tion of domain chains, and the moving chain ends can be pinned when they meet ...... where it is assumed that the magnetization is uniform with a magni- tude equal to ...... To form a resist layer of constant thickness on top of a substrate, a spin-coater .... ular (e.g. block-copolymers) and colloidal systems [KSS+03]. Its striking.
Spin Structure of DomainWalls and Their Behaviour in Applied Fields and Currents
DISSERTATION ZUR ERLANGUNG DES AKADEMISCHEN GRADES DES DOKTORS DER NATURWISSENSCHAFTEN AN DER UNIVERSITÄT KONSTANZ MATHEMATISCH-NATURWISSENSCHAFTLICHE SEKTION FACHBEREICH PHYSIK VORGELEGT VON DIRK BACKES
TAG DER MÜNDLICHEN PRÜFUNG: 8. FEBRUAR 2008 REFERENTEN: PROF. DR. ULRICH RÜDIGER PROF. DR. JENS GOBRECHT Konstanzer Online-Publikations-System (KOPS) URL: http://www.ub.uni-konstanz.de/kops/volltexte/2008/5214/ URN: http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-52141
Summary In this thesis, the spin structure of domain walls in confined magnetic elements was determined and the behaviour of domain walls on the application of external magnetic fields and current pulse injection was observed. For this, magnetic elements of various shapes, materials, and substrates were prepared which were each dedicated to the purpose of the experiment. Different fabrication techniques were described, including several patterning processes and contacting of magnetic elements for current-pulse experiments. The spin structure of transverse walls in constrictions down to 30 nm in permalloy wavy lines was measured using electron holography. It is known that the domain wall spin structure influences both the magnetoresistance and spin transfer torque effects. For the transverse walls, three different types were determined and the domain wall width was found to decrease faster than linearly with decreasing constriction width. The magnetic fields needed to depin the domain walls from such constrictions were measured using magnetoresistance measurements and were directly related to the domain wall spin structure. While an approach was made to image the spin structure of patterned thin films of the halfmetal CrO2 coupled to a permalloy thin film using photoemission electron microscopy (PEEM), a complicated coupling mechanism between the two layers was observed. The spin structure of an array of crossed wires corresponding to an array of holes (antidots) in a cobalt thin film was investigated to understand the switching behaviour on the application of an external magnetic field. It was found that switching occurs by the nucleation and propaga-
ii tion of domain chains, and the moving chain ends can be pinned when they meet the ends of perpendicular domain chains or are blocked due to the formation of a 360◦ domain wall when they approach a perpendicular domain chain. The current-induced domain wall motion in contacted permalloy wires on membrane samples was studied using electron holography. Effects due to the spin torque were separated from heating effects on the domain wall due to the current. A variety of effects such as domain wall transformations, domain wall jumping between two pinning sites, or structural changes of the magnetic material crystallites due to the combined influence of current pulses and heating was observed. A set of indicators was derived to distinguish current-induced domain wall motion due to the spin torque from the heating effects.
Zusammenfassung In dieser Arbeit wurde die Spinstruktur von Domänenwänden in magnetischen Nanostrukturen und das Verhalten dieser Domänenwände unter dem Einfluß von magnetischen Feldern und elektrischen Strompulsen untersucht. Dazu waren magnetische Nanostrukturen nötig, die sich in Geometrie, Material, und verwendetem Substrat unterschieden, und die dem jeweiligen Zweck des Experiments angepaßt waren. Verschiedene Herstellungsmethoden wurden aufgeführt und einige Strukturierungsprozesse vollständig beschrieben. Die Spinstruktur von transversen Domänenwänden in Konstriktionen, die sich in Permalloy-Drähten befanden und die bis auf 30 nm verkleinert werden konnten, wurde mittels Elektronenholografie gemessen. Es ist bekannt, daß die Spinstruktur der Domänenwand den Magnetowiderstand und auch den Spin-Torque-Effekt beeinflußt. Es wurden 3 verschiedene Typen transverser Wände gefunden, deren Domänenwandbreite schneller als linear mit der Konstriktionsbreite fiel. Durch Magnetowiderstandsmessungen wurden die magnetischen Felder bestimmt, die nötig waren, um die Domänenwände von den Konstriktionen wegzubewegen, und die Stärke dieses Feldes wurde mit der Spinstruktur in Verbindung gebracht. Es wurde versucht, die Spinstruktur von strukturierten dünnen Filmen aus dem Halbmetall CrO2 mit Photoemissionselektronenmikroskopie (PEEM) abzubilden. Bei diesem Versuch wurde ein komplizierter Kopplungsmechanismus zwischen dem CrO2 -Film und einer darauf deponierten dünnen Schicht Permalloy beobachtet. Die Spinstruktur von einem dünnen Cobalt-Film mit einem Lochmus-
iv ter (Antidot) wurde abgebildet, um das Umklappverhalten in einem externen magnetischen Feld zu verstehen. Dabei stellte sich heraus, daß das Umklappen durch Nukleation und Propagation von Domänenketten erfolgt. Diese sich bewegenden Domänenketten können gepinnt werden, wenn sie auf die Enden von senkrecht dazu laufende Domänenketten treffen, oder geblockt werden, indem sie mit senkrecht dazu laufenden Domänenketten eine 360◦ Domänenwand bilden. Permalloy-Drähte wurden auf Membranproben aufgebracht und kontaktiert, um strom-induzierte Domänenwandpropagation mittels Elektronenholografie zu beobachten. Spin-Torque-Effekte wurden von Effekten aufgrund thermischer Anregung unterschieden. Eine Reihe von Effekten wie Domänenwandtransformation, Domänenwandsprünge zwischen 2 Pinningzentren und sogar strukturelle Änderung der magnetischen Kristallite können durch die thermische Anregung durch den Strom ausgelöst werden. Indikatoren wurden abgeleitet, damit zwischen strominduzierter Domänenwandpropagation, die auf den Spin-TorqueEffekt zurückzuführen sind, und Effekten aufgrund thermischer Anregung unterschieden werden kann.
Contents Summary / Zusammenfassung
i
List of Figures
xi
List of Acronyms
xii
Introduction
1
1
Theory
4
1.1
Microscopic Origins of Ferromagnetism . . . . . . . . . . .
5
1.1.1
Exchange Interaction . . . . . . . . . . . . . . . . . .
5
1.1.2
Localized Model and Mean Field Approximation .
6
1.1.3
Band Model of Ferromagnetism . . . . . . . . . . .
6
Micromagnetic Systems . . . . . . . . . . . . . . . . . . . .
9
1.2.1
Thermodynamics in Magnetism . . . . . . . . . . .
9
1.2.2
Energy Contributions . . . . . . . . . . . . . . . . .
10
1.2.3
Brown´s Equations and the Effective Field . . . . .
13
1.2
1.3
1.4
Magnetization Dynamics
. . . . . . . . . . . . . . . . . . .
15
1.3.1
Landau-Lifshitz-Gilbert Equation . . . . . . . . . .
15
1.3.2
Micromagnetic Simulations . . . . . . . . . . . . . .
17
Spin Transfer Torque Model . . . . . . . . . . . . . . . . . .
18
1.4.1
Spin Transfer Torque . . . . . . . . . . . . . . . . . .
19
1.4.2
Landau-Lifshitz-Gilbert Equation with Spin Transfer Torque . . . . . . . . . . . . . . . . . . . . . . . .
20
1.4.3
Adiabatic and Non-adiabatic Spin Torque
. . . . .
21
1.4.4
Domain Wall Spin Structure Modifications . . . . .
24
CONTENTS 1.5
Anisotropic Magnetoresistance (AMR) . . . . . . . . . . . . 1.5.1
2
25
AMR Contribution to the Domain Wall Magnetoresistance . . . . . . . . . . . . . . . . . . . . . . . . . .
27
1.6
Halfmetallic Ferromagnets . . . . . . . . . . . . . . . . . . .
28
1.7
RKKY Coupling . . . . . . . . . . . . . . . . . . . . . . . . .
30
Fabrication
31
2.1
Patterning the Resist . . . . . . . . . . . . . . . . . . . . . .
31
2.1.1
Electron Beam Writer . . . . . . . . . . . . . . . . . .
32
2.1.2
Resist Technology . . . . . . . . . . . . . . . . . . . .
35
2.1.3
Photolithography . . . . . . . . . . . . . . . . . . . .
38
2.1.4
X-ray Interference Lithography . . . . . . . . . . . .
39
Pattern Transfer Methods . . . . . . . . . . . . . . . . . . .
40
2.2.1
Deposition . . . . . . . . . . . . . . . . . . . . . . . .
40
2.2.2
Properties of Films and Nanostructures . . . . . . .
44
2.2.3
Lift-off . . . . . . . . . . . . . . . . . . . . . . . . . .
46
2.2.4
Etching . . . . . . . . . . . . . . . . . . . . . . . . . .
48
2.2
2.3
3
vi
Fabrication of Magnetic Structures and Devices . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
2.3.1
Ferromagnetic Rings . . . . . . . . . . . . . . . . . .
50
2.3.2
Wavy Lines with Constrictions . . . . . . . . . . . .
50
2.3.3
Rings on Striplines . . . . . . . . . . . . . . . . . . .
52
2.3.4
Contacted Zigzag Lines . . . . . . . . . . . . . . . .
53
2.3.5
Contacted Notched Rings with Antenna . . . . . . .
57
2.3.6
Patterning Techniques for Epitaxial Films . . . . . .
61
Measurement Techniques
66
3.1
XMCD-PEEM . . . . . . . . . . . . . . . . . . . . . . . . . .
67
3.1.1
X-ray Magnetic Circular Dichroism . . . . . . . . .
67
3.1.2
Photoemission Electron Microscopy (PEEM) . . . .
68
3.2
Lorentz Microscopy . . . . . . . . . . . . . . . . . . . . . . .
70
3.3
Electron Holography . . . . . . . . . . . . . . . . . . . . . .
71
3.4
Kerr Microscopy . . . . . . . . . . . . . . . . . . . . . . . . .
74
CONTENTS 3.5 4
Magnetoresistance Measurements . . . . . . . . . . . . . .
76
Domain Walls in Confined Systems
78
4.1
Introduction to Domain Walls . . . . . . . . . . . . . . . . .
80
4.2
Transverse Domain Walls in
4.3
4.4
5
vii
Nanoconstrictions . . . . . . . . . . . . . . . . . . . . . . . .
83
4.2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . .
83
4.2.2
Domain Wall Types . . . . . . . . . . . . . . . . . . .
84
4.2.3
Domain Wall Type Distribution . . . . . . . . . . . .
91
4.2.4
Domain Wall Width . . . . . . . . . . . . . . . . . .
92
4.2.5
Comparison with Heisenberg Simulation . . . . . .
94
4.2.6
Conclusion . . . . . . . . . . . . . . . . . . . . . . .
97
Pinning of Domain Walls . . . . . . . . . . . . . . . . . . . .
98
4.3.1
Introduction
. . . . . . . . . . . . . . . . . . . . . .
98
4.3.2
Magnetoresistance Measurement . . . . . . . . . . .
99
4.3.3
Spin Structure of Domain Walls . . . . . . . . . . . . 101
4.3.4
Simulations . . . . . . . . . . . . . . . . . . . . . . . 103
4.3.5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . 105
Spin Structure of CrO2 . . . . . . . . . . . . . . . . . . . . . 106 4.4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . 106
4.4.2
Imaging of a Single Layer of CrO2 . . . . . . . . . . 106
4.4.3
Indirect Imaging using a Py layer . . . . . . . . . . . 108
4.4.4
Conclusions . . . . . . . . . . . . . . . . . . . . . . . 113
Antidots
115
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.2
Experimental details . . . . . . . . . . . . . . . . . . . . . . 116
5.3
Magnetization reversal . . . . . . . . . . . . . . . . . . . . . 118
5.4
Magnetic spin configurations . . . . . . . . . . . . . . . . . 124
5.5
Detailed reversal mechanism . . . . . . . . . . . . . . . . . 125
5.6
Size dependence of reversal . . . . . . . . . . . . . . . . . . 129
5.7
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
CONTENTS
viii
6
132
7
Effect of Current and Heating on Domain Walls 6.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.2
Temperature Effect on Spin Structure . . . . . . . . . . . . . 133
6.3
Current-induced Heating . . . . . . . . . . . . . . . . . . . 135 6.3.1
Transformation of the Spin Structure
. . . . . . . . 136
6.3.2
Domain Wall Motion due to Heating . . . . . . . . . 137
6.3.3
Vortex Annihilation . . . . . . . . . . . . . . . . . . 138
6.3.4
Structural Changes by Heating . . . . . . . . . . . . 139
6.4
Heat Conductance Improvement . . . . . . . . . . . . . . . 141
6.5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Conclusions
145
Bibliography
149
Publication List
167
Acknowledgement
172
List of Figures 1.1
Sketch of the band model . . . . . . . . . . . . . . . . . . .
8
1.2
AMR contribution of a domain wall . . . . . . . . . . . . .
27
1.3
Spin-dependent density of states for a 3d-ferromagnet and for a halfmetallic ferromagnet . . . . . . . . . . . . . . . . .
28
2.1
Scheme of the column of the electron beam writer . . . . .
32
2.2
Scheme of Bézier curves . . . . . . . . . . . . . . . . . . . .
35
2.3
Overview over exposure methods of photolithography . .
38
2.4
Scheme of x-ray interference lithography . . . . . . . . . .
39
2.5
Scheme of the DC magnetron sputtering facility . . . . . .
41
2.6
Scheme of a UHV system used for MBE growth . . . . . .
43
2.7
Scheme of a CVD setup
. . . . . . . . . . . . . . . . . . . .
44
2.8
Sample holder for membrane lift-off . . . . . . . . . . . . .
46
2.9
Scheme of pattern writing and lift-off . . . . . . . . . . . .
49
2.10 SEM images of a wavy line with notch forming a constriction 51 2.11 SEM images of a gold waveguide with permalloy elements
52
2.12 SEM images of contacted zig zag lines on silicon substrates
54
2.13 Contacted zig zag lines on membrane substrates . . . . . .
56
2.14 Scheme of the evaporation of gold contacts on the edges of the membrane . . . . . . . . . . . . . . . . . . . . . . . . . .
57
2.15 Scheme of a contacted notched ring with antenna . . . . .
58
2.16 Scheme of the overlay procedure using the GLOKOS routine 59 2.17 SEM image of a contacted notched ring with antenna . . .
