from brightdark contrast in the MFM image. On the right, a 2 µm wide stripe oriented along the hard axis and magnetized perpendicular to the stripe is shown. The wire exhibits a stripe domain pattern visible by the alternating stray field contrast at the wire edges in the MFM image. Here, MFM has the advantage compared to XMCD-PEEM that it is sensitive to stray fields and therefore does not require a high quality magnetic CrO2 surface like PEEM. CrO2 is prepared ex-situ, so that

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it is very difficult to protect the surface from reduction to Cr 2 O3 (by means of capping or transport under UHV conditions). This protection is necessary for a surface sensitive technique as PEEM, because the CrO 2 surface is destroyed after only a few minutes of exposure to air. It can be concluded that CrO2 cannot be imaged easily with XMCD-PEEM due to the difficulties related to the surface stability as discussed. In view of valuable and limited beamtime for XMCD-PEEM it is advantageous to use MFM for imaging CrO2 nanostructures. This strategy has been followed after the described attempts using XMCD-PEEM.

4.9 Conclusions In conclusion, the XMCD-PEEM experiments constitute a solid basis for understanding the domain wall spin structures in the different materials and geometries investigated. Besides the insight into micromagnetism itself from these results, these experiments can be regarded as the prerequisite for the currentinduced domain wall motion and transformation effects discussed in the following chapter. In particular, comprehensive domain wall type phase diagrams for NiFe and Co were obtained from XMCD-PEEM imaging and compared with simulations and calculations. Differences between experiment and theory were explained taking into account thermally activated wall type transformations, which were experimentally observed. The domain wall width was studied in NiFe and found to depend linearly on the width of the nanostructure. Dipolar coupling between adjacent domain walls was also investigated. Together with direct imaging and a quantitative measurement of the domain wall stray field, the energy barrier height distribution for vortex core nucleation was obtained. Furthermore, the spin structure of the halfmetallic ferromagnets Fe 3 O4 and CrO2 was imaged using XMCD-PEEM. While a comprehensive picture of the domain wall formation in Fe3 O4 nanostructures and of the influence of the magnetocrystalline anisotropy was obtained from the combination of PEEM, MFM, and micromagnetic simulations, for CrO2 MFM was identified as the more suitable technique for spin structure investigations.

Chapter 5

Interaction Between Domain Walls and Current 5.1 Introduction and Overview The interplay between currents and domain walls in magnetic nanostructures has been studied intensively, driven by fundamental interest in the basic physical mechanisms involved. Furthermore current-induced magnetization reversal by domain wall motion is a promising alternative to the conventional fieldinduced reversal for technological applications in non-volatile memories and sensors, which has lead to an increase in research in this field as well (e. g. see [Sun06]). A prominent example of a device directly based on domain wall motion is the racetrack memory [Par04]. The phenomenon of current-induced domain wall motion has already been long known theoretically. The development and the present state of the theory is discussed in section 1.5. Experimentally, controlled current-induced motion of single domain walls in magnetic nanostructures has recently been achieved. Oersted fields have been excluded as a possible origin for domain wall motion [KVB+ 03b], which is supported by the observation that both head-to-head and tail-to-tail walls move in the same direction for a given current polarity [KJA+ 05]. Important aspects like domain wall velocities [YON + 04, KJA+ 05], critical current densities [GBC+ 03, VAA+ 04, KVB+ 05], thermally assisted motion [RLK+ 05], and the deformation of the domain wall spin structure due to current [KJA+ 05] have been addressed in order to understand the details of the

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underlying theory and the physics involved. The comparison of experiment and theory can reveal important information on the relative importance of the adiabatic and the non-adiabatic torque and their coaction in domain wall motion, which is still the subject of much debate [ZL04, TNMS05, HLZ05, TTK + 06] (see section 1.5). In this chapter, the experiments and results on current-induced domain wall motion and transformations are reported. The main results are obtained in NiFe rings and zigzag wires. The halfmetallic ferromagnets CrO 2 and Fe3 O4 are investigated as well. • In order to gain information on the (non)-adiabaticity of the spin torque, a

study of domain wall motion as a function of current and field at a constant

sample temperature is needed. Using combinations of current and field allows one to compare the theoretical calculations [HLZ05] of the dependence of the critical current on the applied field with the experimental results. Of particular importance for the comparison of experiment and theory is a constant sample temperature to separate spin torque and temperature effects, because existing theory so far neglects heating effects that lead to increased sample temperatures for high current densities. Since significant Joule heating due to injected current pulses was observed [YNT + 05], this effect must be quantitatively measured and taken into account. A comprehensive study of domain wall motion in NiFe driven by combinations of different fields and current densities at different constant temperatures is presented in section 5.2. The domain wall position in the sample is determined using the AMR contribution of the domain wall as proposed by Kläui et al. [KVB+ 02]. The complete experiment, during which more than 20.000 current pulses were injected, was performed on one single nanopatterned ring element. In particular, the temperature dependence of the critical field (at zero current) and of the the critical current density (at zero field) are obtained and exhibit opposite behavior. The Joule heating due to current is quantitatively determined using the experimental method proposed by Yamaguchi et al. [YNT + 05]. The heating is taken into account in order to obtain data as a function of a constant sample temperature instead of the cryostat temperature. This allows direct comparison with theory. These results are published in [LBB + 06b].

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• Current-induced domain wall motion at room temperature in NiFe wires is also investigated using XMCD-PEEM as a high-resolution imaging

method (see section 5.3). A specific experimental setup was developed that allows in-situ injection of current pulses into the sample. Wall motion as well as domain wall spin structure transformations are observed depending on the width and thickness of the wire. Domain wall velocities and critical current densities are obtained. The dependence of the wall velocity on the current density is compared with theoretical models. Parts of these results are published in [KLH+ 06]. • In cooperation with C. König and G. Güntherodt at the RWTH Aachen,

magnetoresistance measurements were carried out in patterned CrO 2 sam-

ples including current pulse injections and measurements of the Joule heating (see section 5.4). The temperature dependent magnetoresistance contributions of AMR and ITMR are briefly discussed. Then, the Joule heating experiments are presented, in which an already strong heating at moderate current densities is found. Low temperature experiments on CIDM are presented, but the observed effect is shown to be due to Joule heating of the current. Most of these results are reported in [Kön06] and [Büh05]. A publication of parts is in preparation [KGF + 06]. • Efforts were made to observe current-induced domain wall motion or

transformations in Fe3 O4 using XMCD-PEEM. The experiments per-

formed and the difficulties encountered are shortly reported in section 5.5. No spin torque effects in Fe3 O4 have been observed so far.

5.2 Current- and Field-induced Domain Wall Motion at Constant Temperatures in NiFe 5.2.1 Sample Characterization A scanning electron microscope (SEM) image of a 34 nm thick and 110 nm wide NiFe ring structure with 1 µm diameter with electrical contacts, which was fabricated as described in chapter 3 (see also [KVB + 02]), is shown in Fig. 5.1(a). Domain walls in such structures are head-to-head or tail-to-tail 180 ◦ domain walls with a vortex or a transverse spin structure as detailed in section 4.3 (see also

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Figure 5.1: (a) SEM image of the NiFe ring investigated (34 nm thick, 110 nm wide, 1 µm diameter) with the numbered contacts and the polar angles indicated. (b) OOMMF simulation of the spin structure of a vortex domain wall in a ring with the sample geometry. (c) Resistance of the ring area between contacts 2 and 3 as function of the domain wall position (schematically shown) measured at Tcryo =100 K. (d) Hysteresis of the sample resistance between contacts 2 and 3 measured along a field direction of 273◦. The steps indicate hysteretic switching between a vortex wall at low fields and a transverse wall at high fields.

[MD97, LBB+06a, LKB+ 06]). For this particular geometry, the domain wall type was determined to be a vortex wall using magnetoresistance measurements as described in [KVW + 04]: Since the ring geometry (34 nm thick and 110 nm wide) is situated close to the phase boundary in Fig. 4.5 on page 83, it is of particular importance to check the domain wall spin structure in this individual ring sample. Figure 5.1(d) shows a hysteresis loop of the sample resistance between contacts 2 and 3 measured along a field direction of 273◦ . The hysteretic resistance steps occur due to the transformation from a vortex to a transverse wall for increasing field and back to vortex wall for decreasing field. Such a measurement performed for a transverse wall would not exhibit any steps so that the existence of a vortex wall is confirmed. A micromagnetic simulation performed with the OOMMF code [OOM] (parameters used: MS = 800 × 103 A/m, A = 13 × 10−12 J/m, 3 nm cell size) and shown in Fig. 5.1(b) agrees with the experimentally observed vortex wall spin

structure. Magnetoresistance measurements were carried out in the bath cryostat setup described in section 2.2. A constant AC current of typically 5 µA was applied between contacts 1 and 5 while the voltage drop was measured between contacts 2 and 3 (cf. Fig. 5.1(a)). The magnetization configurations with a domain wall situated between and outside the voltage contacts, respectively, correspond to different resistance levels due to the anisotropic magnetoresistance contribution

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of the domain wall (see section 1.6.4.2 or [KVR + 03]). Reference curves, as shown in Fig. 5.1(c) for Tcryo = 100 K, were taken by saturating the sample in directions between 220◦ and 340◦ (cf. Fig. 5.1(a)) and subsequently relaxing the field to zero and measuring the resistance [KVR+ 03]. These curves allow to quickly ascertain the wall position by a resistance measurement.

5.2.2 Current- and Field-induced Domain Wall Motion Current pulses with 10 µs duration were applied between contacts 1 and 4 generating current densities of up to 2.5 × 10 12 A/m2 in the ring structure. The pulse duration was chosen such that even for wall velocities as low as 0.01 m/s the

domain wall is moved out of the area between the contacts 2 and 3. During the lifetime of the sample, more than 20000 current pulses were injected into the same structure. In order to determine the combinations of current and field that result in domain wall motion, the following experimental sequence has been executed typically 10 times for each combination of field strength, current density, and temperature: (i) An external field is applied along 273 ◦ and released, so that a domain wall is created at this particular position. 27 (ii) The resistance is measured. Using the reference curve mentioned before, we crosscheck that the domain wall is correctly positioned. (iii) An external magnetic field is applied perpendicularly to the direction of the saturation field along 3◦ (field and current parallel) or along 183 ◦ (field and current antiparallel), respectively. (iv) A current pulse is injected in addition to the field. (v) The resistance is measured again. From this resistance measurement we discern whether the domain wall has moved out of the area between the voltage contacts or not. 27

Different angles were also checked, but higher depinning fields were obtained. Since the

domain wall is pinned at structural imperfections like edge roughness, local oxidation or crystal defects, the pinning potential and therefore the depinning field depend on the exact wall position. The 273◦ direction was chosen with the view to minimized depinning field strengths.

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Figure 5.2: Domain wall motion at the temperatures Tcryo indicated in the legend for (a) current and field parallel and (b) current and field antiparallel. All lines are guides to the eye. The statistical errors of the critical fields are of the order of ±0.5 to 1 mT. For values above the lines, the domain

wall is displaced, below it remains pinned. Open symbols in (a) show the splitting of the boundary

for high temperatures as explained in section 5.2.5. (c) Critical field as function of the temperature for zero current (black squares) and for j = 2.07 × 1012 A/m2 (red triangles).

This procedure was carried out for different combinations of field, current, and temperature and we obtain the diagrams presented in Figs. 5.2(a) and (b). The different symbols indicate the different temperatures between 2 K and 200 K. For combinations of field and current below the boundary, the wall remains between the voltage contacts, for combinations above the boundary the wall is displaced. We define as critical field and critical current density the minimum values necessary for moving the wall, so the domain wall is also displaced for values of field and current exactly on the boundary. We first turn to the data presented in Fig. 5.2(a), where current and field are parallel.28 At zero current and a temperature of 2 K (black squares), a field of about 22 mT is needed to move the domain wall, which is pinned due to edge irregularities as visible in Fig. 5.1(a). The critical field at zero current decreases with increasing temperature as expected, since the increased thermal energy helps to overcome the energy barrier of the pinning potential. The temperature dependence of the critical field for zero current (black squares in Fig. 5.2(c)) can be described using the model presented in [HOO + 05], which indicates that thermally assisted field-induced domain wall motion is the dominant process. The 28

The case where field and current induce a domain wall motion in the same direction we

denote as the configuration of parallel current and field.