61
2.18 Overview of dry etching techniques for patterning epitaxial films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
LIST OF FIGURES
x
2.19 SEM images of Fe3 O4 rings and wires . . . . . . . . . . . . 3.1
64
Illustration of the X-ray magnetic circular dichroism (XMCD) effect . . . . . . . . . . . . . . . . . . . . . . . . . .
67
3.2
Scheme of a photoemission electron microscope (PEEM) .
68
3.3
Scheme of Lorentz microscopy techniques . . . . . . . . . .
70
3.4
Scheme of electron holography . . . . . . . . . . . . . . . .
72
3.5
Magnetic induction map of three-quarter rings . . . . . . .
74
3.6
Scheme of different MOKE effects . . . . . . . . . . . . . . .
75
3.7
Scheme of a Kerr microscope . . . . . . . . . . . . . . . . .
76
3.8
Scheme of a setup for pulse injection and resistance measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
4.1
Scheme of a Bloch and a Néel wall . . . . . . . . . . . . . .
80
4.2
PEEM images and simulations of vortex and transverse walls 81
4.3
Scheme of a constriction formed by a notch . . . . . . . . .
4.4
Magnetic induction maps showing three transverse wall
84
types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
4.5
Line profiles through a constriction
. . . . . . . . . . . . .
87
4.6
Illustration of the fixed threshold method . . . . . . . . . .
89
4.7
Shape reconstruction from the threshold positions . . . . .
90
4.8
Distribution of transverse wall types . . . . . . . . . . . . .
91
4.9
Dependence of the domain wall width on the ring width .
92
4.10 Dependence of domain wall angle and width on constriction width . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94
4.11 Heisenberg simulations of the spin structure in constrictions 96 4.12 SEM image of a wavy line with a notch . . . . . . . . . . .
99
4.13 Dependence of depinning fields on constriction width . . . 100 4.14 Direct imaging of spin structures around notches . . . . . . 102 4.15 Energy potential around a notch forming a constriction . . 103 4.16 XAS and XMCD spectra of a CrO2 film . . . . . . . . . . . . 107 4.17 Remanent magnetization in a patterned CrO2 /Py film after saturation in easy axis direction
. . . . . . . . . . . . . 108
LIST OF FIGURES
xi
4.18 Remanent magnetization after saturation in hard axis direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.19 Scheme of a CrO2 wire . . . . . . . . . . . . . . . . . . . . . 111 4.20 An exeption for the observed remanent magnetization . . 112 5.1
Scheme of the antidot geometry . . . . . . . . . . . . . . . . 116
5.2
Hysteresis loops
5.3
XMCD images of domain chains . . . . . . . . . . . . . . . 118
5.4
Magnetization reversal via domain chains . . . . . . . . . . 120
5.5
Magnetization reversal with perpendicular magnetic sen-
. . . . . . . . . . . . . . . . . . . . . . . . 117
sitivity direction . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.6
Simulations of the magnetization reversal . . . . . . . . . . 122
5.7
XMCD images showing the locations of ends of orthogonal domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.8
Antidot configurations surrounding an antidot . . . . . . . 124
5.9
Snapshot of the development of spins . . . . . . . . . . . . 126
5.10 Details of the micromagnetic simulations . . . . . . . . . . 128 6.1
Spin structure during heating . . . . . . . . . . . . . . . . . 134
6.2
Multivortex walls . . . . . . . . . . . . . . . . . . . . . . . . 136
6.3
Vortex annihilation . . . . . . . . . . . . . . . . . . . . . . . 139
6.4
Structural changes by heating . . . . . . . . . . . . . . . . . 140
6.5
Current-induced domain wall motion in a Py wire . . . . . 141
List of Acronyms AMR
Anisotropic magnetoresistance
CIDM
Current-induced domain wall motion
CVD
Chemical vapor deposition
DOS
Density of states
DWMR
Domain wall magnetoresistance
fcc
face-centered cubic (crystal structure)
GMR
Giant magnetoresistance
hcp
hexagonal close packed (crystal structure)
LEED
Low energy electron diffraction
LLG
Landau-Lifshitz-Gilbert (equation)
MBE
Molecular beam epitaxy (system)
MOKE
Magnetic-optical Kerr effect
MR
Magnetoresistance
MRAM
Magnetic random access memory
PEEM
Photoemission electron microscopy / microscope
PMMA
Polymethyl methacrylate
RHEED
Reflection high energy electron diffraction
SEM
Scanning electron microscopy / microscope
SLS
Swiss Light Source
TEM
Transmission electron microscopy / microscope
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
Introduction Research into magnetic nanostructures became prominent when the techniques for the fabrication of sub-1 µm magnetic elements became available and the spin structure in the resulting magnetic nanostructures could be investigated using high-resolution measurement techniques. The influence of the geometry on the spin structure in confined magnetic systems gives rise to physical effects which have not been observed before. In summary, the aims of this thesis are: • Developing and optimizing patterning processes to provide magnetic elements. • Imaging of the spin structure in such magnetic elements with the focus on domain walls and their spin structure. • Investigating the behaviour of magnetic domain walls in applied magnetic fields or currents. To reach these aims, the following investigations are carried out: The spin structure of domain walls and the influence of an applied magnetic field is studied (chapter 4). First the question is addressed of what happens with the spin structure of head-to-head domain walls if the dimensions are reduced. The theory predicts new domain wall types and a reduction of the domain wall width. For smaller walls a more efficient spin-torque and higher magnetoresistance effects are expected. Here, the spin structure of domain walls found in constrictions down to 30 nm is investigated and the domain wall types found are compared with the
Introduction
2
theoretical predictions (section 4.2). It is determined whether the size reduction of the constriction influences the width of the domain wall and the dependency of domain wall width on the constriction width is determined. In order to build devices the domain wall propagation either induced by fields or currents must be controlled. One possibility is to introduce artificial pinning sites, for example, creating notches which form a constriction in a magnetic nanowire. By applying a magnetic field and measuring the position of the domain wall with the magnetoresistance effect, the strength of the field required to depin the domain wall from the constriction is determined (section 4.3). This depinning field can be directly related to the spin structure of the domain wall and the energy landscape around the constriction can be determined. There is currently a search for materials which give an improved spintorque efficiency, i.e. faster domain wall movement and lower critical current densities. CrO2 is an example of a high spin-polarized material which is predicted to improve the spin-torque efficiency. An attempt is made here to image the spin structure of a patterned film of CrO2 (section 4.4). The goal is to find domain walls and to measure their spin structure which would allow to study the interaction with applied currents. In addition to constrictions, the influence of the existing spin structure can serve as pinning sites for domain walls. To study such effects, the spin structures in an array of crossed ferromagnetic wires, which is equivalent to an array of holes (or antidot array) in a ferromagnetic film, are investigated (chapter 5). The influence of the holes, formed by the crossed wires, on the spin-configuration around the holes is determined and the switching of the magnetization of the antidot array on the application of an external magnetic field is investigated. It is found that the switching occurs by the nucleation and propagation of domain chains. These moving domain chains ends can be pinned at the ends of perpendicular domain chains or the movement blocked due to the formation of a 360◦ domain wall when the chain ends approach a perpendicular domain
Introduction
3
chain. Finally, the behaviour of domain walls in permalloy nanowires is investigated on the application of current-pulses. Here the goal is to separate the so-called spin torque effect due to spin-polarized currents from Ohmic heating due to the current pulse (chapter 6).
Chapter 1 Theory This chapter presents the theoretical background relevant for the physics and results presented in this thesis. In section 1.1, the microscopic origins of magnetism are briefly discussed, including the exchange interaction and localized as well as delocalized electron contributions to ferromagnetism. In section 1.2, these microscopic approaches are then complemented by a phenomenological view using thermodynamic potentials and macroscopic variables like magnetization and magnetic fields. This allows one to establish a straightforward relation to experiments, where only these macroscopic quantities are available. In section 1.3, the micromagnetic simulations, which are frequently used today in magnetism research and which are based on this approach, are briefly described. In section 1.4, the spin transfer torque theory is discussed. This theory includes the introduction of 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. In section 1.5, the anisotropic magnetoresistance effect in magnetic materials is treated. The material class of halfmetallic ferromagnets with the two prominent members Fe3 O4 and CrO2 is introduced in section 1.6 and the property of theoretically 100% spin polarization in these systems is discussed. Finally, coupling by RKKY interchange is presented in section 1.7.
Theory
1.1
5
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.
1.1.1
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.
Theory
1.1.2
6
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
Jij σ ˆi · σ ˆj .
(1.2)
i,j
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 σ ˆi and the expectation value hˆ σi i of the spin operator of the interacting neighbors. The according mean-field can be written as P BMF = gµ1B j Jij hˆ σi i . Assuming an external magnetic field B0 , the Heisenberg Hamiltonian in the mean-field approximation is obtained in the form [IL99] ˆ = −gµB H
X
σ ˆi · (BMF + B0 ).
(1.3)
i
1.1.3
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 O + Vσ (r) φkσ (r)) = Ekσ φkσ (r), − 2me
(1.4)
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]
Theory
7
E↑ (k) = E(k) − I
N↑ N
(1.5)
N↓ (1.6) N Here, E(k) are the energy values of a non-magnetic one-electron band E↓ (k) = E(k) − I
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 N↑ − N↓ , (1.7) N which is proportional to the magnetization, and by introducing R=
N↑ + N↓ ˜ E(k) = E(k) − I 2N for convenience, we obtain
(1.8)
1 ˜ E↑ (k) = E(k) − IR 2
(1.9)
1 ˜ E↓ (k) = E(k) + IR. (1.10) 2 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)
1X (fk↑ (R) − fk↓ (R)) N k
(1.12)
f (Ekσ ) = exp
Ekσ −µ kB T
+1
the self-consistency condition R=
must be fulfilled. By inserting the above equations, this can be written as
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.
R=
1
1X N
k
exp
˜
E(k)− 12 IR−EF kB T
1
− +1
exp
˜
E(k)+ 12 IR−EF kB T
+1
. (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 density of states per atom and ˜ F ) = V D(EF ), the so-called Stoner criterion for the spin orientation D(E 2N
occurrence of ferromagnetism is finally obtained: ˜ F) > 1 I D(E
(1.14)
EF is the Fermi energy. The detailed derivation of 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 oc-
Theory
9
cupied (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. To determine the majority spin-direction of the magnetization the sum of the 3d-states below the Fermi energy have to be taken into account while for transport phenomena the spin-dependend density at the Fermi edge is important.
1.2
Micromagnetic Systems
Since the microscopic descriptions presented in section 1.1 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 1.2.3 and 1.3.2.
1.2.1
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 to minimise the appropriate 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 1.4. 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 of the potential depends on the experimental conditions. The Gibbs free energy [Ber98]
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10
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 ˆ ≡ M(r) so most practical cases M has to be replaced by a vector field M that the Gibbs free energy is replaced by the Landau free energy [Ber98] ˆ H, T ) = U (M) ˆ − T S − µ0 H · M. ˆ G(M,
(1.16)
ˆ can be regarded as a This assumes already that the magnetization M continuum vector function in the sample instead of taking into account single magnetic moments or spins. This so-called micromagnetic approximation is justified if the cell size is not larger than the exchange length.
1.2.2
Energy Contributions
1.2.2.1
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 Eex
A = ˆ 2 |M|
Z
ˆ 2 dV. (∇M)
(1.17)
The relation between the exchange stiffness A and the atomic scale parameter Jij in eqn. 1.2 can be understood like this: By limiting the sum to nearest neighbors and interpreting the i 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 1.2.2.2
11 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 1.2.2.3). 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] εani = K0 + K1
sin2 θ sin2 (2φ) sin2 (2φ) 2 2 + cos θ sin2 θ + K2 sin (2θ) + ... 4 16 (1.18)
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 (1.20) εani = K0 + Kbiaxial sin2 (2φ) + · · · 4 Also twofold (or uniaxial) anisotropies are observed. All anisotropy energy densities εani can be directly transformed to anisotropy energies using
Theory
12
Z Eani =
ˆ 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 dominate particularly in thin films and multilayers. • Uniaxial anisotropy can be induced by application of an in-plane field during deposition. • The magnetoelastic anisotropy arises in crystals were strain is present in the lattice. • External stress gives rise to analog energy contributions like the internal strain, but due to a different origin. 1.2.2.3
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 2 Edip = µ0 Hd dV = − µ0 Hd · MdV, (1.22) 2 2 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]
Theory
13
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.
1.2.2.4
Zeeman Energy
The Zeeman energy is the potential of a magnetic dipole moment in a magnetic field. For a homogeneous external field H0 , 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
1.2.3
H0 · MdV.
(1.24)
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 Stoner-Wohlfarth model. A detailed description how this can be performed is presented as an example 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:
Theory
14
ˆ H) = GL = (M,
Z V
! A 1 ˆ 2 ˆ ˆ ˆ 2 [∇M] + εani (M) − µ0 Hd · M − µ0 H0 · M dV 2 ˆ |M| (1.25)
Temperature effects are not included in this equation. 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 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 GL is a functional of the entire vector ˆ and thus one has to consider the infinite-dimensional functional field M space of all 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]:
with
∂ ∂n
ˆ × Hef f = 0 M
(1.26)
ˆ ˆ × ∂M = 0 M ∂n
(1.27)
denoting the derivative normal to the surface. The first con-
dition must be fulfilled for every point inside the sample, the second is a boundary condition for the surface. The effective field Hef f is given by Hef f =
1 ∂εani 2 5 (A 5 M) − + HM + H0 . µ0 Ms2 µ0 ∂M
(1.28)
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) ×
∂ m(r) ∂n
= 0,
Theory
15
which is equivalent to the simpler condition
∂ m(r) ∂n
= 0. The mate-
rial parameters like the exchange constant A, the saturation magnetization Ms , all anisotropy constants determining εani , 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 magnetizaˆ tion 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.
1.3
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.
1.3.1
Landau-Lifshitz-Gilbert Equation
From a quantum-mechanical starting point a classical desciption of the change of angular momentum can be derived as detailed in [Wie02] and [Hin02]. The torque exerted on a normalized magnetic moment S by a field is given by ∂S γ = − (S × H0 ef f ) ∂t µs
(1.29)
with the gyromagnetic ratio γ = gµB /~ of the electron (g = Landé factor, µB = Bohr magneton) and by normalizing the moment S = µ/µs .