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underlaying fitting procedure and its results are presented in detail in [Büh05]. In the low temperature regime (≤ 20 K), already small current densities assist the depinning process and reduce the critical field (Fig. 5.2(a)). It approximately halves for 2 K (black squares) and 4.3 K (red discs) when increasing the current from 0 to 0.2 × 1012 A/m2 . We attribute this decrease predominantly to the Joule heating of the current pulses, because even small temperature increases can lead

to a large decrease of the critical field as discussed above (Fig. 5.2(c)). An additional mechanism suggested by He et al. [HLZ05] is that the adiabatic torque of the current helps to displace the domain wall center away from the pinning site which allows even small fields to move it. The presence of this effect cannot be excluded here and it might be superposed with the Joule heating due to the current. As the current density is increased, we see no change in the critical field, until a threshold current density of 0.5 to 0.8 × 10 12 A/m2 is reached, above which a reduction of the critical field takes place. The existence of such a threshold is in

agreement with theoretical results that take into account the edge roughness of a sample [TNMS05, HLZ05]. Above this threshold, we obtain a decrease (continuous lines in Fig. 5.2(a)) of the critical field until the critical current density j cH=0 at zero field is reached, at which the current moves the domain wall without any external field. When field and current act in a way as to move the domain wall in opposite directions, the jc (H)-dependence exhibits a completely different behavior (Fig. 5.2(b)). The decrease for very small currents (black discs and red circles for j = 0.2 × 1012 A/m2 ) can be explained by Joule heating like in Fig. 2(a). The difference in the absolute critical field reduction between the two field directions is

due to the asymmetry of the pinning potential, which can be seen comparing the critical fields in Figs. 2(a) and (b) for zero current. Such asymmetries are always present in these samples due to geometrical irregularities etc., and have been previously reported [KVB+ 04c]. For current densities above 0.2 × 10 12 A/m2 , no significant change of the critical field can be observed up to the critical current

density. This behavior is different from the results of Vernier et al. [VAA + 04], who used continuous currents leading to a reduction of the critical field. In our case, using current pulses, we observe that the spin torque effect and the magnetic field act in opposite senses, which leads to a constant critical field. This means that Joule heating cannot be dominating in this situation. When the mag-

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netic field and the spin torque caused by the current counteract, the domain wall is obviously moved either by current or by field.

5.2.3 Joule Heating due to Current We now turn back to the case where field and current are parallel in order to compare these results with existing theory. Since theoretical work is usually based on a constant sample temperature, we first have to quantitatively analyze the effect of Joule heating due to the current for our samples. Yamaguchi et al. [YNT+ 05] have proposed a simple experimental method to measure the Joule heating and have found a significant heating in their samples, which can exceed the Curie temperature. The resistance of the sample is measured during a pulse injection with a storage oscilloscope. Using the dependence of the resistance on temperature, which was independently measured with a small current, we can deduce the resistance increase and the corresponding temperature increase of the sample during the current pulse. This method is described in section 2.2 in more detail. For our samples, the heating is much weaker than found in [YNT+ 05], which might be due to different substrates used [YYT + 05]. The heating depends on the cryostat temperature T cryo . For low temperatures (Tcryo ≤ 20 K), the sample heats up by ∆T ≈ 100 K at a current pulse density of

Figure 5.3: (a) Joule heating as function of current density for Tcryo = 4 K (red squares) and 200 K (blue circles). (b) Domain wall motion for a corrected temperature of 100 ± 5 K with current and

field parallel. Black squares indicate measured values, red circles are interpolated. (c) Critical current density as function of the temperature. Black squares refer to the cryostat temperature Tcryo , red circles to the real temperature Treal corrected for the effect of Joule heating. Open symbols indicate maximum values of the current density injected during the lifetime of the sample and are therefore lower limits for the critical current density.

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2.1 × 1012 A/m2 while for Tcryo ≥ 100 K, the heating is ∆T ≈ 60 K (Fig. 5.3(a)). This means that for all cryostat temperatures investigated here, the real sample

temperature Treal remains significantly smaller than the Curie temperature of about 650 K. We are thus able to correct for the Joule heating effect and present our data as a function of the real sample temperature T real instead of the cryostat temperature Tcryo . With this correction, we obtain the modified diagram for domain wall motion at Treal = (100 ± 5) K shown in Fig. 5.3(b). The data points are either taken

at different cryostat temperatures T cryo so that the heating leads to a sample

temperature Treal = (100 ± 5) K (e. g. j = 1.88 × 1012 A/m2 injected at Tcryo = 4.3 K causes a heating of ∆T ≈ 96 K and therefore a sample temperature T real ≈ 100 K) or they are interpolated from measured data. 29 Only now we can compare the

experimental data with the theoretical calculations, which assume a constant temperature.

5.2.4 Comparison of Experiment and Theory Fig. 5.3(b) shows the curve for Treal = 100 K, because due to the heating of ∆T ≈ 100 K for the lowest cryostat temperatures, this is the lowest real tempera29

Since measurements for Treal = 100 K are not available for all current densities, some values

have been interpolated from measurements that yield values of Treal just above and just below 100 K using the following procedure: • Treal is determined for all combinations of j and Tcryo investigated. This yields data Hcrit (j) for a variety of different values of Treal , but we are interested in data sets with fixed Treal .

• We restrict now to the data points Hcrit (j) in a range of e. g. ±5 K around a certain Treal . Here we exemplarily chose Treal = 100±5 K. This data set contains points for very low j

(negligible heating) and Tcryo = 100 K as well as for high j (strong heating) and Tcryo ≤ 20 K.

Intermediate values for j are missing, so that interpolation is necessary.

• The dependencies Treal (j) for Tcryo = 20 K and Tcryo = 100 K are averaged. From this dependence we can obtain the current density j0 , for which a heating of ∆T = 40 K at

Tcryo =

100+20 2

K = 60 K yields a value of Treal = 100 K.

• The values Hcrit (j0 ) for Tcryo = 20 K and Tcryo = 100 K are averaged. If the Hcrit (j0 ) have not

been measured for this particular current density j0 and cryostat temperatures Tcryo , an interpolation between two measured values of Hcrit (j 6= j0 ) is performed. We obtain an

additional data point Hcrit (j0 ) at an intermediate j = j0 for Treal = 100 K and Tcryo = 60 K, even though no measurements are available for Tcryo = 60 K. The procedure can be repeated accordingly for other values than Tcryo = 60 K, which yields different values for j0 and thus additional Hcrit (j0 ) for a desired value of Treal .

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ture possible for which the full range of current densities from j = 0 to j = j cH=0 can be obtained. For Treal = 100 K, the critical field decreases with increasing current density above a threshold of about 0.8 × 10 12 A/m2 . This is in qualitative

accordance with results of numerical calculations of the domain wall depinning from an artificial pinning site in a NiFe wire at T = 0 K [HLZ05]. A quantitative comparison is not possible since our geometry is different. If calculations for the geometry investigated here and constant (non-zero) temperature were available, information on the ratio of adiabatic and non-adiabatic torque (non-adiabaticity parameter ξ in [HLZ05], represented by β in [TNMS05], see section 1.5.4) could be directly obtained from our data. The critical current density and the shape of

the jc (H)-curve (Fig. 2 in [HLZ05]) crucially depend on ξ. Fitting of the experimental data can then provide quantitative information on ξ and therefore allow to test the available theory and to gain insight into the relative importance of the adiabatic and non-adiabatic spin torque terms in the extended Landau-LifshitzGilbert equation. When the critical current density is reached, the domain wall is moved without the presence of any external magnetic field. Surprisingly, this critical current density jcH=0 increases with increasing temperature as shown in Fig. 5.3(c). This is a behavior exactly opposite to field-induced motion, where the dependence of the critical field on the temperature indicates a thermally activated motion [HOO+ 05]. This is in line with the observations in Fig. 5.2(c), where the temperature dependence of the critical field for j = 0 (thermally activated motion) is compared with the case of j = 2.07 × 10 12 A/m2 : Opposite behaviors for the field and the current needed for domain wall motion as a function of temperature are

observed, which indicate that thermally activated motion is dominating only in the field-driven, but not in the current-driven case. To our knowledge, only Tatara et al. have so far included thermal effects in the theoretical description of current-driven domain wall motion [TVF05], and they do not predict an increase of the critical current density. Temperature dependent measurements of the critical current density for switching in trilayer pillar elements [MAS+ 02, TSR+ 04, KEG+ 04] show a decrease with increasing temperature, which is explained in the framework of a model of spin accumulation at the interfaces. This model is obviously not applicable in our case, which is corroborated by our observation of the opposite behavior. This leads us to conclude that here a mechanism must exist which reduces the efficiency of the

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spin torque exerted on the domain wall at increased temperature. Spinwave generation can be such a mechanism [TK04] if a symmetry breaking between magnon excitation and annihilation for different directions occurs due to the current flow. When taking into account spin currents, it was theoretically predicted [BJZ98, FBNM04] that the spin wave dispersion ω(k) becomes asymmetric and can be expressed as ω(k) = ω 0 + f0 k2 + f1 (Is ) · k with the spin current Is , a constant f0 , and a function f1 (Is ) of the spin current.

Due to this asymmetry, also the magnon density of states becomes asymmetric with respect to k so that for non-zero temperature the number of thermally excited spinwaves becomes asymmetric as well in presence of a current. With increasing temperature, the number of thermally excited magnons increases as well as the difference between the number of magnons with opposite wavevectors so that more angular momentum is effectively carried away and the current-induced domain wall motion becomes less efficient. For the discussion of other possible origins besides asymmetric thermally excited spinwaves we turn to the possible temperature dependence of the non-adiabaticity parameter ξ = λ2exchange /λ2spinflip [ZL04, TNMS05]. But a decreasing spinflip length λspinflip with increasing temperature leads to an increase rather than a decrease of the spin torque efficiency. The exchange length λ exchange is expected to be only weakly dependent on temperature, so that λ spinflip dominates the temperature dependence of ξ. Different effects might exist that can reduce the spin torque efficiency, but we can exclude heating effects, because we have separated the influence of heating. Thermal activation as found in the field-induced case can be excluded as well due to its opposite temperature dependence. Therefore, possible explanations for the increase of the critical current density with temperature are reduced to the effective dependence of the spin torque efficiency on temperature. Asymmetric thermally excited spinwaves might be such an effect that reduces the spin torque efficiency with increasing temperature.

5.2.5 Splitting of the Boundary for Domain Wall Motion Furthermore, Fig. 5.2(a) shows that there are no significant differences between the results at 2 K, 4 K, and 20 K except for the critical field values at zero current. For these three cryostat temperatures, the Joule heating leads to very similar sample temperatures, which can be attributed to the specific tempera-

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Figure 5.4: Statistical distribution of the critical field for a current density of j = 1.95 × 1012 A/m2

and a cryostat temperature of 100 K. Fields between 0 and 4.8 mT were probed with a stepsize of 0.3 mT 10 times for each step. The data point at 8 mT confirms the expected 100 % probability of wall displacement under sufficiently large fields. A clear maximum at about 1.8 mT followed by a minimum probability at about 3.3 mT can be seen.

ture dependencies of heat capacity and thermal conductivity of the materials involved [Tou70]. The critical fields and current densities, and therefore the three curves shown in Fig. 5.2(a), are nearly identical because the real temperatures are nearly identical even though the cryostat temperatures are different. Fig. 5.2(a) also shows that the curves for T cryo ≥ 100 K split at a certain cur-

rent density into two branches. Experimentally, we have observed that a motion occurs for a low field, not for intermediate fields, and again for higher fields at a given current density. The statistical distribution of the critical field is shown in

Fig. 5.4 exemplarily for a current density of j = 1.95 × 10 12 A/m2 and a cryostat

temperature of 100 K. A first maximum can be seen at about 1.8 mT, and with about 4.8 mT, the domain wall is displaced in every case. We interpret these two branches as the result of two different processes. Either the domain wall is moved by current and field (lower branch) or the current pulse modifies the spin structure of the domain wall in such a way that the necessary critical field is increased (higher branch). The domain wall with

the modified spin structure is not moved anymore by the current densities used here, but only by an appropriately high magnetic field. This explains why the upper branches do not show any dependence on the current density. It was observed experimentally (see section 5.3 or [KJA + 05, KLH+ 06]) as well as inves-

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tigated theoretically [TNMS05] that current pulses can change the spin structure of domain walls. This change of the spin structure can lead to an immobilization [KJA+ 05] with respect to current or to an increased critical field, respectively.

5.2.6 Conclusion In conclusion, we have systematically determined the combinations of critical fields and critical current densities necessary to move a vortex domain wall in our sample. The Joule heating due to the current pulses was quantitatively determined to obtain real constant sample temperatures. The data for a constant sample temperature agrees qualitatively with available theoretical calculations for a different geometry. Further calculations will directly allow to determine the non-adiabaticity parameter in the theoretical description of spin torque from the data presented here and thus contribute to the further understanding of currentinduced domain wall motion. Furthermore, we have observed a significant increase of the critical current density with temperature which is in contrast to the decrease of the critical field in the field-driven case. This indicates that the current-driven domain wall motion is not predominantly a thermally activated process like the field-driven motion. From the measurements we can thus conclude that the intrinsic spin torque efficiency is reduced with increasing temperature, which might be due to thermally excited spin waves or other so far unknown reasons.

5.3 Current-induced Domain Wall Motion and Transformations in NiFe Observed with XMCD-PEEM Compared to the experiments using AMR-based detection of the domain wall position as described in the previous section, the imaging technique of XMCDPEEM provides several advantages. The domain wall spin structure can be resolved directly rather than attributing resistance changes to unknown modifications of the wall spin structure. The domain wall displacement and thus the wall velocity can be measured precisely rather than probing the wall position via the given position of electrical contacts. However, the experiments are more time-consuming than the flexible MR measurements and require beamtime at a

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Figure 5.5: (a) SEM image of the zigzag lines with kinks used in this study (width W = 1µm, thickness t = 28 nm). (b) XMCD-PEEM image taken after initialization with a field in the direction of the black arrow with the white arrows indicating the magnetization directions in one of the lines. Vortex head-to-head domain walls are visible at the kinks, six have a counter-clockwise and two a clockwise sense of rotation. The greyscale bar indicates the magnetization direction.

synchrotron light source. Current-induced domain wall motion and wall transformations in zigzag line elements are investigated here. In particular, we determine the wall type transformations which occur by the nucleation and annihilation of vortex cores. The wall velocities are measured and correlated with the wall transformations and wall types. Furthermore, the dependence of the wall velocity and the transformations on the wire geometry is investigated.

5.3.1 Sample Fabrication and Experimental Setup NiFe zigzag structures with thicknesses between 6 nm and 34 nm, widths W between 100 nm and 2 µm, and lengths of up to 100 µm have been fabricated as detailed in [HKN+ 04] (see also chapter 3). In Fig. 5.5(a), a scanning electron microscopy (SEM) image of such a zigzag structure is shown (W = 1 µm). To image the magnetization configuration, XMCD-PEEM is used (see section 2.1). A pulse injection setup with remote control was developed and integrated into the 20 kV high voltage rack of the PEEM endstation as detailed in section 2.3. We first concentrate on 28 nm thick and 1 µm wide NiFe structures. In Fig. 5.5(b) we present an XMCD-PEEM image of the initial magnetization configuration after saturation at zero field with vortex walls located at the kinks. From the head-to-head domain wall phase diagram [LBB + 06a] (see section 4.3)

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vortex walls are expected and indeed these are observed, as seen in the image. We inject current pulses with a length of 11 µs and varying amplitude. The magnetization configuration was imaged before and after every injection, with the result that any domain wall displacement or change in the spin structure could be determined. Since it was shown that the domain wall velocity can decay after a few injections [KJA+ 05], we have deliberately mostly injected just one to two pulses before remagnetizing the sample. This means that the velocities observed do not systematically vary with the pulse injection number for a constant wall spin structure.

5.3.2 Domain Wall Spin Structure Transformations We first consider the motion of walls which exhibit the same vortex wall spin structure before and after the displacement due to the current pulse (top black solid line and black squares in Fig. 5.6). The motion starts at about

Figure 5.6: Continuous lines are the averaged wall velocities as a function of current density. Black squares: each square represents the velocity of a motion of a vortex wall that did not transform (apart from the value for 11.2 × 1011 A/m2 , which is a lower boundary); Green down triangles: walls which are extended vortex walls before and after the injection, or transform from or to a

single vortex wall; Red discs: walls which are single vortex walls and then transform to a double vortex; Blue up triangles: walls which are multi-vortex walls (double, triple, etc.) before and after the injection.

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Figure 5.7: (a) XMCD-PEEM image of a vortex wall after remagnetization (top) and after injection of a pulse with j = 8.3 × 1011 A/m2 (bottom). An extra vortex has been nucleated downstream. (b)

A high resolution image of the double vortex wall and a micromagnetic simulation (c) revealing the spin structure (parameters as in Ref. [LBB+06a]). (d) Image of an extended vortex wall with a cross-tie structure in the center and arrows indicating the magnetization direction.

8.3 × 1011 A/m2 and the average wall velocity increases with increasing current

density, in line with previously reported experiments [YON + 04].

In addition to the displacement of these unperturbed walls, we also observe transformations of the domain wall spin structure. In Fig. 5.7(a) we present images of a head-to-head wall after remagnetization of the sample (top) and after an injection (bottom). We see that a vortex wall is transformed to a more complicated spin structure, which contains two vortices. A high resolution image of this double vortex wall is shown in Fig. 5.7(b) and a micromagnetic simulation of such a double vortex wall in Fig. 5.7(c). We see that in the center between the vortices, a cross-tie structure is formed [HS98] (cf. section 4.2). The transformation from a vortex to a double vortex occurs by the nucleation of a second vortex with the same sense of rotation as the original one. An analysis of the exact wall position in Fig. 5.7(a) shows that the black part (magnetization pointing down) of the wall has remained in the same position and that to the right of the first vortex (downstream, since the electrons flow from left to right), a second vortex was nucleated. This transformation from a vortex to a double vortex is most common but other transformations do also occur. In Fig. 5.7(d) an extended vortex wall structure is shown with a cross-tie structure at the center [HS98]. This structure is observed less often than the double vortex and can occur by the same nucleation of a second vortex with the same sense of rotation as the transformation to a double vortex. As the two vortices approach, they join to form this extended vortex.

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Figure 5.8: XMCD-PEEM images of two domain walls in adjacent lines after consecutive pulse injections with j = 8.7 × 1011 A/m2 : top wall: (a I) vortex wall after remagnetization which transforms

to a double vortex (a II) and back (a III) during consecutive injections; bottom wall: (b I) a vortex wall that transforms to a triple vortex (b II) and back to a double vortex spin structure (b III). (c) High resolution image of the spin structure of a triple vortex wall. (d) High resolution spin structure of the double vortex wall with two vortices that have opposite sense of rotation.

In addition to the nucleation of vortices, the annihilation of vortices may be expected as well, since a transformation from vortex to transverse walls was already observed in [KJA+ 05]. However, from the wall type phase diagram (see section 4.3, [LBB+ 06a]) we immediately see that in contrast to the 10 nm thick and 500 nm narrow wires in [KJA+ 05], which are very close to the phase boundary between vortex and transverse walls, the 28 nm thick and 1 µm wide structures studied here are far away from the phase boundary. Thus vortex walls are energetically much more favorable than transverse walls, which are therefore not attained. But since both the single vortex walls and the multi-vortex walls are stable, we can expect that double vortices are transformed back to single vortex walls by annihilating vortex cores during subsequent injections. An example of this is shown in Fig. 5.8. We first concentrate on the upper line (a), where a vortex wall (a I) is first transformed to a double vortex wall (a II) and then in the next injection back to a single vortex wall (a III). In the lower line (b) we see that the nucleation of domain walls can occur twice during one injection leading to the transformation from a single vortex (b I) to a triple vortex wall (b II). Annihilating one vortex then switches the wall back to a double vortex as seen in (b III). A high-resolution image of the spin structure of this triple vortex wall with two

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cross-tie structures between the vortices is shown in Fig. 5.8(c). This observation of the nucleation as well as the annihilation of vortices is in line with theoretical considerations and micromagnetic calculations. Recent calculations have shown that due to the spin torque effect a force acts on the vortex core, which pushes the vortex core towards the element edge to annihilate it [SNT+ 06]. For very high current densities, calculations have shown that the single domain state is not the energetically favorable state but that nucleation occurs [STK05]. Thiaville et al. have even predicted a periodic nucleation and annihilation of vortices due to spin torque [TNMS05]. Since we have limited ourselves to a few injections after each remagnetization, we did not probe systematically the periodic transformation from one wall spin structure to another, which has to be reserved for future experiments. Most interestingly, we always observe that a vortex is nucleated that has the same sense of rotation as the one already present, regardless of whether the second vortex nucleates upstream or downstream from the vortex that is already present. We have only twice observed a double vortex structure with two vortices with opposite sense of orientation as shown in Fig. 5.8(d) and neither of these spin structures resulted from a transformation from a single vortex but from a double or triple vortex state, which could happen if one of the cross-tie structures collapses into a vortex. This asymmetry of the vortex circulation direction in nucleated walls rules out thermally activated nucleation, where as a first approximation both vortex circulation directions should then occur in equal numbers. To check for thermal effects, we have directly determined the temperature rise during pulse injections by monitoring the resistance as suggested by Yamaguchi et al. [YNT + 05] and described in section 5.2.3. This resistance is then converted to a temperature using a calibration measurement of the resistance as a function of the temperature performed with a much lower current that causes no significant heating. The maximum heating for the highest current densities used was found to be 60 K, in line with earlier estimates [VAA + 04], but significantly less than observed in [YNT+ 05]. A further indication that the nucleation of vortices is not primarily due to temperature effects is the fact that all the vortices were nucleated in the vicinity of an existing vortex to form the observed spin structures (double, triple vortex, etc.), whereas a thermally activated nucleation occurs anywhere in the wire as observed by Yamaguchi et al. [YON + 04, YNT+ 05]. What is more, the energies of the multi-vortex spin structures are higher than that of the sin-

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gle vortex, which means that we do not observe the thermally activated transition to an energetically more favorable spin structure. This is analogous to the spin torque induced transformation from the energetically favorable vortex wall type to the higher-energy transverse wall type observed for 10 nm thick structures [KJA+ 05]. Thus what remains as a possible reason for the nucleation and annihilation of vortices is the spin torque effect due to the current. To understand the observations further, micromagnetic calculations including the spin torque effect are needed. The transformation from a vortex to a transverse wall as observed for the 10 nm thin elements used in [KJA + 05] has been qualitatively reproduced in micromagnetic simulations by Thiaville [Thi06], but no simulations have been made available for a wider and thicker geometry as used here. Such simulations would be desirable to further understand the nucleation process and possibly control the nucleation by varying the geometry as required for applications.

5.3.3 Spin Structure Dependence of the Domain Wall Velocity Now that we have discussed the observed domain wall transformations, we turn to the consequences for the wall displacement. In Fig. 5.6 the velocity is plotted as a function of current density, not only for the case of the motion of single vortex walls without transformation (black solid line and black squares as discussed above), but also for injections which involve transformations. The up triangles show that complicated multi-vortex (two or more vortices) domain walls do not move significantly for the current densities used here. During injections when the wall transforms from a single vortex to a double vortex or back (discs in Fig. 5.6), the walls move with a very low average velocity. These transformations set in at the same current density as the wall motions, which points to the same origin for transformation and wall motion. Since the red discs include the transformation from a single vortex wall to a double vortex and since we know the average velocity of a single vortex wall (black line), we can infer from the low velocity that the transformation takes place close to the beginning of the pulse. If the transformation occurred only towards the end of the pulse, we would expect that the average velocity would be similar to that of single vortex walls. Finally, we see that the extended vortex walls show a very different behavior from the double vortex wall. The down triangles show the velocity as a function

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of the current density for injections where the wall is transformed from a single vortex wall to an extended vortex or remains an extended vortex. We see that the velocities lie in a distinct region between those of single vortex walls and those of double vortex walls. Since there is no significant difference in the velocities of extended vortex walls that do not change their spin structure and of single vortex walls that transform to extended vortex walls, we can again deduce that the transformation takes place towards the beginning of the pulse injection. The drastic difference in velocities between the single, extended, double and multi-vortex wall structures indicates the importance of the number of vortices for the magnitude of the velocity. As theoretically predicted [TNMS05], walls undergoing a transformation exhibit a much smaller velocity than vortex walls which stay single vortex walls. This is analogous to field-induced motion, where wall spin structure transformations reduce the average velocity as well [BNK+ 05].

5.3.4 Geometry Dependence of Wall Transformations In order to use such elements in applications, the switching speed has to be high and the wall velocity reproducible to allow for fast and reliable switching. From the results presented above we can infer that this requires structures in which no domain wall transformations occur. To prevent transformations to transverse walls [KJA+ 05], we have to be far away from the phase boundary [LBB + 06a] (see section 4.3), which can be achieved by increasing the thickness from the 10 nm used in [KJA+ 05] to the 28 nm discussed above.

t = 6 nm

W ≈ 200 nm

W = 300 nm

t = 34 nm

W = 1 µm

W = 2 µm

M/T [1]

T

M

t = 10 nm t ≈ 28 nm

W = 500 nm M/T* [2]

M/T* [3]

M/T* [3]

M

M

Table 5.1: Wire geometries, for which current-induced domain wall motion and transformations have been investigated. Sources: [1] [KLH+ 06] (part of this thesis), [2] [KJA+ 05], [3] [JKB+ 06]. M and T indicate the observation of wall motion and transformations during the first pulses after remagnetization, respectively. In [KJA+ 05] and [JKB+ 06], a wall velocity decrease was observed after several injections, which was shown to be due to spin structure transformations in [KJA+ 05] (indicated by T*).

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Figure 5.9: XMCD-PEEM images of a domain wall in a 2 µm wide and 28 nm thick wire after consecutive pulse injections of 1.25 × 1012 A/m2 between (a) and (b) and of 1.33 × 1012 A/m2

between (b) and (c). The single vortex wall (a) is transformed to a double vortex (b) and then to an

extended vortex with a sevenfold cross-tie structure (c), which remains unchanged under further pulse injections with the same current density.