Theory
16
The effective field H0 ef f is determined by the derivative of the Hamilton function H0 ef f =
∂ H. ∂S
In the simplest case, where the Hamiltonian con-
tains 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
(1.30)
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 ef f − S × (S × H0 ef f ), ∂t µs µs
(1.31)
where is λ the damping constant introduced. However, investigations of the magnetization reversal time of a magnetic sphere as a function of the dampingλ showed that infinite damping unreasonably leads to zero reversal times (1/λ- dependence) [Kik56]. Gilbert [Gil55] derived the socalled Gilbert equation of motion ∂S(t) γ ∂S(t) = − S × H0 ef f + α(S × ). ∂t µs ∂t } | {z {z } | precession
(1.32)
damping
As in the Landau-Lifshitz equation 1.31, the first term describes the precession and the second the damping. The Gilbert equation 1.32 can be transformed to the general form of the Landau-Lifshitz equation leading to the ∂S(t) γ γα =− S × H0 ef f − S × (S × H0 ef f ), 2 ∂t (1 + α )µs (1 + α2 )µs
(1.33)
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 1.32, is referred to as LLG, which is correct in the sense that both equations can be transformed into each other as described.
Theory
17
It is important to discuss the units used in the equations above. In eqn. 1.29 the moment S is dimensionless with |S| = 1 and the effective field H0 ef f 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 H0 ef f is given in correct units of magnetic fields (A/m) instead of energies ([H0 ef f ] = J) and the magnetization M is introduced instead of the dimensionless magnetic moment S, eqn. 1.29 can be written as ∂M(t) = −µ0 γ(M × Hef f ). ∂t
(1.34)
This finally leads to an implicit LLG equation analogous to eqn. 1.32 of the form ∂M(t) α ∂M(t) = −µ0 γ(M × Hef f ) + (M × ), ∂t Ms ∂t
(1.35)
where Ms denotes the saturation magnetization.
1.3.2
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. In general, other methods also exist to discretize the problem. OOMMF also provides a true threedimensional solver named OXS (OOMMF extensible solver), which is suitable for simulation of layered systems. 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
Theory
18
s lex =
2µ0 A Ms2
(1.36)
r
A , (1.37) K with A being the exchange constant and K being an anisotropy conlwall =
stant [HS98]. A cell 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 if permalloy is chosen as material. For each cell the effective field Hef f as derived in section 1.2.3 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 log2 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. 1.33 is performed. The procedure is iterated yielding a step by step calculation of magnetization configurations ˆ × Hef f (see eqn. 1.26) of the with decreasing energy until the torque M effective field on the magnetization is below a chosen threshold value at each point of the system.
1.4
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
Theory
19
interactions between current and magnetization into the description will be discussed. The main theoretical framework in this context is the spin transfer torque model.
1.4.1
Spin Transfer Torque
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 torque (between the localized 3d-electrons responsible for ferromagnetism and the delocalized 4s-electrons carrying the current), but today it is referred to as spin transfer torque or spin transfer effect. The s-d exchange potential is described by Hsd V (x) = gµB s · Hsd (x) + , 2
(1.38)
where s is the spin of the 4s-electron, Hsd (x) = 2Jsd hS(x)i /(gµB ) is the exchange field with the s-d exchange integral Jsd and the spin of the 3d-electrons, and the coordinate x normal to the wall plane. The first approach to integrate the spin transfer torque into the Landau-Lifshitz-Gilbert equation (eqn. 1.35) by adding additional terms was made by Slonczewski [Slo96]. He considered two ferromagnetic layers separated by a non-magnetic spacer with the macrospins S1,2 = |S1,2 | ˆ s1,2 . The torque exerted by a charge current I on a macrospin was found to be ∂S1,2 g =I ˆ s1,2 × (ˆ s1 × ˆ s2 ) (1.39) ∂t e with the electron charge e and a prefactor g containing the spin polarization P of the current: −1 1 + P3 g = −4 + (3 + ˆ s1 · ˆ s2 ) 4P 3/2
(1.40)
First we see that the torque is proportional to the current and changes its sign when the current is reversed. Secondly, it depends on the spin
Theory
20
polarization P , and the direction of the torque is expressed by the product ˆ s1,2 × (ˆ s1 × ˆ s2 ). When including this torque term into the LLG equation 1.35, we obtain a description of the system with a spin current.
1.4.2
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 co-workers [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 × Hef f + M× − (u · 5)M | {z } ∂t Ms ∂t
(1.41)
extension
γ0 = µ0 γ = µ0 gµB /~ is the gyromagnetic ratio and u is the generalized velocity defined below in eqn. 1.47. They restrict themselves to adiabatic processes, i.e. a local equilibrium between the conduction electrons and the magnetization is assumed. A reformulation of the description has been introduced by Li and Zhang [LZ04a]. In the low temperature regime the magnetization has a constant value and thus they obtain τ[LZ04a] = −
1 M × [M × (u · 5)M]. Ms2
(1.42)
This form of the spin torque is identical with that considered earlier by Bazaliy et al. [BJZ98] for metal-ferromagnet interfaces in the presence of a spin-polarized current τ[BJZ98] = −
a M × [M × m] Ms
(1.43)
Theory
21
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 Slonczewski [Slo96] (see eqn. 1.39). If the torque τ[LZ04a] is integrated across the multilayers investigated in [BJZ98], assuming that the free and the pinned layer are 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 [LZ04a] or the version suggested by Thiaville et al. [TNMV04] in eqn. 1.41 can be regarded as the continuous limit of eqn. 1.39. 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 also performed micromagnetic calculations with their torque ansatz. They obtained current-induced domain wall motion above a critical current density.
1.4.3
Adiabatic and Non-adiabatic Spin Torque
Besides the adiabatic torque discussed so far [TNMV04, LZ04a, LZ04b] also non-adiabatic 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
Theory
22
and Li [ZL04] include a non-adiabatic torque into the description. 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 and the damping constant, respectively. In other words, they slightly affect only the two terms of the established Landau-Lifshitz-Gilbert equation 1.35 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 as the adiabatic and the non-adiabatic torque, included as two additional terms: ∂M(t) α ∂M(t) = −γ0 M × Hef f + M× ∂t Ms ∂t bJ ∂M ∂M cJ − 2M × M × M× − , Ms ∂x Ms ∂x {z } | {z } |
(1.44)
non−adiabatic
adiabatic
where the constants bJ and cJ are given by
bJ = j
P µB eMs (1 + ξ 2 )
and cJ = ξbJ .
(1.45)
ξ is defined as the ratio τex /τsf of an exchange time (see [ZL04] for details) and the spin-flip relaxation time. Its value is of the order of 10−2 for typical 3d-ferromagnets [ZL04]. The second non-adiabatic term is new and can be related to the mistracking of the conduction electron spins. Also Thiaville and his 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 it. The extended LLG equation then reads
Theory
23
∂M(t) α ∂M(t) β = −γ0 M × Hef f + M× − (u · 5)M − M × [(u · 5)M]. | {z } Ms ∂t Ms ∂t | {z } adiabatic non−adiabatic
(1.46) The generalized velocity u=
gP µB j 2eMs
(1.47)
with j being the current density and P its spin polarization, points along the current direction. 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 [YON+ 04, KJA+ 05]. In order to compare the Thiaville approach [TNMS05] with the suggestion of Zhang and Li [ZL04] we can rewrite eqn. 1.46 in the form ∂M(t) α ∂M(t) = −γ0 M × Hef f + M× ∂t Ms ∂t 1 β − 2 M × (M × [(u0 · 5)M]) − M × [(u0 · 5)M].(1.48) Ms Ms It can be seen directly see that both approaches lead to identical extended Landau-Lifshitz-Gilbert equations, but with slightly different expressions for the generalized velocities u (eqn. 1.47) and u0 , respectively, which are equal except a factor of 1/(1 + ξ 2 ) ≈ 1 if eqn. 1.44 and eqn. 1.48 are compared. The parameter β , which was introduced phenomenologically first, can be identified with β = (λex /λsf )2 ,
(1.49)
where λex represents 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
Theory
24
ξ = cJ /bJ , depending on the theoretical description, determine the nonadiabaticity of the spin torque. The doping of 3d-ferromagnets like Py, Fe, and Co with rare earth metals might allow the modification of the spinflip length and therefore the value of β. 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 CrO2 (see section 1.6) 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 non-adiabatic terms discussed above, they introduce two other torques τna and τpin due to non-adiabatic momentum transfer and pinning, respectively. Both non-adiabatic contributions are summed to β 0 ≡ βP + βna , where β is due to spin relaxation, P is the spin polarization of the current, and βna a dimensionless wall resistivity due to high gradients in the domain wall magnetization [TTK+ 06]. Starting from the equations of motion for the domain wall [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].
1.4.4
Domain Wall Spin Structure Modifications
In addition to domain wall motion induced by a current, changes of the domain wall spin structure have been predicted by theory. Thiaville et al. [TNMS05] observed periodic changes between vortex and transverse walls in the results of their micromagnetic simulations of a wall under
Theory
25
spin current in a Py 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]. Results on current-induced domain wall spin structure changes were also obtained using XMCD-PEEM [KLH+ 06]. 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 due to stronger pinning, above which the wall velocity is equal to that of a vortex wall.
1.5
Anisotropic Magnetoresistance (AMR)
The general phenomenon that the resistance of a given magnetic system depends on a magnetic field and therefore its magnetization state is called the 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 today making use of the fact that a 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. The anisotropic magnetoresistance (AMR) was employed for the work of this thesis to detect the presence of DWs. It 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
Theory
26
magnetization direction chosen arbitrarily along the z-axis can be written as [Mar05]
ρ⊥ −ρH 0 ρij = ρH ρ⊥ 0 , 0 0 ρk
(1.50)
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 Ei =
X
ρik jk
(1.51)
k
between the electric field components Ei 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
(1.52)
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
ρk + ρ⊥ 1 2 ρ= + ρk − ρ⊥ cos θ − . 2 2
(1.53)
was obtained. If a random orientation of magnetic domains in zero field is assumed, the mean value of cos2 θ is equal to 12 in a film with in-plane magnetization so that the zero field resistivity is (ρk + ρ⊥ )/2, while the saturation values are ±(ρk −ρ⊥ )/2 for longitudinal and transverse fields, respectively. It can be seen that the effect does not directly depend on the applied field, but on the spin structure of the sample via the angle between magnetization and current. Recently, efforts were made to calculate the AMR for Py quantitatively. A semiclassical approach was used [RCDJDJ95] based on a twocurrent model, which treats currents of electrons with majority and mi-
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27
Figure 1.2: (From [Büh05]) Schematics of the AMR contribution of a domain wall and its measurement. The current flow is indicated. (a) No wall is present and the resistance is high, (b) the presence of a domain wall (here a transverse wall) reduces the resistance.
nority spins independently and therefore assumes a weak spin-flip scattering. Ab initio calculations of the AMR for bulk Py alloys [KPSW03] resulted in a very good agreement with experimental results [Smi51].
1.5.1
AMR Contribution to the Domain Wall Magnetoresistance
The AMR effect can be specific to particular materials but also the sample spin structure and in particular domain wall spin structures can lead to a magnetoresistance signal. 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 of the magnetization inside the wall giving rise to an AMR effect. In the mesoscopic Py 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, i.e. the ring is in the so-called vortex state, the magnetization is aligned parallel to a possible current flow everywhere in the ring (Fig. 1.2(a)). When a domain wall is present, it represents an area in which the magnetization has a component perpendicular to the current flow as depicted in Fig. 1.2(b). This leads to a negative resistance contribution of the domain
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28
Figure 1.3: (From [Kön06])Schematics of spin-dependent density of states for (a) 3d transition metals and (b, c) for halfmetallic ferromagnets.
wall due to the AMR effect, which can be easily measured. An intrinsic MR effect is ballistic magnetoresistance (BMR) which is the difference in resistance between parallel and antiparallel orientation of the magnetic moments at point contacts on a ballistic scale [GMZ99, TZMG99]. The dimensions of the point contacts have to be of the order of the mean free path of electrons in the system. There is much debate about the existence and the possible origins of the effect [HC03, EGE+ 04], which may also be due to a domain wall increase or decrease [TF97, RYZ+ 98].
1.6
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. In addition to Heusler alloys [dGMVEB83], transition metal oxides such as Fe3 O4 [ZFP+ 05], CrO2 [Sch86], and manganites [vHWH+ 93] have been theoretically predicted to belong to the class of halfmetallic ferromagnets. For CrO2 , the spin-dependent density of states (DOS) exhibit a metallic character for one orientation the electrons due to occupied states at the Fermi level, while the second orientation exhibits a semiconducting behavior with an energy gap at the Fermi level as visualized in Figs. 1.3(b).
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29
The spin polarization in general can be written as
P =
D↑ (EF ) − D↓ (EF ) , D↑ (EF ) + D↓ (EF )
(1.54)
where D↑,↓ (EF ) are the densities of states at the Fermi level for spinup and spin-down electrons, respectively. In order to obtain a spinpolarization of 100 % in eqn. 1.54, 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. In Fig. 1.3(b), the bandstructure of CrO2 with a positive spin-polarization is visualized. More details about the bandstructure of CrO2 can be found in [Kön06], as well as in the relevant references therein. Experimental methods for the determination of the spinpolarization of a material are spin-resolved photoelectron spectroscopy [Hüf03], transport measurements in superconductor/insulator/ferromagnet junctions [TM71, TM73] , or point contact Andreev reflection at a superconductor/ferromagnet interface [UPLB98]. The first experimental evidence for the high spin-polarization with a value of 95 % was obtained in 1987 from polycrystalline CrO2 films at room temperature using spinpolarized 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 EF has been also confirmed recently for epitaxial CrO2 (100) films [DFK+ 02, FDK+ 03], which were the basis for the patterned samples investigated in this thesis. CrO2 is a very well established material, it 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 current-induced domain wall displacement at lower critical currents.
Theory
1.7
30
RKKY Coupling
In transition metals, there is a direct overlap of the d electrons and the magnetic coupling is therefore determined by direct exchange. In case of the rare earths with the 4f shells containing the magnetic electrons, this direct exchange is ineffective. Instead, an indirect mechanism involves the outer 5d electrons which partly overlap with the 4f shell. Ruderman and Kittel [RK54] were the first to suggest that a local moment can induce a spin-polarization in the surrounding conduction electrons. Kasuya [Kas56] and Yosida [Yos57] used similar concepts to treat the coupling of localized rare earth 4f moments with the conduction electrons. The coupling, which was named after them RKKY coupling, was either ferromagnetic or antiferromagnetic dependent on the distance from the localized moment. This can be described by an oscillatory RKKY exchange coefficient J(R) which is for large distance R given by J(R) =
2A2 me kF cos(2kF R) . (2π)3 ~2 R3
(1.55)
The RKKY exchange couples localized moments over relatively large distances. If two magnetic layers are separated by a nonmagnetic spacer layer an oscillatory coupling in the direction perpendicular to the layers is observed. The interlayer exchange coupling constant J12 per unit interface area then has the simple form d2 sin(2kF z). (1.56) z2 Here d is the thickness of the spacer layer and z is the distance from one J12 (z) = J0
of the magnetic layers. The induced spin density wave in the spacer layer serves as an indirect coupling mechanism between the magnetic layers which change their coupling from ferromagnetic to antiferromagnetic alignments as a function of the spacer layer thickness d.