In order to study the geometry dependence of the spin structure transformations and of the wall velocities in more detail, we have so far investigated the wire geometries (width W and thickness t) listed in table 5.1, where the prevailing observations (M = motion, T = transformation) are indicated. Available data from other directly comparable sources is included and accordingly cited. In the widest wires investigated (W = 2 µm, t = 28 nm), domain wall transformations from single vortex walls to multi-vortex walls dominated and we did not observe any wall displacement without a transformation for this geometry. Figure 5.9(c) shows the impressing example of an extended vortex with a sevenfold crosstie structure (cf. Fig. 5.7(d)) created via a double vortex (b) from a single vortex (a) by two consecutive current pulses. In the thinnest sample (W = 500 nm, t = 6 nm) as well as in the narrowest structures investigated (W = 220 nm, t = 34 nm) undisturbed domain wall displacement without transformations was observed. The occurrence of transformations depends on the energy barrier height for vortex core nucleation that must be overcome. In very thick structures, a double vortex wall was observed after application of a mag-

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netic field to be a stable configuration in remanence [PHC + 06] (see Fig. 4.3 on page 81), so that current-induced transformations can be expected to occur with increasing thickness.30 The shape anisotropy of a narrow wire impedes the vortex nucleation, so that transformations are only observed in sufficiently wide wires. In conclusion, even from this limited set of widths and thicknesses investigated we can deduce the tendency that in wide or thick wires domain wall transformations of vortex walls are the dominating process, while in narrow wires the undisturbed motion prevails. 31

5.3.5 Geometry Dependence of the Domain Wall Velocity

Figure 5.10: Domain wall velocity as function of the current density for the different wire geometries indicated in the inset. The continuous lines are guides to the eye, the dotted lines are linear fits, and the dashed lines square-root fits to the data points with non-zero velocity as detailed in the text.

For the wire geometries mentioned above we can now compare the domain wall velocities (limited to undisturbed displacements as far as transformations occur) as function of the current density. Figure 5.10 presents the wall velocities 30

According to the phase diagrams (see section 4.3), in thinner elements transverse walls be-

come favorable, but transformations to and from transverse walls are not discussed here. 31 This however refers only the the first few current pulses injected, since also in relatively narrow (W ≤ 500 nm) and partly thin (t = 10 nm) wires spin structure transformations were observed

earlier [KJA+ 05, JKB+ 06] after a larger number of pulse injections. This behavior was not system-

atically studied here.

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C

jcrit

(10−12 m3 /C)

(1012 A/m2 )

t = 28 nm, W =1 µm

1.32±0.10

0.87±0.01

0.063

t = 28 nm, W = 500 nm

0.53±0.04

1.31±0.01

0.003

t = 6 nm, W = 500 nm

0.36±0.03

1.70 (fixed)

0.010

t = 34 nm, W = 220 nm

0.34±0.05

2.90±0.02

0.014

χ2

Table 5.2: Results of the fit of the domain wall velocity as function of the current density according p 2 to Tatara and Kohno [TK04] using v(j) = C j 2 − jcrit .

obtained from XMCD-PEEM imaging for the particular wire geometries listed in the legend of the image. The black squares for the 28 nm thick and 1 µm wide wires are identical to the black average line shown in Fig. 5.6 for undisturbed wall displacements. The data is fitted linearly (dotted lines in Fig. 5.10) as suggested by Barnes and Maekawa [BM05], who have applied this fit also to similar data by Yamaguchi et al. [YON+ 04], as well as by a functional dependence of the form q 2 v(j) = C j 2 − jcrit (5.1)

according to Tatara and Kohno [TK04] (dashed lines in Fig. 5.10), with C and

jcrit as fit parameters. The tables 5.2 and 5.3 show the fit results for these two models, respectively. The critical current densities are identical for both models within the error bars. The constant C is however not in accordance with the value resulting from its definition in [TK04]. The χ 2 values presented in the tables are only slightly lower for the linear than for the square root fit except of the 28 nm thick and 500 nm wide wire, for which, however, the data point with the largest velocity was not included into the fits. From this data set, it cannot wire geometry

A

B

jcrit = -A/B

(m/s)

(10−12 m3 /C )

(1012 A/m2 )

t = 28 nm, W =1 µm

-2.84±0.48

3.46±0.51

0.82±0.18

0.014

t = 28 nm, W = 500 nm

-2.26±0.16

1.76±0.11

1.28±0.12

0.077

t = 6 nm, W = 500 nm

-1.57±0.18

0.94±0.09

1.67±0.16

0.004

t = 34 nm, W = 220 nm

-2.80±0.49

1.01±0.16

2.78±0.66

0.008

χ2

Table 5.3: Results of the fit of the domain wall velocity as function of the current density according to Barnes and Maekawa [BM05] using v(j) = A + Bj.

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Figure 5.11: Critical current density as function of the wire width w with a 1/w-fit (left) compared to the dependence of the switching field (i. e. the critical field in field-driven domain wall motion) on the wire width (right), taken from Lee et al. [LXV+ 99].

be decided which functional dependence is in better agreement with the results. For determining, which fit model agrees better with the experimental data, a larger number of current densities for a given geometry has to be investigated with a sufficient statistical significance. But we can directly see from Fig. 5.10 as well as from the fit results that the critical current density depends on the wire geometry and increases with decreasing wire width. The dependence on the width is plotted in Fig. 5.11(a) and compared to the wire width dependence of the switching field in (b), which is taken from Lee et al. [LXV+ 99]. The switching field can be directly associated with the critical field for field-induced domain wall motion. Both curves show a similar dependence on the wire width, but in order to determine the functional dependence, a larger number of widths has to be studied. This first indication, that both functions exhibit the same functional width dependence, points to identical relevant pinning mechanisms in both current- and field-induced domain wall motion. For the comparison of the domain wall velocities, we have to consider velocities at comparable current densities. Jubert et al. [JKB + 06] have therefore compared the velocity for an approximately constant ratio between current density and critical current density for different wire widths. In other words, they have compared the velocity for current densities of 0–10% above the critical density. Here we use the linear fit presented above for this analysis. The slope of

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Figure 5.12: (a) Domain wall velocities as a function of the wire width. The labels indicate the wire thicknesses and the error bars result from the errors of the linear fits in Fig. 5.10. (b) Domain wall velocity as a function of comparable current densities with respect to the critical current density (j − jc )/jc for different wire geometries.

this fit is the velocity change per current change ∆v/∆j. We are now interested in the velocity increase per current increase normalized by the critical current ∆v/(∆j/jcrit ), which can be identified with (the absolute value of) the intersection A of the linear fit with the vertical axis. 32 The velocities obtained like this are plotted in Fig. 5.12(a) as a function of the wire width. The thickness is indicated next to the data points. The error bars reflect the fit error of the parameter A. The uncertainties of the single data points in Fig. 5.10 are not covered by the error bars, which can thus be regarded only as lower limits of the errors. In contrast to Jubert et al. [JKB+ 06], who observe a decrease of the velocity with increasing wire width at comparable currents, a constant velocity independent of the wire width is consistent with the data presented here as suggested by the dashed line in Fig. 5.12(a). This is confirmed in (b), where the wall velocity is plotted as a function of a comparable current density with respect to the critical current density (j − jcrit )/jcrit and does not depend on the geometry within

the (large) error bars, in particular not in the regime below 10% investigated by

Jubert et al. [JKB+ 06]. They have pointed out [JKB+ 06] that the observed decrease of the velocity disagrees with the models by Li and Zhang [LZ04a] and by Thiaville et al. [TNMS05], who predict using one-dimensional models that the velocity is independent of the wall width, which is in turn known to depend linearly on the wire width (see section 4.5). This contradiction with theory does 32

Assume that the fit is given by v(j) = A + Bj as above. Then the critical current is −A/B, the

slope is B, and the value of interest is given by B/[1/(−A/B)] = B(−A/B) = −A.

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not occur in the velocity data presented here. However, a wider and thus more reliable data set including a larger number of widths and thicknesses is needed to determine the wall velocity dependence of the geometry in more detail.

5.4 Domain Walls in CrO2 Since the imaging of CrO2 with XMCD-PEEM was not directly possible as described in section 4.8, CrO2 structures were studied using magnetoresistance measurements and MFM. These experiments have been performed in a joint project together with C. König and G. Güntherodt from the RWTH Aachen.

5.4.1 Temperature Dependent Magnetoresistance In the course of the MR measurements, it turned out that a careful study of the temperature dependent magnetoresistance effects in the CrO 2 samples was necessary in order to understand the switching behavior of the structures before proceeding to current injection experiments for the investigation of CIDM. The results of these experiments are discussed in detail in [Kön06] and [Büh05]. The magnetoresistance measured as a function of the applied field direction for structures oriented differently with respect to the crystallographic axes at different temperatures allowed to discriminate the influence of the anisotropic magnetoresistance (AMR) and the intergrain tunneling magnetoresistance (ITMR) (see section 1.6). At low temperatures, the ITMR is dominating (≈ 0.2% MR at 4.3 K), while at higher temperatures the ITMR is suppressed and the AMR is the dominating effect (≈ 0.09% MR at 120 K) [Büh05]. The values were obtained on a 2 µm wide wire oriented along the easy axis of the CrO 2 film. Hysteresis loops and corresponding minor loops measured at low temperatures can be explained by using one single concept of the magnetization reversal and by taking into account the expected ITMR contributions. A publication of these results is in preparation [KGF+ 06]. Besides the necessary prerequisite of understanding the MR effects in the structures investigated, it is necessary to be able to reproducibly create a domain wall at a defined position of a structure using homogeneous external magnetic fields. Furthermore, as already known from NiFe, it is essential to study the Joule heating of injected current in order to discriminate thermally induced effects and possible spin transfer torque effects. This is of particular importance

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a)

140

b)

[001]

Figure 5.13: (from [Kön06]) SEM images of a CrO2 wire oriented parallel to the easy [001] axis with a constriction and electrical contacts for current injection and resistance measurement.

because of the Curie temperature of only 385 K [Kön06], which means that a heating of only 100 K as observed for NiFe (see section 5.2.3) would lead to exceeding the Curie temperature in an experiment at room temperature.

5.4.2 Magnetization Reversal in Wires With Constrictions In order to reproducibly pin a domain wall during a magnetization reversal, wires with constrictions as shown in Fig. 5.13 were fabricated. The constriction acts as an artificial pinning site [KER + 05], which is expected to lead to a two step magnetization reversal process. This process is initiated by a domain wall nucleation at the triangular shaped wire end (bottom end in Fig. 5.13(a)), then the wall moves towards the constriction and is pinned at the constriction before it is depinned again at a higher field and the reversal is completed. This reversal is expected to result in steplike resistance changes in a hysteresis loop. Figure 5.14 shows a series of loops measured between different voltage contact pairs as indicated in the insets. The current flows always from contact 6 to contact 10. Stepwise resistance changes due an abrupt change of the wire magnetization are observed at about ±17 mT and ±60 mT. Depending on the voltage contact

configuration, steps at both field values occur (particularly for contacts 18/8) or at one of these two values only (e. g. for 18/11 or 11/8). The occurrence of two steps (four in a complete loop) points to a magnetization reversal process like explained above. Starting from saturation of the wire, a wall is nucleated at one end in an opposite field of about 17 mT and immediately reverses half the wire by domain wall motion, which gives rise to the first resistance change. The wall remains pinned until the stronger depinning field of about 60 mT is reached and

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Figure 5.14: Hysteresis loops at 4.3 K. The applied field and the long axis of the wire are parallel to the easy axis. The current flows from contact 6 to 10, the voltage contacts used are indicated in the insets.

then the depinned wall completes the magnetization reversal. Depending on the contact configuration, the measurement is sensitive to magnetization changes in different parts of the wire. Therefore, we observe the first, the second, or both switchings in the hysteresis loops. However, the picture of the reversal process obtained from the six loops in Fig. 5.14 is conclusive only, if we assume that the domain wall is not (or not always) pinned at the constriction, but at pinning centers due to defects or structural imperfections (see [Büh05] for a more detailed discussion). This behavior was observed also in other structures.

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Figure 5.15: Average switching fields for the magnetization reversal of the CrO2 wire with standard deviations as error bars.

In order to substantiate the above interpretation in terms of a two step switching process with a domain wall nucleation and a depinning process, the hysteresis measurement was repeated at different temperatures for typically ten times. The average values of the switching fields are presented in Fig. 5.15 with the standard deviations as error bars. As discussed by Kläui et al. [KVB + 04c] the switching field for nucleation processes exhibits a weak temperature dependence, while the switching field for depinning processes exhibits a stronger dependence. The same tendency applies for the temperature dependence of the corresponding switching field distribution widths. While no significant conclusion can be drawn from the temperature dependence of the distribution widths, the average values exhibit a stronger relative dependence on temperature for the upper curve (higher field) than the lower curve (lower field). According to [KVB+ 04c] this supports the understanding of the reversal process suggested above with a domain wall nucleation and a wall pinning at the constriction or at a defect.

5.4.3 Joule Heating The Joule heating was studied in CrO 2 using the identical experimental setup as for NiFe (see sections 2.2.2 and 5.2.3). The complete set of results of the heating measurements is displayed in Fig. 5.16(a), which clearly shows that for all

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143

Figure 5.16: (a) Joule heating of a CrO2 structure (t = 60 nm, W = 5 µm) due to current pulses with 10 µs duration as function of (a) the current and the current density and of (b) the deposited power of the pulse current. The labels indicate the cryostat base temperatures.

cryostat base temperatures the Joule heating increases with increasing current density as expected. The fact that the temperature increase at identical current densities is much stronger for higher base temperatures can be explained with the large increase of the resistance with temperature as presented in Fig. 5.17 for a part of a 5 µm wide and 60 nm thick wire. The resistance differs by about two orders of magnitude between 4.3 K and 325 K. The residual resistance ratio RRR equals 23.0, where RRR is defined as R(T = 300 K)/R(T = 4.3 K), which is much higher than the value of 1.57 for the NiFe samples discussed in section 5.2. Therefore, the Joule heating is shown as a function of the deposited power instead of the current density in Fig. 5.16(b) and an approximately linear increase is obtained. For an ambient temperature of 250 K, a current pulse with a density of 2.1 × 1010 A/m2 increases the sample temperature already to 325 K. Using the

Figure 5.17: Resistance as a function of the temperature for a part of a 5 µm wide and 60 nm thick CrO2 wire.

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144

saturation magnetization of Ms = 6.55 × 105 A/m for CrO2 [YCL+ 01], which is

similar to the value of 8.00 × 105 A/m for NiFe, the critical current density in CrO2 can be estimated to be roughly halved in comparison to NiFe due to the

approximately doubled spin polarization. This would yield a value in the lower 1011 A/m2 regime, which is still one order of magnitude larger than the current density already causing a temperature increase from 250 K to 325 K. Thus we can expect that the Curie temperature of 385 K [Kön06] would be exceeded by far at current densities in the range of the expected critical current density. The material would become paramagnetic and attain an arbitrary domain configuration after cooling down. Increased temperatures can also lead to structural damages for example by electromigration. The situation can be expected to be different at lower cryostat temperatures due to the weaker temperature increase and the larger absolute difference to the Curie temperature. Thus we can conclude that spin torque effects in the available CrO 2 samples cannot be studied in the room temperature regime, because the Joule heating and the related spin structure changes are dominating. Low temperature experiments might allow to observe current-induced domain wall motion.

5.4.4 Current-induced Domain Wall Motion Experiments According to the results of the Joule heating experiment discussed before, the current-induced domain wall motion experiments were limited to the low temperature regime. A 2 µm wide wire with a constriction was used, which exhibits the typical two-step switching behavior shown in Fig. 5.14. After saturation in one direction, an opposite field was applied that is sufficient for the first switching so that a domain wall is prepared. A current pulse is then injected and the magnetoresistance measurement is continued. This procedure is repeated with different fields at which the pulse is injected and with different current densities. A possible resistance change due to the current pulse is used to determine, whether the second switching has occurred. The measurement has to be repeated because the resistance levels are not as reproducible as for NiFe so that a significant number of measurements has to be discarded, because the measured resistance does not allow for a clear interpretation. It turns out that the value of the switching field decreases with increasing current density as indicated by the filled symbols in Fig. 5.18. This means that

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Figure 5.18: Critical field for domain wall depinning in a CrO2 structure (t = 60 nm, W = 5 µm) as a function of the temperature. Open symbols show the values for field-induced depinning at variable cryostat temperatures and filled symbols for current-assisted depinning at variable temperature due to Joule heating.

a current-assisted domain wall depinning takes place. In order to discriminate between a thermally assisted depinning due to Joule heating and a possible spin torque effect, the data is compared to the decrease of the switching field with increasing temperature for field-induced depinning represented by the open symbols in Fig. 5.18. Despite the offset between the two data sets, we can see that the decrease of the depinning field due to an increase of the ambient temperature is approximately identical to the decrease due to the corresponding Joule heating. This suggests that Joule heating due to current is still dominating in this experiment so that spin torque effects could not be detected. Motivated by these results on Joule heating, MFM experiments with current pulse injections were carried out at about 20 K (not in the frame of this thesis). So far, no current-induced domain wall motion was observed, but several structures significantly changed its resistance at certain current densities, which points to damages possibly due to electromigration. In conclusion, we have found that Joule heating in CrO 2 is strong compared to NiFe, which prevents the observation of spin torque effects in room temperature experiments. At low temperatures it might be possible to observe the expected spin torque effects, but the measurements carried out suggest that Joule heating is the dominating effect also in this temperature regime.

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5.5 Current-induced Domain Wall Motion in Fe3 O4 Due to its high spin polarization (see section 1.7) and lower saturation magnetization compared to 3d-ferromagnets, stronger spin torque effects are expected in the halfmetallic ferromagnet Fe 3 O4 . Theoretically, the spin torque efficiency is governed by the generalized velocity u (cf. eqn. 1.54 on page 23), because both the adiabatic and the non-adiabatic torque depend on u. This generalized velocity u is proportional to the current density and the spin polarization of the current and inversely proportional to the saturation magnetization. Reduced critical current densities or higher wall velocities might occur for example. This main reason has motivated to investigate current-induced domain wall motion in Fe3 O4 . So far only one indirect experimental evidence has been brought forward indicating current-induced domain wall motion in Fe 3 O4 nanostructures [CWC+ 05]. In order to be able to detect wall motion and possible wall spin structure modifications directly, XMCD-PEEM was chosen as the most suitable method to study these effects.33 However, the experiments did not reveal any information about current-induced effects on the spin structure so far. Besides the difficulties in the sample fabrication discussed already in section 4.7, additional problems have been identified in current injection experiments. The measured resistance of Fe3 O4 (16 parallel wires each with 500 nm×45 nm cross-section and 120 µm length exhibit a resistance of 40 kΩ corresponding to a resistivity of 1.2 × 10−2 Ωcm), which is in approximate agreement with literature

values for epitaxial and sputtered thin films [ZFP + 05, PPZ+ 05], is roughly two orders of magnitude higher than for NiFe. This requires the application of rel-

atively high voltages in order to obtain sufficient current densities for possible domain wall motion. A pulse amplifier was developed that allows to generate pulses with amplitudes up to 310 V. It turned out that the sample design with 100 µm long wires cannot be taken over from the experiments on NiFe, because the wire resistance would be much too high. The design was changed accordingly, but this will prevent the observation of longer wall propagation distances. Furthermore, the electrical connection between the halfmetallic Fe 3 O4 structures 33

Experiments using magnetoresistance measurements are also planned. This requires first to

test and fully understand possible MR contributions of a domain wall in Fe3 O4 [ZB00, CWC+ 05], ideally also as a function of temperature.

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and the metallic Au contacts turned out to be usually non-ohmic, which causes an additional uncertainty in determining the current flowing through the structure at a given pulse voltage. The work on current-induced domain wall motion in Fe 3 O4 is still in progress. At the time of writing this thesis, the focus is on the XMCD-PEEM technique. Different experimental problems have been already identified and partially solved. Relevant results were not obtained so far.

5.6 Conclusions The combinations of critical fields and critical current densities necessary to move a domain wall in NiFe rings have been systematically studied. The Joule heating due to the current pulses was quantitatively determined to obtain real constant sample temperatures. The data for a constant sample temperature agrees qualitatively with available theoretical calculations. Further calculations will directly allow to determine the non-adiabaticity parameter in the theoretical description of the spin torque. Furthermore, the critical current density significantly increases with temperature. This indicates that the current-driven domain wall motion is not predominantly a thermally activated process like the field-driven motion. It can be concluded that the intrinsic spin torque efficiency is reduced with increasing temperature, which might be for example due to thermally excited spin waves or other so far unknown reasons. Domain wall motion in NiFe wires was imaged using XMCD-PEEM, and wall spin structure transformations due to the spin torque effect were observed depending on the wire geometry. The domain wall velocity is correlated with the domain wall spin structure and decreases with increasing number of vortices inside the wall. Furthermore, the dependence of the critical current density and the velocity on the wire geometry was investigated. The critical current was found to increase with decreasing wire width. The velocities at comparable current densities were found to be independent on the wire geometry within the error bars. In CrO2 the temperature dependence of MR effects was studied. While the AMR dominates at higher temperatures, the ITMR is dominating in the low temperature regime. The magnetization reversal of nanowires at low temperature could be fully explained in terms of the ITMR. Joule heating was found to be

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strong compared to NiFe, which prevents the observation of spin torque effects in room temperature experiments due to heating above the Curie temperature. At low temperatures it might be possible to observe the expected spin torque effects, but the measurements carried out suggest that Joule heating is dominating also in this temperature regime.

Chapter 6

Conclusions and Outlook Domain Wall Spin Structures In conclusion, the results of the XMCD-PEEM experiments performed constitute a solid basis for understanding the domain wall spin structures in the different materials and geometries investigated. A comprehensive picture of the spin structures of 180◦ head-to-head domain walls in NiFe and Co was obtained in this thesis. The spin structure of the halfmetallic ferromagnets Fe 3 O4 and NiFecapped CrO2 was also imaged using XMCD-PEEM. A comprehensive understanding of the domain wall formation in Fe 3 O4 nanostructures, in particular of the influence of the magnetocrystalline anisotropy, was obtained from the combination of PEEM, MFM, and micromagnetic simulations. For CrO 2 , MFM was identified as the more suitable technique for spin structure investigations. Besides the insight into micromagnetism itself obtained from these results, the experiments can be regarded as the necessary prerequisite for the currentinduced domain wall motion and transformations studied in the second part of this thesis.

Interaction Between Domain Walls and Current The performed experiments on current-induced domain wall motion provide insight into the underlying spin transfer torque effect. In particular, the combinations of critical fields and critical current densities necessary to move a domain wall in NiFe rings have been systematically determined taking into account the inevitable Joule heating due to the current pulses. The critical current density increases with increasing temperature, which means that the intrinsic spin torque

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150

efficiency is reduced. Domain wall spin structure transformations due to the spin torque effect were observed in NiFe depending on the wire geometry. The domain wall velocity is found to be correlated with the domain wall spin structure. The critical current density increases with decreasing wire width. The velocities at comparable current densities are independent of the wire geometry within the error bars. In CrO2 the AMR was found to dominate at higher temperatures, while the ITMR is the dominating effect in the low temperature regime. The magnetization reversal of nanowires at low temperature could be fully explained in terms of the ITMR. Joule heating was found to be strong compared to NiFe, which prevents the observation of spin torque effects in room temperature experiments. Only at low temperatures spin torque effects might be observed, but measurements suggest that Joule heating is dominating also in this regime.

Outlook to Future Experiments Based on the insights gained in this thesis, several further experiments promise interesting results. Some ideas are briefly outlined in the following. The spin structures in NiFe, Co, and Fe 3 O4 have been comprehensively studied with a view to experiments in the field of current-induced domain wall motion, but further extensions of these experiments are possible and partly essential. The phase diagrams for NiFe and Co can be extended to the high thickness regime, where double vortex walls were recently found to be stable wall configurations [PHC+ 06]. In the case of Fe3 O4 , the influence of the anisotropy on the domain wall spin structure is known and 180 ◦ head-to-head domain walls were observed, but systematic geometry dependent studies of the wall spin structures are missing. For CrO2 the process of domain wall formation in nanostructures is understood, but a method for more reliably preparing single domain walls by external fields has to be identified using MFM and MR measurements. Many interesting questions obviously remain open in the very active field of interaction between current and domain walls. The study of critical fields and currents for domain wall motion presented in section 5.2 can be repeated with NiFe rings capped or doped with materials like Dy, Pd, or Pt serving as spin scatterers. Due to the strongly modified spin flip length, which influences the non-adiabaticity parameter in the spin torque theory, and due to the influence of

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151

such doping or capping on the damping constant α [YAMM05, YAMM06], the different torque contributions in the extended LLG equation can be artificially adjusted in order to test available theories. Domain wall velocities and critical current densities are expected to be modified. The planned combination of current injection, magnetoresistance measurements, and a non-intrusive high-resolution magnetic imaging technique like XMCD-PEEM or SEMPA will allow to simultaneously study effects of the spin structure on the current (i. e. domain wall magnetoresistance) and of the current on the spin structure (i. e. spin transfer torque). In particular, the MR contributions of novel wall spin structures created by current pulses can be investigated. High-resolution imaging of the spin structure together with magnetoresistance measurements will allow to determine directly to what extend the MR effects can be explained by AMR and which role the intrinsic DWMR plays. Furthermore, these experiments will yield valuable information for MR measurements performed in cryostat setups without the possibility of imaging. Another important aspect is to extend the domain wall motion experiments to Fe3 O4 and CrO2 . For CrO2 the low temperature regime has been identified as the only regime, in which current-induced wall motion might be observed. Further careful MFM measurements should allow to decide, whether Joule heating is still dominating at low temperatures as suggested here or if CIDM can be observed. In Fe3 O4 the aim is to demonstrate current-induced domain wall motion using XMCD-PEEM or MFM, since no evidence by imaging exists so far. Also MR measurements for the detection of domain walls as presented for NiFe and CrO2 can yield additional insight [CWC+ 05]. Demonstrating CIDM in the halfmetallic ferromagnets Fe3 O4 and CrO2 will open a wide field of possible future experiments, which have been already performed for 3d-ferromagnets. Since saturation magnetization and spin polarization govern the efficiency of the spin torque, the comparison of results for Fe 3 O4 and CrO2 with that for 3dmetals provides a powerful tool for testing existing theories. In the recent literature, interesting results and approaches have been brought forward, which can be stimulating for further experiments related to the results presented in this thesis. Hayashi et al. [HTB+ 06] have recently demonstrated the measurement of wall velocities by a time resolved measurement of the AMR contribution of domain walls. A modification of existing experimental setups would allow to per-