Chapter 2 Fabrication The fabrication of magnetic elements can in general be divided in two parts; first, the patterning of a polymer resist, and second, the transfer of the pattern from the resist to the magnetic thin film. In section 2.1 an overview of resist exposure techniques is given. Section 2.2 summarizes the pattern transfer methods for thin films. This includes the deposition of thin films (section 2.2.1), lift-off (section 2.2.3), and etch techniques (section 2.2.4). In the last part of this chapter (section 2.3), it is illustrated how these techniques can be combined to fabricate magnetic elements and devices at the nanoscale. The choice of the patterning method depends on the materials to be investigated and the measurement to be made.
2.1
Patterning the Resist
Here different resist exposure techniques and resist technology are introduced. Special emphasis will be placed on electron beam lithography as it was involved in the fabrication of most of the samples used for this work.
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Figure 2.1: Scheme of the column of the Leica Lion LV-1 electron beam writer.
2.1.1
Electron Beam Writer
The advantage of electron beam lithography is its high resolution. The pattern has to be exposed in a serial manner which can lead to long writing times. In the following the most important parts of the electron beam writer in our laboratory, a Leica Lion LV-1 from Leica Microsystems Jena, shall be explained. Low voltage optical column
The central part of this electron beam wri-
ter is the electron-optical column designed by Integrated Circuit Testing GmbH (ICT GmbH) (Fig. 2.1). It allows setting of the electron beam to a desired voltage level anywhere between 1 kV and 20 kV. Usually it is set to a low acceleration voltage of 2.5 kV to avoid the proximity effect (see 2.1.2). A thermal field emission cathode is used as an electron emitter. It is made of tungsten (W) and coated with zirconiumoxid (ZrO) to lower the work-function and it is heated up to 1600◦ C. For operation, the pressure is kept < 10−8 mbar. A suppressor close to the emission cathode with a bias
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of typically -300 V suppresses unwanted thermal electrons. The emitted electrons are accelerated by an extractor which is biased to +8000 V. This makes the electron beam largely insensitive to magnetic fields from outside. A beam blanker consisting of 2 plates which deflect the beam away from the sample by applying a voltage Vbb in addition to the 8000 V to one of the plates, essentially switching it off. With gun alignment coils the beam can by directed through holes of 10, 17, 30, 60, and 120 µm on an aperture strip. The 30 µm hole is in the optical axis of the column. If any other aperture is chosen, the beam can be brought back on the optical axis with aperture alignment coils behind the aperture strip. The column provides a spot size as small as 5 nm (at 1 kV) through the use of a compound objective lens. An electrostatic lens produces a diverging field, while the surrounding magnetic lens converges the beam. The complementary lenses reduce chromatic aberration, similar to a compound optical lens. Stage control
The stage motion is measured by a two-coordinate dou-
ble-beam metering system. The measurement beams are emitted by a frequency stabilized HeNe-laser and the position of the stage is measured with interferometers. The mechanical positioning accuracy is 0.1 µm. Discrepancies in the measured and desired stage position are corrected by an electromagnetic deflector system (beam tracking system / BTS). This leads to an accuracy of 2.5 nm over a range of 20 µm. Exposure control
Each substrate holder is fitted with a Faraday cup al-
lowing measurement of the actual probe current. Prior to exposure, the beam alignment is carried out on a calibration substrate which is virtually identical to the height of the substrate to be exposed. A difference in height will be sensed and recorded by an optical height meter and corrected. The accuracy of the height measurement is 2.2 µm. All major components are supported in a soft spring suspension to ensure that floor and building vibrations do not affect the accuracy. The line width is adjusted by changing the dose and the defocus of the electron beam
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34
[DH99]. Continuous path control For this work quasi-continuous path following (Continuous Path Control / CPC) was employed. This means that the stage moves under the beam which remains virtually stationary. Deviations of the stage’s actual position from its required position are compensated with the help of the beam tracking system (BTS). The maximum possible extension of the structures that can be exposed is dependent on the substrate size alone. All structures subject to exposure are by approximation represented as Bézier elements. Data format The files containing the exposure data are called BEZ files. They are text files which can be produced with every program or programming language which is able to provide ASCII-text as an output. The simplest geometrical structure is a straight line. This can be represented by a 1st order Bézier curve which can be described as → − → − → − P = P 1 (1 − t) + P 2 t
t ∈ [0, 1] .
(2.1)
Here, the line is created by varying the parameter t in a continuous → − → − manner from 0 to 1 and P 1 marks the beginning and P 2 the end to the line (Fig.2.2(a)). Curved lines are Bézier curves of higher order. Important for this work were rings or segments of rings. The latter is a special case of a 2nd order Bézier curve which is given by − → − → − → → − P1 (1 − t)2 + 2g P3 (1 − t)t + P2 t2 P = t ∈ [0, 1] (2.2) (1 − t)2 + 2g(1 − t)t + t2 → − As can be seen in Fig. 2.2(b), P 3 represents a guiding point for the curve and is located in the intersections of the tangents at the starting → − → − point P 1 and end point P 2 . For a ring segment the factor g is given by ϕ g = cos( ), 2
(2.3)
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35
Figure 2.2: (a) Bézier curve of 1st order, (b) Ring segment being a special case of a Bézier curve of 2nd order, (c) Scheme showing the stage movement during writing of a Bézier curve in Continuous Path Control mode.
ϕ being the angle of the ring section at the center (Fig. 2.2(b)). A full ring comprises, for example, four quarter rings or three one third rings because only sections of rings with ϕ < 180◦ can be processed by the Lion electron beam software. Each curved line is approximated by a zigzag of straight lines corresponding to the address grid of the electron beam writer (Fig. 2.2(c)). The calculation of the zigzag path from the input Bézier data is done in realtime during the exposure. Because the grid period is very small, the resist line finally obtained after development has the similar shape as the initially given Bézier curve.
2.1.2
Resist Technology
A pattern can be written in a resist which is sensitive to energetic radiation. Locally the chemical properties change because of the absorbed energy. The choice of resist depends on its sensitivity to different exposure methods. The most prominent example for a resist, polymethyl methacrylate (PMMA), can be exposed with an electron beam. Here, a beam of primary electrons with an energy in the keV range propagates through the resist and broadens because of forward scattering. Secondary electrons of low energy are produced if primary electrons transfer fractions of their energy to electrons in the resist. With their small energy of up to 50 eV, the secondary electrons penetrate approx. 10 nm in the resist which gives the limiting factor for its resolution. When electrons reach the substrate they experience large angle scat-
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36
tering. Some of the electrons are backscattered into the resist and expose it again. The exposed area is larger compared to the area exposed by the incident beam. This is called proximity effect and is not wanted because it limits the resolution. The intra proximity effect leads to overexposure with the consequence that small features turn out to be bigger than intended and the inter proximity effect causes small resist bridges separating elements to disappear. To address this problem the energy of the primary electrons can be set to a low energy, e.g. 2.5 keV, to reduce the backscattering of the electrons and therefore the proximity effect. The disadvantage is that relatively thin resist layers below approx. 200 nm have to be used. The key resists employed are described below:
PMMA The most commonly used resist for electron beam lithography is PMMA (polymethyl methacrylate). It consists of an organic polymer which forms large molecules consisting of chains if monomers. Exposure breaks the inter atomic bonds, resulting in shorter molecules which are more soluble and therefore can be removed with a developer. This is called a positive resist. To form a resist layer of constant thickness on top of a substrate, a spin-coater is used. After dropping some resist on the substrate, it is rotated at high speed up to 5000 rpm. The concentration of the PMMA in a solvent, the rotation speed and duration determine the resist thickness. After spin coating, the sample is baked on a hot plate (170◦ for 1 min for PMMA). The temperature should be above the boiling temperature of the solvent and above the glass transition temperature of the resist. The latter is important to transform the resist from the polycrystalline to an amorphous state giving a smoother surface of the resist layer. After exposure, the PMMA resist was developed with methyl-isobutyl-ketone (MIBK) and isopropyl alcohol (IPA) in a 1:3 mixture. A Hamatech development unit (Steag-Hamatech HME 500) was used: first,
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37
the developer is sprayed on the sample while it is rotating. In a second step, the developer is rinsed away with isopropyl alcohol and finally the sample is dried by high speed rotation. Any residues from the isopropyl alcohol on the sample surface can be removed by rinsing the samples in water for several seconds.
HSQ Hydrogen silsesquioxane (HSQ) resist is basically a cross-linked silicon dioxide structure which provides small linewidth fluctuation (2 nm) due to its small polymer size [NYN+ 98]. Moreover, for isolated features, linewidths smaller than 10 nm have been demonstrated using 50 kV electron beam lithography [WAB03]. On exposure, cross-linking converts the HSQ resist to an amorphous structure similar to SiO2 and consequently prevents the resist from being soluble in alkali hydroxide solutions used as a developer. In this state it is quite etch resistant which makes it interesting as an etch mask. For this work a double layer resist, consisting of a PMMA lower layer and a HSQ upper layer, is employed. Exposed HSQ is employed as a mask during ion milling of a thin film of magnetic material, e.g. Fe3 O4 . The PMMA allows the removal of any remaining resist using acetone and ultrasound and to obtain a device at the end of the fabrication process (section 2.3.6.2). An HSQ FOX-12 resist from Dow Corning is spin coated for 45 s on an MgO substrate. At 1000 rpm, this gives a resist thickness of 170 nm. After spinning the resist has to be baked out for 3 min at 180◦ on a hotplate. The exposure can be carried out using electron beam lithography but photon based lithography such as photolithography and X-ray lithography is also possible. For development the sample is dipped into MFA26A for 10 min and rinsed with clean water afterwards.
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38
Figure 2.3: Overview showing the three different exposure methods for photolithography.
2.1.3
Photolithography
The basic parts of photolithography are a light source which provides a uniform illumination, a mask with a pattern, and a substrate with a photoresist layer on top. The mask has to be aligned with respect to the substrate. There are three different exposure methods; in contact printing, the resist-coated silicon wafer is brought into physical contact with the photomask. This contact can cause damage to the mask and therefore defects in the pattern. The resolution is around 1 µm. The proximity exposure method is similar to contact printing with the exception that a small gap, 10 to 25 µm, is maintained between the wafer and the mask during exposure. This gap minimizes (but may not eliminate) mask damage. Approximately 2 to 4 µm resolution is possible with proximity printing. In projection printing, an image of the pattern on the mask is projected onto the substrate, which is many centimeters away. Projection printers are capable of approximately 1 µm resolution. The photolithography machine used in this work, also called mask aligner, is a Karl Süss MA6. For exposure the contact printing method is employed. The light source is a UV lamp and the mask consists of a glass plate with a patterned chromium coating. Typically 4” silicon wafers are used. The advantage of this technique is that large patterns can be exposed in a short time. Therefore the main application for this work is to produce large alignment marks on wafers to prepare them
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39
Figure 2.4: Use of diffraction gratings patterned on a membrane mask to obtain interference fringes. (a) 2-beam scheme (b) 4-beam interference (courtesy of H. Solak, PSI) .
for exposure with a high resolution lithography technique such as X-ray interference lithography and electron beam lithography.
2.1.4
X-ray Interference Lithography
X-ray interference lithography (XIL) uses partially coherent x-rays produced by an undulator at a synchrotron source. This technique enables the fabrication of arrays of nanometer-scale magnetic particles [Ser06] or periodic templates for directed-assembly of self-assembling macromolecular (e.g. block-copolymers) and colloidal systems [KSS+ 03]. Its striking advantage is the combination of high resolution (demonstrated smallest period 25 nm) with a high throughput (up to 10000 times more than EBL). Its limitation is that only periodic patterns with a simple geometry can be exposed. The basic principle of interference lithography (IL) is that two or more mutually coherent beams are brought together to form interference patterns which are exposed in a photoresist material. The XIL beamline operates at a wavelength of 13.4 nm (in the extreme ultraviolet EUV range) at the SLS, which is capable of providing fully coherent illumination. The interferometer at the XIL beamline consists of gratings that diffract the beam into a common area where interference fringes are formed. Oneor two-dimensional patterns are obtained by the use of two or multiple
Fabrication
40
beams respectively (Fig. 2.4). The intensity distribution obtained in this interferometer is determined by the period of the diffraction gratings and their relative positions [SDG+ 02].
2.2
Pattern Transfer Methods
The pattern in a resist can be transferred into a thin film using different techniques. The exact choice of method depends on the material which has to be patterned and on the subsequent measurements to be made. In this section, deposition methods for thin films are introduced (section 2.2.1). Furthermore, lift-off (section 2.2.3) and etching techniques (section 2.2.4) are described.
2.2.1
Deposition
In the frame of this work, different thin film deposition techniques are used. These are thermal evaporation to produce contacts and etch masks, sputter deposition for single and multilayer magnetic films, and molecular beam epitaxy and chemical vapor deposition for single layer magnetic films. These techniques are described below. 2.2.1.1
Thermal Evaporation
The material to be deposited is placed in a crucible and heated by applying an electrical current at the crucible. It requires only moderate vacuum at the level of 10−6 mbar which is enough for most of the emitted atoms not to collide with atoms of residual gases. Then they ballistically travel through the recipient until they hit the substrate. The used evaporation system is a Balzers BAE 250T with two crucibles for thermal evaporation which allow two different materials to be evaporated without venting the system. The thickness of the deposited material is measured by a piezoelectric oscillator and the deposition can be stopped by a mechanical shutter.
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Figure 2.5: The DC magnetron sputtering facility TIPSI
2.2.1.2
Sputter Deposition
DC magnetron sputtering is a widely used technique for thin film deposition. It is a fast process compared to molecular beam epitaxy using electron beam evaporation or pulsed laser deposition. Nevertheless, in sputtering it is also possible to control the growth of thin films and therefore their crystalline orientation by using adequate sputter conditions and single crystal substrates or special seed layers. DC magnetron sputtering is suited to deposit films with a very homogeneous thickness over a large area. In sputtering, a target consisting of the material of the desired thin film is bombarded by ions, which are generated in a glow discharge. Normally argon is used as sputter gas due to its inert nature and relatively high mass, which results in high sputtering rates. In magnetron sputtering, a magnetic field confines the electrons in front of the target. They are forced to be on spiral trajectories around the magnetic field lines, which effectively increases the length of their path in the plasma. Therefore the glow discharge can be even preserved at relatively low pressure (typ. 10−3 mbar). The applied voltage for the glow discharge is typically several 100 V. When a gas ion hits the target, momentum transfer from the ions to the atoms of the target occurs. Target atoms are released when the transferred energy is higher than their binding energy. The emitted target atoms lose kinetic energy by elastic scattering at the atoms of the sputter gas. Finally, they condense at surfaces of the substrate and of the
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42
sputter chamber. Using DC magnetron sputtering, thin films of pure metals and metallic alloys can be sputtered from their respective targets. For the latter, the composition of the target material is usually maintained in the film. In DC sputtering, the target represents the cathode, thus it is not possible to use insulators. Thin films of insulating materials can be deposited using RF sputtering. In DC magnetron systems, it is possible to prepare certain insulator films, e.g. Al2 O3 , from a metallic target by reactive sputtering, e.g. in an oxygen gas. The schematic representation (Fig. 2.5) shows the sputtering machine at the Paul Scherrer Institute (PSI) in Villigen, Switzerland. It is equipped with three targets. The targets have the shape of discs and are combined with magnets which provide the magnetic field in front of the target. The pressure of the sputter gas can be adjusted using mass flow controllers. The plasma is ignited by applying a voltage for the glow discharge close to the desired target. The samples are fixed on a translation table which moves at a constant velocity below the targets. At a constant deposition rate, the layer thickness is controlled by the velocity of the translation. To ensure a homogeneous layer thickness perpendicular to the translation an aperture is placed in front of the target. For the preparation of multilayers, power is supplied alternately to the desired targets and the substrate is translated below. The complete process is computer controlled. For the evacuation of the sputter chamber a turbo pump in combination with a membrane pump is installed.
2.2.1.3
Molecular Beam Epitaxy
In molecular beam epitaxy (MBE) the ultra-high vacuum leads to a very clean film and the condensation of single atoms can give epitaxial growth with well-defined interfaces. A collimated beam of atoms hits a substrate and the atoms then stick to the surface. This crystallization by condensation is done in ultra-high vacuum (UHV). The resulting surface structure depends on several parameters such as the surface energies and the lattice mismatch of the materials involved, but also on the temperature and
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Figure 2.6: (From [Klä03]) Schematic view of the UHV system used for MBE growth of Py and Co. P1 to P4: vacuum pumps; V1 to V6: valves; W1 to W3: glass windows; G1: ion gauge.
pressure during growth. For this work, thin films were grown in two different MBE systems, one in the group of Prof. Bland at Cambridge University and one in the group of Prof. Rüdiger at Universität Konstanz. Here the Omicron Multiprobe RM Surface Science UHV system operated at the Universität Konstanz is described. The samples are grown in an ultra high vacuum (UHV) chamber with a base pressure of 2 × 10−10 mbar. The system consists of a main chamber and a sample loading system, which allows the sample replacement to be performed without breaking the vacuum of the main chamber. The growth chamber is equipped with an Auger electron spectroscopy (AES) system to check 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 (effusion (or Knudsen) cells). It was used to grow polycrystalline Permalloy (Py) films on silicon wafers in UHV conditions and epitaxial mangnetite (Fe3 O4 ) films on MgO sub-
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44
Figure 2.7: (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.
strates. A diagram of the growth chamber is given in Fig. 2.6. 2.2.1.4
Chemical Vapor Deposition (CVD)
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 CrO3 , 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, TiO2 (100) substrates were used with a lattice mismatch of 3.7 % along the in-plane a-axis and of 1.5 % along the c-axis [Kön06]. CrO3 was used as precursor material in the chemical vapor deposition (CVD) process. A schematic view of the setup is shown in Fig. 2.7. Details of the necessary substrate pretreatment, the complete film deposition process, and the setup can be found in [Kön06].
2.2.2
Properties of Films and Nanostructures
After the film deposition, the general properties of the films have to be studied. They are already monitored during the fabrication process, for example using electron diffraction techniques during MBE growth. The
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relevant properties, mainly referring to the crystalline structure and the general magnetic properties, are briefly discussed in the following section for the different materials investigated. 2.2.2.1
Permalloy and Cobalt Samples
The permalloy (Py) and cobalt (Co) samples have a polycrystalline structure with a 10 nm crystallite size. The Py being used is the alloy Ni80 Fe20 . Since the Py fcc crystallites exhibit a negligible magnetocrystalline anisotropy, the spin structure of the Py nanostructures investigated is primarily governed by the shape anisotropy. The Co nanostructures also exhibit a negligible averaged uniaxial anisotropy, but a relatively stronger crystalline anisotropy of the single hcp grains. Especially advantageous for measurements are the high saturation magnetization of Co and the large anisotropic magnetoresistance ratio for Py. In Ref. [Klä03], more details about the crystalline and magnetic properties of such Py and Co films can be found and differences between polycrystalline and fully epitaxial films are discussed. 2.2.2.2
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 CrO2 . HF pretreatment of the substrates yielded films with an improved surface quality: an averaged peak-to-peak roughness of about 5 nm in a 2µm × 2µm area and a rmsroughness 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 (SQUID), and spin-resolved photoemission spectroscopy. MOKE hys-
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46
Figure 2.8: Sample holder for lift-off for Si3 N4 membrane substrates
teresis 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 1.6 and to be found in [DFK+ 02, FDK+ 03, Ded04].
2.2.3
Lift-off
Following deposition of e.g. a thin film of metal, the resist layer is removed using a solvent. During this lift-off process, any unwanted material on top of the resist is removed at the same time. The material in the regions where resist has been removed during development remains on the surface of the substrate. PMMA, the most commonly used resist, is soluble in acetone. First, the sample is placed in a beaker filled with acetone. Then, ultrasound
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is applied in periods of 1 - 5 min with 1 min breaks. The time required to complete the lift-off depends on the relation of the resist to film thickness, on the deposition technique, and on the dimensions of the structures. The material which lifts off remains as particles in solution and should be removed by exchanging the acetone. Here, most of the contaminated acetone is decanted away and replaced with clean acetone. This ensures that the sample always stays in the solvent. This is critical to prevent unwanted particles or residues adhering to the sample surface as a result of drying. Then, the samples are put for about 1 min in acetone of MOS quality. MOS stands for metal oxide semiconductor and indicates that the chemical has to fulfill high requirements for purity and contamination with particles. Afterwards the acetone is removed by placing the sample 1 min in MOS isopropyl alcohol. Finally, the sample is dried with a nitrogen gun. Inspection with an optical microscope reveals if the sample is clean and if the material has lifted off properly. If not the process can be repeated.
If Si3 N4 membranes are used, ultrasound can not be applied because it would destroy the membranes [HKS+ 05]. Instead, the membranes can be manually agitated in acetone using tweezers for a considerable time. During this process many membranes can be damaged which significantly reduces the output. A special holder was constructed to make the lift-off easier (Fig. 2.8). The membrane sample is mounted on the sample holder which fits on a glass beaker filled with acetone. In the beaker a magnetic rod stirs the liquid by a rotating magnetic field and creates a flow which facilitates the lift-off. The sample faces down so that material can fall down into the liquid away from the membrane surface. Handling of the sample, i.e. changing to other beakers and drying the sample in nitrogen, is simplified because the membrane sample is safely attached to the metal plate which can be removed (screw fit).
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48
Etching
Etching was employed using two dry etch techniques; reactive ion etching and ion milling.
2.2.4.1
Reactive Ion Etching
Reactive ion etching (RIE) is a chemical process resulting in a high selectivity, i.e. the difference of etching rates is very big for the materials being involved. For etching, a plasma is triggered by a radio frequency discharge of a gas mixture between two electrodes with the sample being mounted on one electrode. Due to the different mobility of ions and electrons, a self-bias voltage builds up so that no net current is flowing. Due to the self-bias voltage, the sample electrode is at a negative voltage almost permanently although a rf voltage is applied to initiate the discharge for the plasma. Therefore ion bombardment of the sample is almost permanent. The etch profile depends on many factors. A higher self-bias voltage leads to a higher directionality of the etching. This can be achieved by a higher rf voltage or by choosing a proper geometry of the electrodes. Other important parameters influencing the etch result are the gas pressure, the gas flow, the supplied RF-power and the substrate temperature. The BMP Plasmafab 100 etcher was used for isotropic etching. It was employed to etch chromium layers with a chlorine based process and to remove organic residues, e.g. resist or isopropyl alcohol, on the substrate surface with oxygen gas. The Cl2 and CO2 flow is typically 100 sccm and the process pressure 300 mTorr.
2.2.4.2
Ion Milling
Ion milling is a physical etch process rather than a chemical process. It is carried out with a Von Ardenne LA440S sputtering machine with 1 keV argon ions. The principle is similar to sputter deposition as described in 2.2.1.2. The difference is that here the sample serves as the target.
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Figure 2.9: Process using electron beam lithography for writing the patterns and lift-off after deposition for pattern transfer.
In contrast to RIE here a chemically inert gas, e.g. argon, is used. The base pressure is at around 10−7 mbar. Argon pressure is around 0.005 mbar and argon flow at around 14 sccm. The DC bias is around 950 V. As the etching is physically, the selectivity, i.e. the difference of etching rates between the chemical components of the materials which have to be etched, is small compared to the RIE processes being used, e.g. the chlorine based process. The etching is anisotropic, this means that vertical sidewalls can be achieved. For ion milling, structured metallic thin films and silicon based resists were used as etch masks (section 2.3.6).
2.3
Fabrication of Magnetic Structures and Devices
After having introduced writing and pattern transfer techniques, in this section it is shown how they can be combined to a give complete patterning process. Here the material and the measurements to be made define which processes are employed.
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50
Ferromagnetic Rings
In this section, the fabrication of rings on silicon substrates whose spin structure was observed using photoemission electron microscopy (PEEM, section 3.1) is described. The rings were written with an electron beam writer and the pattern was transferred using a lift-off process after deposition (Fig. 2.9). First, a 130 nm thick PMMA layer is spin-coated on a 2 × 2 cm2 and 380 - 500 µm thick silicon substrate.
The bake-out on a hotplate is 1
minute at 170◦ C. Then the substrate is ready for electron beam exposure. Arrays of rings with linewidths in the range of 100 nm to 3 µm and outer ring diameters between 2.7 µm and 10 µm are exposed. For each ring geometry, arrays with different ring separations are exposed. After exposure the sample is developed and rinsed in water, and the pattern in the resist is inspected with an optical microscope. For pattern transfer a thin film of permalloy is deposited using MBE or by sputtering. As a rule of thumb, the thickness of the deposited material should not exceed half of the resist layer thickness, although it may be possible to lift-off thicker films. A capping layer on top of the magnetic material, e.g. 2 nm of gold, prevents oxidation. The pattern transfer is completed by lifting off the unwanted material on top of the resist.
2.3.2
Wavy Lines with Constrictions
Wavy lines with constrictions down to 30 nm are fabricated by introducing triangular notches to determine the spin structure of domain walls in such narrow confinements using off-axis electron holography. A schematic of such magnetic elements with element width we and constriction width wc in addition to SEM images are shown in Fig. 2.10 (a)(c). The pattern is exposed in resist on silicon nitride (Si3 N4 ) membrane substrates (required for transmission electron microscopy) using electron beam lithography and transferred into the required material by MBE and lift-off [BHD+ 06]. First, a 5 nm chromium layer is thermally evaporated on the bottom of
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Figure 2.10: (a) Schematic of the permalloy element geometry, with element width we , constriction width wc , and notch angle of 70◦ . SEM images of (b) a wavy line with a notch and (c) a magnification of the notch which forms a constriction. The dashed lines show the writing path of the electron beam.
the membrane. This is important for electron beam exposure because the membrane is insulating. Without the chromium layer, charging would lead to a deflection of the beam and prohibit writing. Then, the membrane surface is prepared in an oxygen plasma to allow PMMA to adhere better to the substrate during spin-coating. During spin-coating, the membrane sample is fixed on a special sample holder with clips rather than a vacuum which would break the membrane. During exposure, a silicon wafer support is needed as a support for the membrane because the membrane substrate (thickness 150 µm) is too thin for the sample holder of the electron beam writer (required sample thickness at least 250 µm) and second, the support provides a sharp corner as a reference position for electron beam exposure. The relative position of the membrane window with respect to the corner of the silicon support is measured with an optical microscope. To include constrictions in the curved section of the elements, thin lines with widths of the order of 50 nm are combined together in the electron beam exposure. The writing strategy is indicated by the dashed white lines in the inset of Fig. 2.10(c) which represent the electron-beam path. The path is adjusted, and can either be continuous or have a gap at the position of the notch, to give a certain constriction width [BHD+ 06]. In order to maximize the effect of the constriction on a magnetic spin structure, the width of the constriction is made as small as possible
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Figure 2.11: SEM image of (a) a gold waveguide with Pd capping. The stripline is 10 µm in width. Rings and curves have been exposed on top of the stripline. (b) Magnification of Py halfring with and without notch. The outer diameter is 8 µm leaving a 1000 nm gap to the stripline edge.
[BSK+ 07]. After development, instead of rinsing which may break the membranes, the membranes are kept in a beaker filled with water for 20 s. In order to obtain transverse DWs [KVB+ 04a], a permalloy film with thicknesses below 20 nm is deposited in an ultra-high vacuum molecular beam epitaxy deposition chamber. Lift-off is performed using a special membrane holder as described in section 2.2.3. For closed rings the inner part of the material would not lift off without the application of ultrasound. Therefore an open geometry such as wavy lines is chosen.
2.3.3
Rings on Striplines
Rings are fabricated on striplines for dynamic measurements. Since the exposure itself is the same as described in section 2.3.1, i.e. pattern exposure by electron beam lithography and pattern transfer by lift-off, only the description of the positioning of the elements on the stripline is given here. This procedure is called overlay and the method used depends on the accuracy requirements which are approximately 1 µm in this case. The problem is to find reference points on the stripline sample which can be reproducibly measured in the electron beam writer for accurate place-
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ment of the exposed structures. This can be the corners of the substrate itself if they are sufficiently well-defined or corners of the stripline. One should be aware that an area is exposed during this measurement. Therefore the reference points should be well away from the area to be exposed. Care should be taken not to expose the isolation between contacts. Before the exposure, the position of the stripline relative to the reference points are measured in the electron beam writer. The rotation of the sample can be calculated if 2 points on the sample are measured. Then the position of the stripline can be calculated taking into account the rotation and the rings can be placed on the stripline. If no reference points can be found on the sample a two step overlay procedure has to be carried out. For this procedure (described in section 2.3.4), alignment marks are used to position the rings on the stripline. The SEM images in Fig. 2.11 show striplines samples where the gold striplines and alignment marks were produced in a lift-off procedure using photolithography in the same step. In Fig. 2.11(b) it can be seen that the magnetic elements are only 500 nm away from the edges of the stripline. This requires a high accuracy of approx. 100 nm which could be achieved because the alignment marks were sufficiently close to the stripline, i.e. 200 µm away.