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form this type of experiments. So far, measurements of wall velocities base on imaging techniques, which in turn drastically limits the possible statistics because every single event has to be imaged. The availability of this complementary and flexible technique would allow to transfer experiments, where the detailed spin structure of domain walls is of minor importance or already known, from XMCD-PEEM, SEMPA, and MFM to MR based measurements and also allow for temperature dependent studies in the range from 2 K to 300 K. However, since the method of Hayashi et al. [HTB + 06] is a pump-probe technique, this is limited to repeatable processes, for which a single shot measurement (like e. g. the XMCD-PEEM imaging) is not mandatory. Grollier et al. [GBC+ 03] have investigated current-induced domain wall motion in stripe shaped Co/Cu/NiFe spin valve multilayers by measuring the GMR signal. This signal depends on the amount of magnetization in the soft NiFe layer that has been reversed by domain wall motion. Thus this method constitutes a MR-based measurement technique of the domain wall velocity, which in contrast to [HTB+ 06] enables single shot measurements of individual wall motions. However, the experimental geometry is not directly comparable to the systems studied in this thesis, since the current flow in such a multilayer is more complicated (interface scattering, different conductivities of the materials) and the coupling between hard and soft layer influences the reversal process and thus possibly the critical current and the domain wall velocity. Furthermore, the investigation of the dynamics of a domain wall is a related field of interest. Pioneering work has been performed by Saitoh et al. [SMYT04], who have studied the current-induced resonance of a domain wall and estimated a domain wall mass from the resonance behavior of the wall. Kiselev et al. [KSK+ 03] have experimentally demonstrated that microwave oscillations in a nanomagnet can be driven by a DC current via spin transfer torque.

Appendix A

Resistance of Capped NiFe Wires A.1 Introduction In this appendix, the resistance behavior of NiFe zigzag wires capped with Au is investigated quantitatively. This type of structures was used for the XMCDPEEM experiments described in section 5.3. Also the magnetoresistance measurements in section 5.2 were performed using Au capped NiFe rings. From the sample fabrication point of view, an immediate capping after the NiFe deposition is essential because an oxidized NiFe layer would prevent obtaining ohmic electrical contacts between the Au wires and the NiFe structures in the overlay step (see section 3.3). However, currents flowing through the wire distribute between the Au capping and the NiFe structure. Any current density calculated from the measured total resistance, the cross-section of the structure, and the applied voltage has to be regarded as an average current density of the system. The current density in the NiFe layer will be overestimated because the Au capping can be expected to carry more current per thickness than the NiFe layer due to the higher conductivity of gold. Bulk and interface scattering mechanisms contribute to the NiFe resistance depending on the wire thickness. In view of planned experiments on NiFe structures with different cappings, as detailed in the conclusions (see chapter 6), it is essential to understand in detail how the current distributes between the NiFe layer and the capping. This is also important for thickness dependent studies of the critical current density or of the domain wall velocity as discussed in section 5.3. But the results presented in section 5.2 are expected to be not significantly affected, because the 2 nm thin Au capping is negligible compared to the 34 nm thick NiFe.

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Figure A.1: Conductance of Au capped NiFe wires as a function of the NiFe wire thickness for the constant widths indicated in the diagram.

A.2 Experimental Results In order to quantitatively study the resistances of the Au capped NiFe structures, a set of eight samples with different NiFe thicknesses t between 4 nm and 34 nm capped with 2 nm Au was investigated. On each sample, eight groups of four wires each were patterned with wire widths W between 100 nm and 2 µm. All samples were fabricated in the same run, which assures identical Au cappings on all structures and precise relative NiFe thicknesses, independent of a possible absolute thickness calibration error. The resistance of each group of four wires connected in parallel has been measured at room temperature. The corresponding conductances are shown in Fig. A.1 as a function of the NiFe thickness for the different wire widths as indicated by the legend, the color code, and the different symbols. The resistance of a wire can be modeled by two parallel resistors R Au and RNiFe representing the resistance contributions of the two layers. Thus the corresponding conductances GAu and GNiFe are additive so that Gtotal (W, t) = GAu (W ) + GNiFe (W, t).

(A.1)

The dependence on the width W and the NiFe thickness t is indicated. The conductance GNiFe contains contributions due to surface and interface scattering Bulk GIF NiFe as well as due to scattering processes in the bulk material G NiFe . Depend-

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ing on the thickness and width of the wire, i. e. the ratio of the cross-section area t · W and the circumference 2(t + W ), the one or the other contribution is dom-

inating. While the conductances of the Au and the NiFe layer can be assumed

to be additive as explained before, the bulk and the interface contributions are modeled as two resistors in series, so that the resistances rather than the conductances are additive. This is motivated by the fact that the maximum thicknesses investigated are of the order of the electron mean free path. Thus identical electrons are expected to scatter in the bulk material as well as at interfaces during their travel through the wire. Both scattering processes occur randomly in series for all electrons justifying the model of two resistors connected in series. 34 The total conductance can therefore be written as −1  1 1 Gtotal (W, t) = GAu (W ) + + Bulk GIF GNiFe (W, t) NiFe (W, t)  −1 1 1 = GAu (W ) + + . α/(W + t) βW t

(A.2) (A.3)

This equation assumes that the NiFe bulk contribution to the resistance can be

L Bulk = ρ written in the usual form RNiFe NiFe 4A , where ρNiFe is the (bulk) resistivity, L

the wire length, and 4A the total cross-section of the four parallel wires, which in turn results in GBulk NiFe (W, t) =

4A ρNiFe L

=

4W t = βW t ρNiFe L

(A.4)

with β = 4/(ρNiFe L). The interface contribution to the conductance is expected to be inversely proportional to the NiFe interface and surface area 4 · 2L(W + t)

so that we can write

α W +t with a constant α. Equation A.3 can be rewritten in the form

(A.5)

αt , + W t + t2

(A.6)

GIF NiFe (W, t) =

Gtotal (W, t) = GAu (W ) +

α βW

which has been used for fitting the data sets for constant wire widths W as indicated in Fig. A.1 by straight lines. This fit yields values for the conductance of the Au capping GAu and for the bulk and interface constants of the NiFe layer α and β as displayed in table A.1. 34

In macroscopic wires, it would be reasonable to assume two parallel resistors for modeling

bulk and interface contributions because a part of the electrons will mainly undergo surface scattering events while others mainly contribute to the bulk scattering within a certain time interval. Both processes occur in parallel for different electrons justifying two parallel resistors.

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width

GAu

(nm)

(10−4

100

0.9 ± 0.5

1.39 ± 10.15

1.66 ± 0.77

3.01 ± 1.40

1.6 ± 0.6

0.78 ± 0.31

1.98 ± 0.52

2.53 ± 0.66

2.0

1.24 ± 0.05

1.56 ± 0.06

2.62 ± 0.10

150 220 300 500 600 1000 2000

S)

–

1.7 ± 0.4 2.1 ± 0.5

2.5 ± 0.9 6.2

α

β

(S · nm)

(10−7

–

0.90 ± 0.12 1.40 ± 0.06

2.17 ± 0.06

3.32 ± 0.12

ρNiFe S · nm−2 )

–

1.87 ± 0.27 1.55 ± 0.23

1.44 ± 0.30

0.85 ± 0.07

(10−7 Ωm) –

2.67 ± 0.39 3.23 ± 0.48

3.47 ± 0.72

5.88 ± 0.48

Table A.1: Fit results obtained by fitting the data of Fig. A.1 using the model described in the text. The fit algorithm did not converge for 150 nm width, and GAu was fixed for 500 nm and 2 µm width to allow for a conversion to reasonable values of α and β. The values for ρNiFe are obtained using ρNiFe = 4/(Lβ) with L = 80 µm.

First we see that the bulk resistance values for NiFe are of the order of 10−7

Ωm (3.34 × 10−7 Ωm averaged over the width), which is in good agreement

with a literature value of 1.52 × 10−7 Ωm [Lid01]. This supports the applicability of the resistor model developed above.

The conductance contributions of the Au capping layer as displayed in in the left column of table A.1 are shown in Fig. A.2(a) (black lower parts of the lines)

Figure A.2: (a) Total conductances of the Au capped NiFe wires as a function of the wire width and thickness (blue circles). The black and red parts of the lines indicate the Au and the NiFe contributions respectively. (b) Ratio of the Au layer conductance to the total conductance as a function of the wire width and thickness.

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together with the NiFe contribution (red upper parts of the lines) as a function of the wire width and thickness. It can be seen that the total conductance (blue circles) increases with increasing width and thickness as expected and as already indicated by the data shown in Fig. A.1. Also as expected, the Au conductance becomes more relevant for thinner NiFe layers as quantitatively displayed in Fig. A.2(b). Here, the ratio of the Au conductance to the total wire conductance is shown and we see that for the thinnest and widest wires (t = 4 nm, W = 2 µm) the Au conductance is dominating, while for thick and narrow wires (t ≥ 28 nm,

W ≤ 1 µm), the ratio is between 10% and 15%. This supports the assumption made in section 5.2 that the Au capping can be neglected when calculating cur-

rent densities, because a 34 nm thick and 110 nm wide ring was studied there.

A.3 Conclusion In conclusion, the studied set of Au capped NiFe wires with different widths and thicknesses allows to quantitatively determine the conductance contributions of the NiFe layer and the Au capping in the frame of a simple resistor model. The capping layer exhibits a significant conductance compared to the total value of the multilayer in particular for thin and wide wires, while for thick and narrow wires the influence is weak. The bulk conductance contribution of the NiFe layer, or the corresponding resistance respectively, agrees within a factor of two with literature values. The proposed model allows to quantitatively determine the conductance of an Au capping layer and thus the fraction of current not carried by the NiFe layer. This is of particular importance, when critical current densities or current density dependent domain wall velocities are investigated as a function of the NiFe thickness, i. e. when a precise knowledge of the current carried by the ferromagnetic layer is crucial.

Appendix B

Work Performed at the INESC-MN in Lisbon During a nine month’s stay at the Instituto Natiónal de Engenharia de Sistemas e Computadores in the "Microsistemas e Nanotecnologias" group of Prof. Freitas I have worked in collaboration with the group of Prof. Hillebrands at the TU Kaiserslautern before beginning the work at the University of Konstanz. The main focus was the sample design and preparation process by means of ion beam deposition of magnetic multilayers and optical lithography. All measurements were performed using micro-focus Brillouin light scattering by V. E. Demidov at Kaiserslautern, where I helped with the measurements during one month of secondment stay and learned about the technique. The results of this work – even though not a formal part of this thesis – are presented here and are published in [DDH + 04, DDH+ 05], where parts of this appendix are directly taken from.

B.1 Introduction and Experimental Setup Spin valve elements (two magnetic layers separated by a nonmagnetic, but conducting spacer layer) as well as TMR elements (two magnetic layers separated by a thin, nonmagnetic isolating spacer layer) were designed. These elements can be used in applications such as magnetic random access memory (MRAM) elements [ERJ+ 02]. One method to write data to such elements is the novel technique of current-induced switching, which overcomes the necessity to design

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159

Figure B.1: (from [DDH+ 04]) Layout of the µ-BLS experimental setup.

additional field-generating striplines and therefore allows for higher storage densities by a simplified chip design. Improving storage density and operation speed requires a detailed understanding of the high-frequency magnetization dynamics in such structures. A powerful and flexible measurement tool to investigate magnetization dynamics in such systems is Brillouin light scattering (BLS) spectroscopy of spinwave excitations [DHS01], which has been improved by the group in Kaiserslautern to a so-called µ-BLS. A micro-focus sample stage allows measurements on a spatial length scale of less than 500 nm and thus on single magnetic elements. The aim of the work was to understand the dynamic coupling of a magnetic element with the magnetic environment. As a test case the high-frequency magnetization dynamics of a micrometer-sized magnetic element having a geometry typical for magnetic memory elements based on the effect of current-induced magnetic switching was studied. It is found that radiation of spinwaves takes place via localized spinwave modes confined to the element. The layout of the BLS setup is schematically shown in Fig. B.1. An argon ion laser produces a vertically polarized probing beam with a Gaussian width of 2 mm and a wavelength of λ = 514.5 nm. The beam is focused by a microscope objective lens onto the surface of the magnetic sample placed into a magnetic

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Figure B.2: (from [DDH+ 04]) Schematic view of a magnetic memory element with partially patterned magnetic hard layer: (a) top view, (b) cross section.

field applied parallel to its plane. The sample is mounted on a piezoelectric stage, which allows for positioning in the two directions perpendicular to the beam with a precision of 50 nm. At the surface of the magnetic sample the probing light is inelastically scattered by spinwave excitations. As a result, the frequency of the scattered light is shifted by the frequency of the spinwave. The spectrum of the scattered light is analyzed by means of a tandem Fabry-Pérot interferometer operating in multipass configuration [Hil99]. A CCD camera supplied with a telescopic objective is used to monitor the position of the laser spot on the sample surface during measurements. More details about the experimental setup can be found in [DDH+ 04].