2.3.4
Contacted Zigzag Lines
For the measurement of velocities and critical current densities of domain walls, zigzag lines were needed to nucleate domain walls and measure the displacement of domain walls. What is more, the elements have to be contacted to be able to apply current pulses. Magnetic elements and contacts are fabricated by pattern transfer using lift-off, but additionally an alignment procedure is needed to apply the contacts on the magnetic elements using electron beam lithography. For measurements, PEEM (section 3.1) and different transmission electron microscopy methods, i.e. electron holography (section 3.3) and the Fresnel mode of Lorentz microscopy (section 3.2) were employed. In
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Figure 2.12: SEM images (a) showing an overview of the design of the contacts. In the inset the exposure pattern of the alignment marks is shown. The area surrounded by the white frame is magnified in (b) showing different sets of 28 nm thick permalloy zigzag lines which are contacted with gold pads and wires. The set of wires surrounded by the white frame can be seen magnified in (c) showing 1000 nm-wide zigzag lines with kinks consisting of quarter rings.
the following it is described how samples for PEEM measurement are fabricated on silicon substrates. Second, it is explained what one has to take care of if membranes are needed for transmission electron microscopy techniques. 2.3.4.1
Fabrication on Silicon Substrates
At first, a 130 nm-thick PMMA layer is spin coated on a 2 × 2 cm2 silicon substrate. The choice of the silicon substrate is crucial for this kind of experiment. To avoid leakage through the substrate a material with high resistivity is preferred as a substrate. The fabrication of the magnetic elements is carried out according to section 2.3.1. Several sets of zigzag lines are written using electron beam lithography. The kinks of the lines consist of quarter rings and allow the positioning of domain walls in a controlled manner on application of a magnetic field. One set of lines comprises 4 lines each; 2 with one kink and 2 with 3 kinks (Fig. 2.12(c)) to observe more than one domain wall in the field of view of the PEEM. The lines with a single kink allow the measurement of large displacements of domain walls without them getting pinned at the next kink. The sets of zigzag lines are 220 µm apart with each having a different linewidth ranging from 100 nm to 1500 nm (Fig. 2.12(b)). In addition, two alignment marks are written on the top and the bottom of the area where the
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zigzag lines are written (see inset of Fig. 2.12(a)). Permalloy is deposited by MBE or by sputtering. If the zigzag lines are fabricated, the contacts are written by an overlay procedure using electron beam lithography in PMMA resist. To position the electron beam, the coordinates of the alignment marks are determined. A resist layer with thickness < 130 nm allows the observation of the Permalloy alignment mark below the resist using a 2.5 kV electron beam. Since the accuracy of this overlay procedure is in the order of 1 µm, the measurement can be done before alignment of the electron beam. If the accuracy needs to be better than that, the measurement should be done directly before starting the exposure. Otherwise the changing of the sample holder which has to be done for beam alignment, introduces an error of about 1 µm. A highly precise overlay is described later (section 2.3.5).
Once the position of the alignment marks is known, the position of the sets of zigzag lines and the rotation of the sample (only if the rotation is critical to the overlay) with respect to the first exposure can be calculated. The contacts consist of 70 µm-wide and 90 µm-high pads which overlap with the zigzag lines. 400 µm-wide and 400 µm-high pads close to the border of the substrate are meant for bonding, and 20 µmwide wires connect the bondpads with the pads close to the zigzag lines (Fig. 2.12(a)). After development, the samples are shortly etched in oxygen (about 3 seconds) using the BMP reactive ion etcher. This can help to remove organic residues, e.g. the resist or isopropyl alcohol. One should note that it also can cause oxidation of the sidewalls of the magnetic elements which are not protected by the capping layer. In any case the sample should not be rinsed in water at this point.
The contacts are deposited by thermal evaporation. An 8 nm chromium layer is evaporated as an adhesion layer for a 50 nm gold layer. The gold layer is evaporated in the second step without breaking the vacuum. Pattern transfer is completed by lift-off using ultrasound.
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Figure 2.13: (a) Optical image of a Si3 N4 membrane showing the gold contacts. The frames indicate the regions of (b-d). (b) SEM image of a contacted zigzag line with 3 kinks (Py 8 nm thick, 250 nm wide). (c) Exposure pattern of the corner of a big pad. The inner part is exposed using wide lines and the edges using many narrow lines to improve lift-off. (d) Exposure pattern of an alignment mark consisting of a grating with 40 µm spacing between the lines and 1 µm linewidth. The lines consist of many narrow lines to improve lift-off.
2.3.4.2
Fabrication on Si3 N4 Membranes
Zigzag lines on membranes are needed for current-pulse experiments using the Fresnel mode of Lorentz microscopy and electron holography. The high current densities required lead to considerable heating. As Si3 N4 is a bad heat conductor, the thermal effects and current-induced effects cannot easily be distinguished and above all, the structures can get damaged. To solve this problem, a 30 nm aluminum layer was thermally evaporated on a 5 nm chromium layer on the back of the membrane substrate before processing to increase the thermal heat conductance. The Si3 N4 membranes being used are from Silson Ltd., UK. The size of the membrane sample is 2.65×2.65 mm2 and the thickness 200 µm. The size of the membrane window is 500 × 500 µm2 and the thickness 50 nm. Because of the limited space for the contacts only one set of 4 zigzag lines can placed on one membrane (Fig. 2.13(a)). As the for silicon samples, the set consists of lines with 1 and 3 kinks (a line with 3 kinks is shown in Fig. 2.13(b)). The pads close to the zigzag lines are rhomboids with the parallel sides of 150 µm and 310 µm length being 80 µm apart. The bondpads are 500 × 500 µm2 in size and the wires are 50 µm-wide. To make lift-off possible without ultrasound, it is important to write frames
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Figure 2.14: Schematic representation of the evaporation of gold contacts on the edges of the membrane sample if the resist layer is too thick to be exposed using electron beam lithography. Wafer pieces fixed with clamps cover the inner part of the membrane sample. The resulting contact pad can be seen in Fig. 2.13(a).
consisting of lines with small linewidth around the contacts, which gives sharp resist edges (Fig. 2.13(c)). Alignment marks located on the membrane frame are used to position the contacts (Fig. 2.13(d)). The resist close to the border of the membrane substrate is too thick to be exposed with a low energy electron beam. In order to fabricate bond pads the inner parts of the design are covered with a wafer piece and gold is deposited directly on the substrate (to the left in Fig. 2.13(a) and schematic representation of the evaporation procedure in Fig. 2.14).
2.3.5
Contacted Notched Rings with Antenna
Domain walls trapped in a potential can be excited by an oscillating magnetic field. The notch can serve as a pinning potential and the oscillating magnetic field can be provided by an alternating current. The behaviour of the domain wall can be investigated by measuring the magnetoresistance. The sample which was constructed to meet this requirement con-
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Figure 2.15: Scheme of the exposed structures during each of 3 steps; ring with notches (a), small contacts applied to the ring with notches (b), big contacts and antenna (c).
sists of a ring with several notches to pin the domain wall (Fig. 2.15 and 2.17). Contacts close to the notch allow the magnetoresistance to be measured. A gold wire with a round shape inside of the ring serves as an antenna providing an oscillating magnetic field. In the first step, a ring with notches similar to the wavy lines with notches (Fig. 2.15(a)) is fabricated by pattern transfer using lift-off (see section 2.3.2). 23 × 23 mm2 silicon wafer substrates are cut with a wafer saw providing straight, orthogonal edges which improve the positioning of the substrate in the sample holder, facilitating the precise overlay procedure required to create this device. Since the MBE deposited permalloy film is only 12.5 nm thick, the resist can be thin (52 nm). The outer ring diameter is 10 µm and the line width 500 nm. Each ring has 7 notches, at the bottom a ring segment is missing giving an opening. This opening is important for magnetoresistance measurement and application of currents to obtain a well-defined current flow direction. It also serves as opening for the antenna. Arrays consisting of 15 × 15 rings each are fabricated with a 80 µm period in each direction. Besides the rings several alignment marks were exposed having 5 mm separation from each other and being 5 mm away from the first row of ring arrays. After the fabrication of the rings with notches, the substrate is spun
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Figure 2.16: Scheme showing the position of the alignment marks with respect to the devices. The origin (”0”) of the coordinate system is the starting point of the GLOKOS routine. The detected regions are indicated by lines and the order of detection is given by the numbers. The magnification shows the geometry of an alignment mark.
with a resist layer of 130 nm PMMA. Care has to be taken that the aligment marks can be detected with the highest precison. Therefore a piece of silicon is put on top of the alignment marks during spin coating to prevent the marks to be covered by the resist. Any remaining resist can be removed with acetone. The best method here is to take a cleanroom tissue soaked with acetone and press it with a tweezer on the sample. Contact of the acetone with the resist close to the ring arrays must be prevented. During the second lithography step small line contacts with 150 nm linewidth are written (Fig. 2.15(b)). The two contacts for each notch should be as close and as symmetrical as possible to each notch. This requires an accuracy of tens of nanometers which demands that any rotation of the sample with respect to the first exposure has to be compensated. In the following it is described how the coordinate system of the electron beam writer can be transformed to match it again with a rotated sample. With the so-called GLOKOS (Globales Koordinaten System) procedure alignment marks on the sample are detected using sweep routines
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of the electron beam and from this the rotation and position is calculated. As mentioned before the alignment marks have to be free from resist because otherwise the sweep routines might work not precisely enough or might simply fail. Then, the coordinate system of the electron beam writer is transformed accordingly. Therefore the exposure data needs to be changed. During a trial run of the GLOKOS routine it should be checked if the alignment marks can be detected at all positions (indicated in Fig. 2.16 in the same order as they are detected). This is important because remaining resist or particles can still disturb the detection procedure. In this case the routine can be modified to search at an alternative position. The starting position of the routine has to be saved which represents the zero point of the coordinate system (”Origin” in Fig. 2.16). This means that all writing positions for the exposure have to be relative to this (arrow in Fig. 2.16). After the fundamental alignment of the electron beam, the holder is exchanged and this introduces an error of the beam position which is in the order of 1 µm. Therefore it is essential to measure the starting position coordinates after the holder exchange and immediately before starting the electron beam exposure. Finally the exposure can be started which includes the GLOKOS routine and the writing of the pattern. The GLOKOS routine can not compensate a z-tilt of the sample, i.e. if the sample substrate does not lie flat, and inaccuracy of the stage. Especially the tilt of the sample can significantly reduce the precision of the overlay to several 100 nm. The required precision can be achieved as follows: an array of rings is produced where the positions of the small contacts with respect to the rings are shifted from ring to ring by multiples of 80 nm, e.g. -7×80 nm, -6×80 nm,..., 0×80 nm,..., 6×80 nm, 7×80 nm both in x and y direction. After exposure of the fine contacts, the ring with the most accurately positioned contacts is found using an optical microscope and only this ring is processed further. During the deposition of the 8 nm Cr/50 nm Au layer for the small contacts the alignment marks have to be covered with wafer pieces as they will be used again for the final step. In the third and final step, large contacts and the antenna are written
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Figure 2.17: SEM image of a notched permalloy ring of 10 µm outer diameter, 500 nm linewidth, and 12.5 nm thickness. The ring includes 7 triangular notches with an opening angle of 70◦ each forming a constriction. Small gold pads contact the ring close to the constrictions leading to wires which end in bigger pads. A microwave antenna inside of the ring provides an oscillating magnetic field.
in a resist layer of 130 nm PMMA (Fig. 2.15(c)). The alignment procedure is carried out in the same way as described in step 2. This step requires a high precision, and only one attempt can be made to put the big contacts on the fine contacts. Therefore the overlap of the large contacts with the small contacts has to be big enough, e.g. 2 µm. For the arrangement of the contacts and antenna, attention has to be paid that none of the rings with contacts in the surrounding area short circuits the device. An SEM image of a device is shown in Fig. 2.17.
2.3.6
Patterning Techniques for Epitaxial Films
Several approaches to pattern an epitaxial film, i.e. Fe3 O4 have been used. One can distinguishs between pre- and post-patterning. In the first case, a raw substrate is patterned and the magnetic material is deposited afterwards. This results in an array of elevated structures and continuous material beneath. The post-patterning was carried out directly on the film after deposition. The pre-patterning has the advantage that damage during etching of the film is avoided since the deposition occurs after patterning. The disadvantage is that current pulse experiments are not
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Figure 2.18: Overview of patterning methods using electron beam lithography for pattern writing and etching for pattern transfer. (a) Pre-patterning of a substrate and (b) postpatterning of a magnetic film using metallic etching masks. (c) Post-patterning using a PMMA/HSQ resist combination as etching mask.
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always possible because the material on top of structures may not be isolated from material between structures in the valleys. This problem is avoided in a post-pattering process. In addition, the growth on the raw substrates can be much better controlled. However, damage of the film during processing can occur and if insulating substrates are used charging can make measurement and adding contacts with an electron beam overlay procedure very difficult. The charging problem can be solved by removing only small areas of the Fe3 O4 film to electrically isolate the contacts from each other. The damage problem was addressed by using a resist combination as etching mask instead of metal layers. The details are discussed below. It is explained why this problem could still not be solved and how this process can be optimized to serve as a non-destructive technique for Fe3 O4 and other epitaxial films.
2.3.6.1
Pre-patterned Substrates for Fe3 O4 Contacted Zigzag Lines
Pre-patterning of MgO substrates was performed by a combination of pattern transfer using lift-off to fabricate a metallic etch masks and subsequent dry etch steps to transfer the pattern into the substrate (Fig. 2.18(a)). In the first step, a 100 nm thick chromium mask is evaporated on the substrate. Then, an 80 nm PMMA resist layer is spin-coated on the chromium mask. The resist is exposed using electron beam lithography, and developed and rinsed in water after the exposure. In the next step, a 20 nm aluminum layer is deposited by evaporation and the unwanted material lifted off. Oxygen plasma etching is used to remove any organic rests from the sample. The pattern in the aluminum is transferred into the chromium by reactive ion etching using a chlorine plasma. The etch rate is around 1 nm/sec. The double layer structures of chromium with aluminum on top provide a etch mask for ion milling the MgO. The ion milling etch rates depend on the material and are difficult to determine due to the many layers in the sample and were not reproducible due to modifications to the sputter equipment. Typically the etching time
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Figure 2.19: SEM images of (a) Fe3 O4 rings fabricated by post-patterning using a metal mask and (b) Fe3 O4 wires with kink using a resist mask.
is around 45 - 60 min for the parameters given in section 2.2.4.2. After etching to the required depth any remaining chromium is removed using again chlorine etching. The etching of the chromium can be stopped as soon as no metal mask remains. Finally, the prepatterned substrate consists of a pattern of plateaus on the substrate corresponding to the electron beam exposed structures.
2.3.6.2
Post-patterned Fe3 O4 Rings
Using metal mask
Post-patterning of Fe3 O4 films is performed using
the same patterning process as described for the pre-patterning of MgO substrates (Fig. 2.18(b)). This means that the Fe3 O4 film is deposited before patterning. Therefore, the patterned plateaus consist of the MgO substrate coated with Fe3 O4 while the material between the plateaus is removed (Fig. 2.18(b)). The influence of the patterning steps, e.g. reactive ion etching and ion milling, on Fe3 O4 is not well understood. It seems that the material is affected. Special care should be taken not to overetch during the final chlorine etch step. The SEM image in Fig. 2.19(a) shows rings made of Fe3 O4 . A magnetic contrast could not reproducibly be measured using XMCD-PEEM (section 3.1). Magnetic force microscopy (MFM) measurements were more successful. MFM is sensitive to stray field originating from all parts of the thin film layer while XMCD-PEEM
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is only sensitive to the first 5 nm of the thin film. This leads to the conclusion that the top part of the thin film is damaged or material is deposited during the etch or ion bombardment steps. Also intermixing with the chromium layer is possible. Using resist mask
To avoid the interference of the metallic etch mask
with the Fe3 O4 film, a combination of PMMA and HSQ can be used instead as described in [ASA+ 05]. In Fig. 2.18(c) the process steps are shown. 80 nm PMMA and 160 nm HSQ double layer resist are spun on the Fe3 O4 film successively. Exposure of this double layer of resist needs a higher energy of at least 5 keV of the electron beam. This resist mask protects the film during ion milling for 35 min. The remaining resist can be removed by dissolving PMMA in acetone and using ultrasound which also removes the HSQ layer on top of the PMMA layer. The SEM image in Fig. 2.19(a) shows lines with a kink and pads made of Fe3 O4 . The result was the same as for Fe3 O4 films processed using metallic etching masks; magnetic contrast was not observed in these samples using XMCD-PEEM. The damaging of the Fe3 O4 film can be explained by a too thin HSQ layer which does not protect the film suficiently during ion milling. For the future a thicker layer of HSQ could be tried out to protect the magnetic film better. A thicker HSQ resist thickness requires a high energy of the electron beam to expose the resist, e.g. a 500 nm thick HSQ resist can be exposed by a 30 keV electron beam [ASA+ 05]. Such a thicker resist would offer a better protection during ion milling. No metallic etch mask is needed which may interfere with the film. Furthermore the RIE etch steps are avoided and chemically reactive gases like chlorine cannot interfere with the Fe3 O4 film.
Chapter 3 Measurement Techniques In this chapter, the various techniques used to measure the spin structure of ferromagnetic elements are presented. Each technique has its own advantages and disadvantages: XMCD-PEEM (section 3.1) is a nonintrusive technique and is element specific. The main disadvantages are that discharges can destroy the sample and that measurement in an applied magnetic field >50 Oe is hardly possible. Lorentz microscopy comprises several measurement modes. One of them is the Fresnel mode (section 3.2) which makes the positions of domain walls visible, has a sufficient resolution to make visible the position of domain walls and the image interpretation is straightforward. Another mode is electron holography (section 3.3) which provides the same high resolution but, in addition, the images give quantitative information about the magnetic induction following some time consuming image processing. Electron holography and Fresnel microscopy both have the disadvantage that the sample preparation is difficult since the magnetic elements have to be fabricated on fragile membranes. Finally Kerr microscopy was employed to measure the hysteresis loops of ferromagnetic films and elements (section 3.4) and magnetoresistance measurements employed to determine the position of domain walls in ferromagnetic elements (section 3.5). In the following section, these measurement techniques are explained in more detail.
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Figure 3.1: (From [SS06]) The X-ray magnetic circular dichroism (XMCD) effect illustrated for the L-edge absorption in Fe-metal. The color code of the spectra corresponds with the shown sample magnetization.
3.1
XMCD-PEEM
X-ray magnetic circular dichroism (XMCD) is a technique which can be used to investigate the magnetization of a ferromagnet. This is due to the difference of x-ray absorption if the spectroscopy experiment is performed using circular polarized light of opposing helicity (section 3.1.1). This effect can be measured with a photoemission electron microscope (PEEM) revealing the spin structures in a sample (section 3.1.2).
3.1.1
X-ray Magnetic Circular Dichroism
In x-ray absorption spectroscopy (XAS) electrons are excited from a core state to a valence state. For a magnetic transition metal this can be the transition from a 2p core state into free states in the valence band above the Fermi level. The ferromagnetism of transition metals is dominated by the 3d valence electrons whereas s and p electrons contribute less. The absorption spectrum is the convolution of the initial states with the density of unoccupied states above the Fermi level. Because of the spin-orbit interaction, the 2p core states are energetically split into 2p1/2 and 2p3/2
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Figure 3.2: Schematic of the photoemission electron microscope (PEEM) at the Surface / Interfaces Microscopy (SIM) beamline at the Swiss Light Source (SLS) (courtesy of Ch. Quitmann, SLS).
levels which give rise to the maxima of the intensity near the L2 and L3 absorption edges. If light is circularly polarized, depending on the helicity of the light, more electrons of one spin direction are excited into the unoccupied 3d states than of the other spin direction. For a ferromagnet the density of unoccupied states is different for the two spin directions (Fig. 3.1). Consequently the number of possible transitions depends on the alignment of the light helicity with respect to the direction of the magnetization. This leads to a difference in absorption for opposite helicities (XMCD).
3.1.2
Photoemission Electron Microscopy (PEEM)
Photoemission electron microscopy (PEEM) was pioneered by Tonner et al. [TH88]. Here, photoelectrons are detected which are generated by xray absorption. Stöhr et al. [SWH+ 93] imaged the magnetic domains of a ferromagnet with PEEM employing the XMCD effect . Despite the name,
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the secondary electrons are detected. The schematic of the ELMITEC PEEM at the Surface / Interfaces Microscopy (SIM) beamline [QFP+ 01] at the Swiss Light Source (SLS) is shown in Fig. 3.2 and the following description is based on it. The sample is illuminated by a monochromatic, circularly polarized x-ray beam with a 100 µm spotsize and angle of 16◦ with respect to the sample surface. As a result of the x-ray absorption, electrons are emitted with a broad range of energies from zero to the energy of the absorbed photons minus the workfunction of the material. Only electrons with a kinetic energy greater than the workfunction are able to leave the sample. These electrons are directed towards the analyzer by applying 20 kV between the grounded sample and the objective lens of the microscope. The kinetic distribution of the electrons leads to chromatic aberration. With slits and a hemispherical energy analyzer these aberrations can be reduced. The energy filtering is tuned to the photo secondary electrons which have a small range of kinetic energy of about 1-2 eV. For finetuning to the maximum intensity of the secondary electrons the start voltage is adjusted. Secondary electrons provide a good combination of signal intensity and spatial resolution. For detection the secondary electrons are projected on a electron multichannel multiplier and converted to visible light by a phosphor screen which is imaged with a CCD camera. The first step after alignment of the sample is to find the correct energy of the desired absorption edge which is a characteristic of the material. For example, the energy is tuned to 707 eV to measure at the L3 absorption edge of iron. Now, two images are taken with opposite helicities of the circular polarized light and subtracted by the imaging software. The XMCD signal is highest if the orientation of the helicity and the magnetization are parallel to each other, lowest if they are antiparallel to each other and zero if they are perpendicular. If a second image of the sample rotated by 90◦ is taken, full information about the in-plane magnetization can be obtained. More details about XMCD-PEEM can be found in [Kuc05] and [SS06].
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Figure 3.3: (From [PLC05]) Schematic ray diagram indicating the path followed by electrons passing through a magnetic specimen. A lens converges the electron beam and an aperture blocks parts of the electrons. The image contrast is shown at the bottom.
3.2
Lorentz Microscopy
Lorentz microscopy comprises several different imaging modes which make use of the fact that electrons which travel through a magnetic field experience a deflection. For this transmission electron microscopy (TEM) technique, an electron beam is generated which passes through a magnetic sample. The Lorentz force acting on the electrons can be written as: → − → − − F = e(→ v × B ),
(3.1)
− where e = −1.60217646×10−19 C is the electron charge, → v is the veloc→ − ity of the electrons, and B is the magnetic induction averaged along the electron trajectory. Components of the induction normal to the electron beam cause a deflection. Additionally, stray fields above or below the sample contribute to the deflection. These are not significant in samples with in-plane magnetization. The Lorentz deflection angle is in general
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very small and depends on the sample thickness and the electron wavelength. In Fig. 3.3 the principle of two of the imaging modes of Lorentz microscopy are shown. In Fresnel mode, an out-of-focus image of the sample is taken. The domain walls appear as bright (convergent) or dark (divergent) lines. Imaging in this mode is easy to implement and can be used for real-time studies of magnetization reversal or current-induced domain wall propagation. Its disadvantage is that defocusing reduces the spatial resolution. In Foucault mode, the image is taken in-focus but one of the split spots in the diffraction pattern is blocked by an aperture. The contrast results then from the magnetization within the domains: Bright areas correspond to domains where the magnetization orientation is such that electrons are deflected through the aperture and dark areas to those where the orientation of magnetization is aligned antiparallel to this direction i.e. the electrons are blocked by the aperture. The difficulty of this technique is the precise alignment of the aperture. Electron holography as a further Lorentz microscopy mode is described in section 3.3. For this work the Fresnel mode was employed as an alternative to electron holography. Its advantage is the fast imaging. Therefore it is suitable to observe the displacement of domain walls in current pulse experiments. More details and image examples concerning Lorentz microscopy can be found in [PLC05, Hey91].
3.3
Electron Holography
As mentioned before, electron holography is a Lorentz microscopy technique where the electrons are transmitted through the sample. Here, two or more coherent electron waves are interfered to produce a hologram. In off-axis electron holography, the most commonly used electron holography method, an electrostatic biprism is used to overlap the electron wave scattered by the sample with the reference wave which usually goes through vacuum [MD55]. From the interference pattern, the amplitude
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. Figure 3.4: (From [DBMK+ 00]) (a) Schematic of electron holography. (b) Schematic illustrating the use of specimen tilt to provide the in-plane component of the external field for in situ magnetization reversal experiments.
and phase shift of the electron wave that has passed through the sample can be reconstructed. The phase shift can be used to provide quantitative information about electrostatic and magnetic fields within the sample to a resolution that can approach the nanometer scale under optimal conditions [MDBS05, DBMK+ 00]. The phase shift of the electron wave is due to the mean inner potential of the sample and the in-plane component of the magnetic field integrated along the beam direction. The phase change relative to the reference wave is given by Z φ(x) = CE
e V (x, z) − ~
Z Z B⊥ (x, z)dxdz,
(3.2)
where z is the incident beam direction, x the direction in the plane of the sample, V the mean inner potential, and B⊥ is the component of the magnetic induction perpendicular to both x and z. The constant CE is given by the expression 2π E + E0 , (3.3) λE E + 2E0 where λ is the wavelength, and E and E0 are the kinetic and rest mass CE =
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energies, respectively, of the incident electron. If neither V nor B vary with z within the sample thickness t, and neglecting any electric and magnetic fringing fields outside of the sample, this expression can be simplified to e φ(x) = CE V (x)t(x) − ~
Z B⊥ (x)t(x)dx.
(3.4)
Differentiation with respect to x leads to d e dφ(x) = CE (V (x)t(x)) − B⊥ (x)t(x). dx dx ~
(3.5)
In the easiest case the sample has uniform thickness and composition. Then the first term on the right side in Eq. 3.5 is zero and the phase gradient can be interpreted directly as the in-plane magnetic induction. For non-uniform samples additional processing is required. In order to interpret the magnetic contribution to the phase of the hologram, the mean inner potential contribution may have to be subtracted from the recorded phase image. This mean inner potential contribution can be obtained from the phases of pairs of holograms that differ only in the (opposite) directions of magnetization within each patterned element. The magnetic and mean inner potential contributions to the phase are then calculated by taking half the difference and half the sum of the phases of the two holograms, respectively [DBMSP98]. The measurements were carried out at the Department of Materials Science and Metallurgy at the University of Cambridge using a Philips CM 300-FEG TEM. A field emission electron source provides electrons which are accelerated by a potential of 300 kV towards the sample. The biprism causing the overlap of the electron beams consists of a quartz wire coated with Pt or Au and having a diameter smaller than 1 µm. A positive voltage of 50 V to 200 V is applied to it. The domain walls can be nucleated using the magnetic field produced by the objective lens of the electron microscope. The interference pattern is recorded with a CCD camera and has to be processed digitally to give magnetic induction maps.
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Figure 3.5: (From [BHD+ 06]) Magnetic induction map recorded using electron holography placed over an equivalent bright field image to show the shape and position of threequarter permalloy rings (350 nm linewidth, 1.65 µm outer diameter and 10 nm thickness with a 70 nm spacing between them). A magnetic field Ha was applied along the indicated direction and relaxed to zero before recording the image.
Further image processing makes the magnetic flux lines inside and outside of the magnetic elements visible. An example for a magnetic induction map can be found in Fig 3.5. Here electron holography was employed to image the spin structure in three-quarter rings [BHD+ 06]. The contours correspond to magnetic lines of force associated with the magnetic dipolar moments of the magnetic material. The direction and relative strength of the field is given by the direction and the density of the lines, respectively. The colour within the magnetic elements indicates the field direction and strength when compared with the colour wheel shown in Fig. 3.5. Sample preparation is more challenging because the magnetic elements have to be fabricated on fragile transparent membranes (section 2.2.3).