B.2 Sample Preparation The samples were prepared with a geometry typical for magnetic memory elements based on the effect of current-induced magnetic switching (see [KSK + 03, MRET05] as well as many others). They consist of a soft and a hard magnetic layer separated by a nonmagnetic conducting spacer layer with the layout shown in Fig. B.2. The samples were prepared on glass substrates. The bottom electrode is a 40 µm wide and 60 nm thick Al stripe. This stripe was completely

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covered by a 10 nm thick Co80 Fe20 film. The magnetic element with lateral dimensions of a × b = 1.3 × 2.3 µm2 was fabricated on top of the bottom electrode.

For this purpose a 4 nm thick Cu spacer film, a 5 nm thick Ni 81 Fe19 film, and a

2 nm thick protective Au film were deposited. The element was patterned by means of direct write laser lithography and consecutive ion milling. The etching was stopped in the CoFe layer. Accordingly, the thickness of the CoFe film in the area of the magnetic element was left to be 10 nm, whereas in the areas outside the element the thickness was reduced by 20–40% (see Fig. B.2(b)). After patterning, a 100 nm thick Al2 O3 layer was deposited, which provides the electrical insulation between the bottom and top electrodes. Finally the insulating layer was opened in the area of the element and a 60 nm thick and 500 nm wide Al upper electrode was deposited and patterned by lithography and lift-off. Besides the described samples, with which the successful measurements were performed, also samples with different multilayers and pillar sizes were fabricated, in particular TMR stacks with an isolating spacer layer were deposited and patterned. The particular challenge for the sample preparation process was the specially adapted design shown in Fig. B.2(a). In contrast to standard TMR or spin valve junctions, the top electrode may not cover the multilayer pillar and the surrounding area to allow for optical measurements with BLS, which would be impossible when the system is completely covered with 100 nm Al of the top electrode. The lateral target size of the pillar was chosen to be 1 × 2 µm. However, the direct write laser lithography system available had

a minimum laser spot size of 800 nm diameter, only the sample stage could be positioned under the laser spot with a stepsize of nominally 100 nm. In order to

realize the desired sample design, a special two step process for the top electrode deposition was developed. The process is visualized in Fig. B.3, the sub-µm sized structure to be patterned is indicated in green (b). Photoresist is spun onto the sample, exposed and developed as shown in (c). However, since the resolution of the exposure is limited by the spot size of about 800 nm diameter, the sample has to be aligned very precisely making use of the 100 nm stepsize of the sample stage, which can be moved while the laser spot position remains fixed. The exposed resist serves as a mask of an ion milling step that transfers the pattern into the material, here into the top electrode (d). This milling depth has to be calibrated very carefully to be able to stop the milling at the desired depth and not to damage the multi-

Work Performed at the INESC-MN in Lisbon (a)

(b)

(c)

(d)

(e)

(f)

162

ion milling

(g)

ion milling

(h)

substrate layer to be etched sub-µ-structure photo resist

Figure B.3: (Color online) Schematics of the sample fabrication process: Layer (here top electrode) to be patterned is deposited. (b) Sub-µm sized structure to be patterned is indicated in green. (c) Photoresist is spun onto the sample, exposed, and developed. (d) First ion milling step. The resist serves as a mask. (e) Sample after removal of resist. (f) Second lithography step. (g) Second ion milling step. (h) Final shape of the sample (see legend for explanation of colors).

layer below. The resist mask is removed (e). Then the lithography step and the pattern transfer via ion milling is repeated as shown in (f) and (g). Finally, the desired structure is left with lateral dimensions down to 100 nm (h). In principle, the process can be repeated for patterning perpendicular to the axis arbitrarily chosen in Fig. B.3 so that structures with a size down to 100 nm × 100 nm can be obtained.

It should be mentioned however that the process can only be successful, if an exposure series is performed in which a range of different offsets for the sample position is used. In the first lithography step, the alignment has to be sufficiently precise with respect to the buried multilayer stack. In the second step, the alignment has to be precise with respect to the first pattern transfer. Since the positioning error – assuming a perfect sample alignment, which is never possible to achieve – is ±100 nm and thus in two consecutive steps ±200 nm, with a target size of e. g. 200 nm width one can end up having "nothing left" as well as twice

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163

Figure B.4: (from [DDH+ 04]) Spectra of spinwaves in the CoFe film surrounding the magnetic element measured at different distances from the edge of the element with applied external excitation. The spectra are vertically shifted for clarity.

the desired width. The yield of the process is therefore very low and it took several attempts to obtain samples that could be used for the measurements. It would have been favorable to use electron beam lithography (see section 3.3.1 on page 68), because feature sizes in the range of 100 nm can easily be achieved with this technique. But since electron beam lithography was not available, the project was performed as described above.

B.3 Results In the µ-BLS setup described above, a uniform static magnetic field of 38 mT was applied parallel to the long side of the magnetic element. The element was excited by a microwave current supplied by the electrodes and flowing through

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the element in vertical direction. The frequency of the exciting current was continuously swept in the range from 7.5 to 13 GHz, which corresponds to the frequency range of dipolar spinwaves in a CoFe film. Spectra of spinwaves existing in the CoFe film surrounding the element were measured at different distances d from its edge with a step size of 250 nm (see Fig. B.2(a) for details). Typical spinwave spectra are presented in Fig. B.4. The six spectra shown correspond to six different values of the distance d between the edge of the magnetic element and the center of the laser spot. We first consider the spectrum measured nearby the edge of the magnetic element at a distance of d = 250 nm (Fig. B.4, bottom spectrum). Three pronounced peaks are observed near frequencies of the the exciting current of 8, 10, and 12 GHz (marked as F1, F2, and F3 in Fig. B.4) as well as a few other peaks with smaller amplitudes. In a continuous film, the dispersion of spinwaves and their intensities are monotonous functions of the wave vector or the frequency. The surprising result of the observed peaks can only be understood by assuming that the microwave current flowing through the magnetic element excites discrete spinwave modes quantized in the two-dimensional element due to the lateral confinement [DHS01] and these modes serve as a radiation source for spinwaves in the surrounding continuous CoFe film. The efficiency of mode excitation by the microwave current is different for modes with different spatial distributions of dynamic magnetization. This causes an appearance in the experimentally measured spectra of less and more pronounced peaks. Most probably, the most intensive peaks at frequencies F1, F2, and F3 correspond to the lowest-order eigenmodes whose excitation is most efficient. Furthermore, we observe that the intensity of spinwaves corresponding to the frequency F2 monotonously decreases, whereas the intensities of waves corresponding to the frequencies F1 and F3 exhibit clear maxima at distances d equal to 500 nm and 750 nm (see Fig. B.4). Such a behavior can be understood by different spatial distributions of the intensity of the radiation sources corresponding to different frequencies (i.e. quantized spinwave modes), which leads to different diffraction scenarios for the waves excited by different modes. These findings motivated a more in-depth study of the lateral intensity distribution of modes. A closed loop control of the sample position was implemented and the geometry changed such that the sample stage is mounted horizontally instead of vertically. The position of the laser spot is automatically monitored

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Figure B.5: (from [DDH+ 05]) Experimental (left column) and theoretical (right column) spinwave radiation patterns. Below the patterns the excitation area is shown (rectangular for experimental patterns or linear for theoretical ones). Below the theoretical patterns the corresponding distributions of dynamic magnetization along the linear excitation area are given. Dashed lines show directions of radiated rays in accordance with the theoretical results.

and possible drifts are corrected by adjusting the sample stage position. This improvements were crucial to obtain a stable sample position during the acquisition time of the spectra. The experimental radiation patterns obtained from such a spatially resolved measurement in the vicinity of the pillar are shown in Fig. B.5 in the left column. The corresponding excitation frequencies are indicated. As seen from the figure, all radiation patterns exhibit several spots where the intensity of the dynamic magnetization significantly increases, but the positions and the number of these

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spots are different for different radiating eigenmodes. The slight asymmetry of the measured patterns with respect to the middle line can be associated with an asymmetrical distribution of the current exciting the element. In order to understand these complicated radiation patterns, calculations were performed based on the Damon-Eshbach dispersion law. For the sake of simplicity, a radiation process from an infinitely thin area with a length of 1.3 µm was considered, which corresponds to the length of the magnetic rectangle in the direction of spinwave quantization. Distributions of the dynamic magnetization along the excitation area were defined in the form of standing waves with the number of antinodes varying from 1 to 4. The amplitude of the dynamic magnetization in every point of a region adjacent to the excitation area was calculated taking into account the interference of spinwaves coming from different points of the excitation area. Magnetic dissipation was neglected. The results of the calculations are presented in the right column of Fig. B.5. Each pattern in the right column was calculated for the experimental conditions corresponding to the patterns shown in the left column. Below each of the theoretical radiation patterns the distributions of the dynamic magnetization along the excitation area are shown. The calculated radiation patterns allow for a qualitative understanding of the experimental findings. Figure B.5(e) shows that, if the radiating source has a distribution with one antinode, spinwaves are radiated in two rays starting at the point where the distribution has its maximum. If the distribution has two antinodes (see Fig. B.5(f)) the number of rays increases to four. In this case, on the middle line, where the rays intersect each other, a complete suppression of the dynamic magnetization is observed caused by the interference. In the cases of three and four antinodes the number of rays becomes six and eight, respectively (see Figs. B.5(g, h)). In these cases some of the intersection points demonstrate a constructive interference, whereas others demonstrate a destructive one. Comparing the experimental and theoretical radiation patterns one can conclude that for the eigenmodes with n =1 to 3 the radiation follows the scenario predicted by the model. This can be easily seen if one draws rays in accordance with the theoretical results at the top of the experimental patterns as shown in Figs. B.5(a–c) by dashed lines. As seen from Fig. B.5, the only deviation of the experimentally measured radiation patterns from the calculated ones consists in a nonmonotonous be-

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havior of the amplitude of dynamic magnetization in the direction along the rays. For example, for the simplest case of two rays (see Figs. B.5(a, e)) instead of a monotonous decrease of the amplitude along the rays when moving away from the radiating area a local increase is observed at a certain distance. This fact might be connected with an additional interference caused by the twodimensionality of the real radiating rectangle and an influence of the magnetic dissipation. In contrast to the radiation patterns of the first three eigenmodes, the pattern corresponding to the fourth mode (Fig. B.5(d)) cannot be understood in the framework of the model used. Such a transformation in the radiation behavior for higher order eigenmodes characterized by a large wavenumber k of radiated spinwaves can be associated with a modification of their dispersion characteristics due to the increasing contribution of the exchange interaction, which is not taken into account in the Damon-Eshbach theory.

B.4 Conclusion The magnetization dynamics of a single micrometer-sized magnetic element has been investigated using micro-focus Brillouin light scattering. Spin valve as well as tunnel junction multilayers with top and bottom contact electrodes were fabricated. For the top electrode, a special two-step lithography process was developed to obtain the desired feature size with the available direct write laser lithography system. The experimental results showed that, due to the spatial confinement of spinwaves in the magnetic element, radiation of spinwaves into the surrounding magnetic film occurs at discrete frequencies corresponding to the frequencies of quantized spinwave modes of the element. It was found, that the resulting two-dimensional radiation patterns consist of several interfering rays forming spots where the intensity of dynamic magnetization locally increases. The exact radiation pattern depends on the order of the radiating eigenmode. The main result, discrete radiation of spinwaves into the surrounding film, might serve to better understand parasitic dynamic coupling in arrays of magnetic memory elements.

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Publication List Journal Papers • C. König, G. Güntherodt, M. Fonin, M. Laufenberg, A. Biehler, W. Bührer, M. Kläui, and U. Rüdiger, Micromagnetism and Magnetotransport of MicronSized Expitaxial CrO2 (100) Wires, in preparation • M. Kläui, P. Dagras, M. Laufenberg, L. Vila, G. Faini, C. A. F. Vaz, J. A. C. Bland, and U. Rüdiger, The influence of thermal excitations and the intrinsic

dependence of the spin torque effect in current induced domain wall motion, submitted to J. Phys. D: Appl. Phys. • M. Laufenberg, W. Bührer, D. Bedau, P.-E. Melchy, M. Kläui, L. Vila, G. Faini, C. A. F. Vaz, J. A. C. Bland, and U. Rüdiger, Temperature Depen-

dence of the Spin Torque Effect in Current-induced Domain Wall Motion, Phys. Rev. Lett. 97, 046602 (2006). • M. Kläui, M. Laufenberg, L. Heyne, D. Backes, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, L. J. Heyderman, S. Cherifi, A. Locatelli, T. O. Mentes, and L. Aballe, Current-induced Vortex Nucleation and Annihilation in Vortex Domain Walls, Appl. Phys. Lett. 88, 232507 (2006). • M. Laufenberg, D. Bedau, H. Ehrke, M. Kläui, U. Rüdiger, D. Backes, L. J. Heyderman, F. Nolting, C. A. F. Vaz, J. A. C. Bland, T. Kasama, R. E. Dunin-

Borkowski, S. Cherifi, A. Locatelli, and S. Heun, Quantitative Determination of Domain Wall Coupling Energetics, Appl. Phys. Lett. 88, 212510 (2006). • M. Laufenberg, D. Backes, W. Bührer, D. Bedau, M. Kläui, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, L. J. Heyderman, F. Nolting, S. Cherifi, A. Lo-

catelli, R. Belkhou, S. Heun, and E. Bauer, Observation of Thermally Activated Domain Wall Transformations, Appl. Phys. Lett. 88, 052507 (2006).

PUBLICATION LIST

193

• M. Fraune, J. O. Hauch, G. Güntherodt, M. Laufenberg, M. Fonin, U. Rüdiger, J. Mayer, and P. Turban, Structure-induced Magnetic Anisotropy in the

Fe(110)/Mo(110)/Al2 O3 (11-20) System, J. Appl. Phys. 99, 033904 (2006). [Work performed in frame of diploma thesis at RWTH Aachen] • V. E. Demidov, S. O. Demokritov, B. Hillebrands, M. Laufenberg, and P. P. Freitas, Two-dimensional Patterns of Spin-wave Radiation by Rectangular Spin-

valve Elements, J. Appl. Phys. 97, 10A717 (2005). [Work performed at INESC-MN Lisbon and TU Kaiserslautern] • V. E. Demidov, S. O. Demokritov, B. Hillebrands, M. Laufenberg, and P. P. Freitas, Radiation of Spin Waves by a Single Micrometer-sized Magnetic Ele-

ment, Appl. Phys. Lett. 85, 2866-2868 (2004). [Work performed at INESCMN Lisbon and TU Kaiserslautern]

Review Article • M. Laufenberg, M. Kläui, D. Backes, W. Bührer, H. Ehrke, D. Bedau, U. Rüdiger, F. Nolting, S. Cherifi, A. Locatelli, R. Belkhou, S. Heun, C. A. F.

Vaz, J. A. C. Bland, L. J. Heyderman, T. Kasama, R. E. Dunin-Borkowski, A. Pavlovska, and E. Bauer, Domain Wall Spin Structures in 3d Metal Ferromagnetic Nanostructures, appears in Adv. Solid State Phys.

Conference Contributions • M. Laufenberg, D. Backes, W. Bührer, D. Bedau, L. Heyne, P.-E. Melchy,

M. Kläui, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, L. J. Heyderman,

F. Nolting, S. Cherifi, A. Locatelli, T. O. Mentes, L. Aballe, L. Vila, and G. Faini, Current-assisted Domain Wall Propagation at Variable Temperatures, DPG-Frühjahrstagung 2006 Dresden, Poster contribution. • D. Bedau, M. Laufenberg, M. Kläui, D. Backes, W. Bührer, A. Biehler, C. Hartung, M. Fonin, U. Rüdiger, F. Nolting, L. J. Heyderman, G. Faini,

L. Vila, E. Cambril, C. A. F. Vaz, J. A. C. Bland, H. Ehrke, T. Kasama, R. E. Dunin-Borkowski, E. Bauer, S. Cherifi, A. Locatelli, R. Belkhou, and S. Heun, Geometrically Confined Domain Walls, DPG-Frühjahrstagung 2006 Dresden, Poster contribution.

PUBLICATION LIST

194

• M. Laufenberg, D. Bedau, D. Backes, W. Bührer, M. Kläui, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, L. J. Heyderman, F. Nolting, S. Cherifi, A. Lo-

catelli, S. Heun, G. Faini, and E. Cambril, Domain Wall Spin Structure, Depinning and Dynamics in Ferromagnetic Nanostructures at Variable Temperature, 364. WE-Heraeus-Seminar "Nanoscale Magnets – Top down Meets Bottom up" Bad Honnef, 2006, Poster contribution. • M. Laufenberg, M. Kläui, H. Ehrke, C. A. F. Vaz, J. A. C. Bland, L. J. Heyderman, F. Nolting, E. Bauer, S. Cherifi, S. Heun, A. Locatelli, R. E. Dunin-

Borkowski, and U. Rüdiger, Geometry-dependent Head-to-head Domain Wall Phase Diagram and Domain Wall Widths in Ferromagnetic Ring Structures, INTERMAG ASIA 2005 Nagoya: Digests of the IEEE International Magnetics Conference, 460 (2005). • U. Rüdiger, M. Laufenberg, C. A. F. Vaz, J. A. C. Bland, L. J. Heyderman, F. Nolting, S. Cherifi, S. Heun, A Locatelli, and E. Bauer, Geometry-

Dependent Head-to-Head Domain Wall Phase Diagram and Wall Widths in Ferromagnetic Ring Structures, ICMAT 2005 Singapore, Poster contribution. • M. Laufenberg, D. Backes, D. Bedau, H. Ehrke, M. Kläui, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, L. J. Heyderman, F. Nolting, E. Bauer, S. Cherifi,

S. Heun, A. Locatelli, T. Kasama, and R. E. Dunin-Borkowski, Spin Structure of Domain Walls in Ferromagnetic Ring Magnets, DPG-Frühjahrstagung 2005 Berlin, Poster contribution. • M. Kläui, M. Laufenberg, C. A. F. Vaz, J. A. C. Bland, L. J. Heyderman, F. Nolting, E. Bauer, S. Cherifi, S. Heun, A. Locatelli, and U. Rüdiger, Geometry-dependent Head-to-head Domain Wall Phase Diagram and Domain Wall Widths in Ferromagnetic Ring Structures, 338. WE-Heraeus-Seminar "Nanomagnetism: New Insights with Synchrotron Radiation" Bad Honnef, 2005, Poster contribution.

Acknowledgement / Danksagung Many people have supported this work in many different ways and I would like to express my most sincere thanks to all these people here. Viele Menschen haben zum Gelingen dieser Arbeit auf unterschiedlichste Weise beigetragen, bei denen ich mich bedanken möchte. • Prof. Ulrich Rüdiger danke ich für die Möglichkeit, diese interessante Doktorarbeit an seinem Lehrstuhl in Konstanz in der "Startmannschaft"

durchzuführen, und für sein offenes Ohr bei Erfolgen wie Problemen. Ebenso danke ich für seine Unterstützung meines vorangehenden Aufenthalts in Lissabon, der sich unmittelbar an die von ihm betreute Diplomarbeit in Aachen anschloss. • Prof. Günter Schatz danke ich für die Übernahme des Zweitgutachtens. • Dr. Mathias Kläui danke ich für seine intensive Betreuung dieser Arbeit, für die vielen Diskussionen (insbesondere während der zahleichen "Iterationsschritte" beim Schreiben der Publikationen), für die Möglichkeit, an vielen interessanten, erfolgreichen und anstrengenden Messzeiten an der SLS und Elettra zu partizipieren, sowie für seine hilfreichen Kontakte zu Kollegen in Cambridge (UK), Marcoussis (F), Villigen (CH), Trieste (I) und Grenoble (F), von denen ich erheblich profitieren konnte. Die Zusammenarbeit mit ihm war in jeder Sicht herausfordernd. Sowohl fachlich als auch persönlich habe ich dabei viel gelernt, das mir über die Promotion hinaus von Nutzen sein wird. • Wolfgang Bührer danke ich für seine exzellente Diplomarbeit, die auch

das Vorankommen meiner Arbeit unterstützt hat, für seine permanenten Anstrengungen, kleine und große Probleme am Messaufbau zu lösen, und für die problemlose und sehr angenehme Zusammenarbeit im Labor.

• Daniel Bedau als unmittelbarem Doktoranden-Leidensgenossen und di-

rektem Nachbarn im Transportlabor danke ich für zahlreiche wertvolle

Tips und konkrete experimentelle Hilfe insbesondere in ungezählten elektronischen und messtechnischen Fragen.

196 • Erwin Biegger, Stephen Krzyk, Lukas Emele und Jörn Klinger danke ich für die sehr angenehme und lustige Arbeitsatmosphäre im Büro.

• Henri Ehrke und Christian Resch danke ich für ihre Hilfe beim experimentellen Aufbau in Konstanz, Henri Ehrke außerdem für exzellente Holographie-Daten während seines Praxissemesters in Cambridge. • Christine Hartung danke ich für ihre Arbeit an den Fe 3 O4 -Proben, für hervorragende MFM-Bilder und interessante mikromagnetische Simula-

tionen dazu, die sie in ihrer Diplomarbeit angefertigt hat. • Alexander Biehler danke ich für die Zusammenarbeit bei den Ex-

perimenten zur strominduzierten Domänenwandverschiebung als dem

zuständigen Experten am MFM und für seine Hilfe bei den AFMMessungen. • Manfred Keil danke ich für seine technische Hilfe beim Aufbau des Experiments im Labor. Friederike Stuckenbrock danke ich für ihre effiziente Hilfe in allen administrativen Fragen. • Den Mitarbeitern der wissenschaftlichen Werkstätten, in der Feinmechanik namentlich Herrn Seeburger, Herrn Jauch und Herrn Weiland,

danke ich für ihre schnelle und sehr gute Arbeit insbesondere bei Modifikation und Nachbau der PEEM-Probenhalter. Dieses Lob lässt sich leider nicht uneingeschränkt auf die elektronischen Werkstätten übertragen, wo die Zusammenarbeit oft von Problemen geprägt war. • Für den hervorragenden und effizienten Support im Vorfeld und während der zahlreichen Strahlzeiten an der SLS danke ich Dr. Frithjof Nolting.

• Für die gute Zusammenarbeit und Arbeitsatmosphäre in Tag- und Nachtschichten an der SLS danke ich allen voran Dirk Backes, Dr. Mikhail

Fonin und Dr. Mathias Kläui, ebenso Daniel Bedau, Wolfgang Bührer, Christine Hartung, Alexander Biehler und Sönke Voss. • The very intensive beamtimes of typically 6 × 24 h at Elettra would not

have been so interesting and successful without the excellent support

of Dr. Salia Cherifi from the Laboratoire Louis Neél in Grenoble, of the Nanospectroscopy beamline team with Dr. Andrea Locatelli, Dr. Tefik

197 Onur Mentes, Dr. Lucia Aballe, Dr. Stefan Heun, and Dr. Rachid Belkhou, and of Prof. Ernst Bauer from the Arizona State University. • I would like to express my thanks for the very good cooperation during the Elettra beamtimes to Dr. Carlos Vaz, Dr. Mathias Kläui, Dirk Backes,

and Lutz Heyne. • I gratefully acknowledge the support of many people involved in the

preparation of excellent samples: Dirk Backes and Dr. Laura Heyderman

at the PSI in Villigen (CH), Dr. Carlos Vaz at the Cavendish Laboratory in Cambridge (UK), Dr. Laurent Vila and Edmond Cambril at the LPN-CNRS in Marcoussis (F), Dr. Christian König at the RWTH Aachen, as well as Christine Hartung, Dr. Mikhail Fonin, and Dr. Mathias Kläui in Konstanz. • Bei allen ehemaligen und aktuellen Mitgliedern des Lehrstuhls, na-

mentlich Daniel Bedau, Erwin Biegger, Alexander Biehler, Wolfgang

Bührer, Michael Burgert, Pascal Dagras, Lukas Emele, Henri Ehrke, Dr. Mikhail Fonin, Christine Hartung, Lutz Heyne, Manfred Keil, Christine Kircher, Dr. Mathias Kläui, Jörn Klinger, Stephen Krzyk, Sebastian Lohss, Pierre-Eric Melchy, Dr. Thomas Moore, Christian Resch, Mathias Schnepf, Lorenz Staeheli, Friederike Stuckenbrock und Sönke Voss, möchte ich mich recht herzlich für Hilfe und Unterstützung in allen Situationen bedanken, die ich hier nicht besonders erwähnen konnte. • During my time at INESC-MN, I learned about different sample prepara-

tion and characterization techniques in the very stimulating atmosphere

of the group of Prof. Paulo Freitas. I would like to thank all members of the group for the support during a very enjoyable time in Lisbon, in particular Teresa Adrega, José Bernardo, Natércia Correia, Ricardo Ferreira, Prof. Paulo Freitas, Dr. Susana Freitas, Dr. João Gaspar, Dr. Marc Rickart, Fernando Silva, and Guandong Zhang – some of them also for unforgettable times outside the lab. I would like to thank the AG Magnetismus in Kaiserslautern for their hospitality, in particular Dr. Vladislav Demidov, Prof. Sergej Demokritov, and Prof. Burkard Hillebrands. • Als letzter und wichtigster Person möchte ich schließlich meiner lieben

Frau Magdalena für den Zuspruch und die Unterstützung danken, die die Grundlage für den erfolgreichen Abschluss dieser Arbeit waren.