3.4
Kerr Microscopy
J. Kerr discovered in 1877 that for linearly polarized light reflected at a magnetic material, there is a rotation of the polarization direction [Ker77]. To understand the physics behind this effect, one can consider the Lorentz force acting on light-agitated electrons. The incident light causes electrons in the magnetic material to oscillate parallel to the plane of polar-
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Figure 3.6: Depending on the magnetic sensitivity direction, three different MOKE effects can be distinguished: (a) longitudinal (magnetization in the plane of incidence of light and in the plane of the interface), (b) transverse (magnetization perpendicular to the plane of incidence of light) and (c) polar (magnetization in the plane of incidence and perpendicular to the interface).
ization. Regularly reflected light is polarized in the same plane as the incident light. At the same time, the effective magnetic field produced by the magnetization acts on the resonant electrons due to the Lorentz force and introduces a small component of vibrational motion perpendicular to the original oscillation and to the magnetization. This secondary motion of the electrons generates a secondary amplitude, the Kerr amplitude (Huygens’s principle). The superposition of the regularly reflected light and the Kerr amplitude leads to a magnetization-dependent polarization rotation. One can distinguish between different Kerr effects depending on the magnetic sensitivity directions. The longitudinal and the transverse Kerr effect measure components of the magnetization parallel and normal to the plane of incidence which are in both cases parallel to the sample surface. The polar Kerr effect measures magnetization components normal to the sample surface (Fig. 3.6(a-c)). For the longitudinal Kerr effect the light beam has to be inclined relatively to the surface. It yields a magnetooptical rotation both for parallel and perpendicular polarization of the incoming light with respect to the plane of incidence. For a light beam normal to the sample surface no rotation is detectable. The set-up for the Kerr microscope used in this thesis is shown in Fig. 3.7. It employs the longitudinal Kerr effect. An argon ion laser beam (wavelength 488 nm) can be focused to a spot on the sample of minimum
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Figure 3.7: (From [MMK+ ]) Schematic representation of a Kerr microscope.
diameter 1 µm. An oscillating external magnetic field can be applied to the sample with a magnetic field frequency up to ~1 kHz and an amplitude of 500 Gauss. Here a 50/50 beam splitter splits the laser beam after reflection from the sample surface and the two beams are each detected by a photodiode. Differential photodetection and averaging over 1000 field loops ensures that the signal-to-noise ratio is high. Kerr microscopy is applicable if the sample has a reflective surface which is the case for metallic thin films. Since measuring in an external magnetic field is possible, hysteresis loops can be recorded. Information about the magnetization reversal can be retrieved by this method, e.g. for cobalt antidot arrays (section 5). In Fig. 5.2 of this section examples of hysteresis measurements are shown.
3.5
Magnetoresistance Measurements
This technique makes use of the fact that the resistance of a magnetic element depends on its magnetization configuration. The experimental setup described here was built by M. Laufenberg [Lau06]. It consists of a bath cryostat which allows measurement at temperatures between 1.6 K and 300 K. With a vector field setup, an in-plane magnetic field can be
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Figure 3.8: (From [Büh05]) Measurement circuit for pulse injection and consecutive resistance measurement.
applied in any desired in-plane direction. It consists of a resistive magnet with a core which provides magnetic fields up to 520 mT and is stabilized with an accuracy of about 0.01 mT. A single solenoid perpendicular to the first delivers fields up to about 130 mT. For resistance measurements, a lock-in technique was used, which means that the frequency of the lockin current can be optimized for the best signal-to-noise ratio, and that noise at different frequencies is greatly reduced. The input signal is multiplied by a reference signal, and integrated over a specified time. The resulting signal is essentially a DC signal, where the contribution from any signal that is not at the same frequency as the reference signal is essentially attenuated to zero, as well as the out-of-phase component of the signal that has the same frequency as the reference signal. To eliminate the influence of the electric leads, 4-point measurements were performed, from which the resistance of just the area of the magnetic element between the voltage contacts can be extracted. Furthermore, a DC current can exert a force on magnetization via a spin-torque effect which influences the measurement, whereas the total force exerted by an AC current is averaged out to zero. By applying a magnetic field while monitoring the resistance, the domain wall depinning fields are determined.
Chapter 4 Domain Walls in Confined Systems The knowledge about the spin structure of domain walls in patterned magnetic films is essential for understanding current-induced [KJA+ 05] and field-induced domain wall motion [NTM03, BNK+ 05]. For a better understanding of the physics involved but also for applications, solutions are sought to increase the efficiency, e.g. the current-induced domain wall velocity. This can be achieved by a reduction of the dimensions or by using materials with a high spin-polarization. Control of the domain wall behavior, and in particular of the magnetic switching, is essential for applications. One possibility for control is the use of artificial pinning centers. Towards this aim the pinning potential of constrictions is studied. First, a brief introduction into domain walls in bulk materials, thin films, and nanostructures is given in section 4.1. Then, the following topics are discussed: • Transverse Domain Walls in Nanoconstrictions (section 4.2) The spin structure of domain walls in magnetic wires and rings elements has been largely investigated [MD97, KVB+ 04a, LBB+ 06a], but the influence of further miniaturization remains unclear. For the first time the spin structure of transverse walls found in constriction down to 30 nm is directly measured using electron holography. For
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narrow constrictions a new method is developed to determine the shape of the transverse walls. The walls are classified and the distribution of transverse wall types being found in a certain constriction range is summarized. A definition for the domain wall width is proposed and the dependence of the domain wall width on the constriction width is presented. Simulations are performed using a Heisenberg model which are compared with the experimental results. • Pinning of Domain Walls (section 4.3) The pinning potential of constrictions formed by a notch is investigated. To correlate the strength of the pinning potential with the wall spin structure, the nanoscale spin structure and position of head-to-head and tail-to-tail domain walls is measured using electron holography. From the nanoscale wall configuration, the energy barrier to depin the wall from a constriction is quantitatively determined using simulations. A comparison with the experimentally measured depinning field reveals that the depinning field is a good measure for the energy barrier height connected with the pinning potential. • Spin structure of CrO2 (section 4.4) For elements consisting of a high spin-polarized material like CrO2 , a method is required to measure the spin structure using measurement techniques like PEEM. Direct measurement of the CrO2 turns out to not to be possible. Assuming exchange coupling of a permalloy layer deposited on top of the CrO2 film, the spin structure of the permalloy layer should reflect the spin structure of the CrO2 layer. The coupling turns out to be more complicated than expected, revealing interesting coupling effects between the two layers.
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Figure 4.1: (From [HS98]) The rotation of the magnetization vector from one domain through a 180◦ wall to the other in an infinite uniaxial material. Two alternate rotation modes are shown: the Bloch wall (a) and a Néel wall (b).
4.1
Introduction to Domain Walls
The spin structure of domain walls in a ferromagnetic material is strongly dependent on the geometry of the system under consideration [HS98]. In an infinite uniaxial material, the spin structure of a planar 180◦ wall separating two domains of opposite magnetization can have two configurations. In a Bloch wall the magnetization rotates parallel to the wall plane (Fig. 4.1(a)) and in a Néel wall the magnetization rotates in a plane perpendicular to the wall plane. In a bulk material, the Bloch wall is the more favourable domain wall type because there will be no magnetic divergence inside the wall so that there are no uncompensated magnetic charges on the face of the wall, giving zero stray field energy. The Bloch wall structure can be calculated using equation [HS98] x sinϕ = tanh( p ) A/K
(4.1)
with ϕ the magnetization angle and x the direction normal to the wall. p The Bloch domain wall width is defined as wDW = π A/K according to Lilley [Lil50]. If the thickness of the film is of the order of the domain wall width, the stray field generated by the out-of-plane component of the magnetization
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Figure 4.2: (From [LBB+ 06a]) Spin structure of a vortex wall (a) and a transverse wall (b) simulated using the OOMMF code [OOM]. PEEM images of rings with thickness / width / outer diameter: 30 nm, 530 nm, 2.7 µm (c), 10 nm, 260 nm, 1.64 µm (d), and 3 nm, 730 nm, 10 µm (e). The gray scale shows the magnetization direction.
of a Bloch wall becomes considerable. In this case a Néel wall (Fig. 4.1) can have a lower energy than the classical Bloch wall if the domain wall width is larger than the thickness of the film [Née55]. More complicated walls, e.g. cross-tie walls, consisting mainly of 90◦ Néel walls instead of 180◦ Néel walls [FT65], are the lower energy configuration at intermediate thicknesses. Above all, magnetocrystalline anisotropies, defects and roughness influence the spin structure. Modern patterning techniques allow the fabrication of thin film ferromagnetic elements. Here the geometry rather than the material parameters determines the domain wall type and spin structure. Domain walls confined in wires or ring elements exhibit head-to-head or tail-totail wall structures with two types prevailing: transverse and vortex domain walls [MD97, KVB+ 04a, LBB+ 06a]. In 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. Therefore these ring structures were intensively used to study the influence of the thickness and width of the rings on the domain wall type. The theoretical predictions for the domain wall type [MD97] were confirmed
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experimentally for polycrystalline hcp cobalt [KVB+ 04a] and for permalloy [LBB+ 06a]. As seen in Fig. 4.2, the magnetization configurations are rather complicated and it is not obvious how such domain walls can be characterized by a domain wall width.
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83
Transverse Domain Walls in Nanoconstrictions
4.2.1
Introduction
Since modern patterning techniques allow the reduction of the dimensions of ferromagnetic elements, the question arises how the spin structure is affected. This is of great importance because many interesting effects, e.g. the velocity in current-induced [KJA+ 05] and field-induced domain wall motion [NTM03, BNK+ 05], depend on the spin structure and width of domain walls. Nakatani et al. [NTM05] simulated the spin structure in nanowires with linewidths in the range from 40 to 500 nm and found transverse and vortex walls and in addition a type not considered before: asymmetric transverse walls. Direct imaging of such domain walls, in particular very narrow ones, would be of high interest because non-adiabatic contributions to the electron transport are predicted to become significant if the domain wall width becomes equal or smaller than the relevant length scales [ZL04, TNMS05, XZS06]. This would increase the current-induced domain wall velocity, important for applications. Bruno [Bru99] predicts for Bloch walls that a reduction of the lateral dimensions is necessary to reduce the domain wall width. By introducing triangular notches in the magnetic elements, constrictions down to 30 nm can be fabricated [BHD+ 06]. It would be interesting to determine the domain wall width here but this is already beyond the resolution of measurement techniques like PEEM (section 3.1) and so another higher resolution measurement technique is required. The necessary high-resolution is provided by electron holography and in this section, for the first time measurements of the spin structure in constrictions down to 30 nm are presented using this techiques. In section 4.2.2, it is described how transverse walls are found inside the constrictions, which can be categorized into three different transverse wall types. The experimentally found domain wall types are compared with the theoretical predictions. In section 4.2.3, the distribution of domain
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Figure 4.3: Schematic of the permalloy element geometry, with element width we , constriction width wc , and a notch angle of 70◦ .
wall types found in a certain constriction range is presented. In section 4.2.4, the dependence of the domain wall width on the constriction width is investigated. Since the spin structure of head-to-head domain walls in such elements is quite complicated (see section 4.1), a definition for the domain wall width is proposed. In section 4.2.5, simulations are performed using a Heisenberg model which are compared with the experimental results. Parts of this chapter have been published in Ref. [BHD+ 06, BSK+ 07].
4.2.2
Domain Wall Types
The detailed spin structure of wavy lines with notches forming a constriction was imaged using electron holography. The magnetic elements consisted of permalloy films with thicknesses of 5 to 20 nm. The element width we was between 100 - 400 nm and the constriction width wc could be made as small as 30 nm. A schematic of such magnetic elements is shown in Fig. 4.3. A detailed description of the fabrication process is given in section 2.3.2. While it is already known that transverse walls are located within the constriction and vortex walls adjacent to it depending on geometry (see section 4.3), the detailed spin structure of transverse walls in constrictions varying wc , we and the element’s thickness (Fig. 4.3) has to be determined. Electron holography images of domain walls in large constrictions could be directly used to determine the shape of the transverse walls. Here the opening angle of the transverse wall can be measured.
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Figure 4.4: (a-c) Off-axis electron holography images of the observed transverse domain wall types with 11 nm permalloy thickness; wc / we : (a) 138 nm / 400 nm, (b) 103 nm / 300 nm, (c) 191 nm / 300 nm. The color code for the magnetization direction is given in Fig. 4.11. The domain wall opening angle αDW is shown in (a).
However, for narrow constrictions it is not possible to measure the opening angle because of a lack of resolution and contrast. Therefore several methods were developed to determine the spin structure of domain walls in small constrictions. A comparison of the domain wall shape and angle with experimental results for wide constrictions revealed the reliability of each method. The fixed threshold method (section 4.2.2.2) turned out to show a good agreement and was therefore chosen to investigate the spin structure in narrow constrictions. 4.2.2.1
Shape of Domain Walls in Wide Constrictions
From the high spatial resolution electron holography images, the shape of the domain walls in wide constrictions with wc & 50 nm could be determined systematically. It helps if the images exhibit the magnetic flux lines where the boundary between a domain wall and the surrounding domains can be recognized easily. In agreement with micromagnetic predictions [NTM05], symmetric (Fig. 4.4(a)) and asymmetric tilted (Fig. 4.4(b)) transverse walls were found experimentally. Furthermore, a third type was found; because of its shape, this wall is given the name: asymmetric buckled transverse domain wall type (Fig. 4.4(c)). All three types have a triangular shape in
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common, with the opening angle of this triangle defined as the domain wall angle αDW (as indicated in Fig. 4.4(a)). The dashed line marks the threshold between the domain wall (indicated by “DW”) and the surrounding domains (indicated by “DL ” and “DR ”). It marks the location where the magnetization changes its direction half with respect to the magnetization in the domain wall (“DW”) and in the domains (“DL ” and “DR ”, respectively) if a magnetic flux line is followed (Fig. 4.4(a)). This method yields important qualitative results about the shape of the domain wall. For wide constrictions, αDW could be measured. This measurement could be used to test the reliability of other methods. It was not possible to determine the shape of the domain walls in the smallest constrictions because of a lack of resolution. In the next sections a solution to this problem is addressed.
4.2.2.2
Shape of Domain Walls in Narrow Constrictions
Three different methods are presented to determine the shape of transverse domain walls which use line profiles of the magnetization. These line profiles are derived from the magnetic induction maps. The methods differ in the definition of the threshold between domain wall and surrounding domains and how the position of this threshold is detected. Once the threshold is defined, the shape of the domain wall can be easily derived using the line profiles. In the inset of Fig. 4.5, line profiles parallel to the upper edge of the magnetic elements are shown. A software was developed which automates the edge detection. Roughness of the edges is compensated by a smoothing procedure which averages each point of the edge with a certain number of neighbours, e.g. 10 next neighbours in both directions. Line profiles are taken through each point in the constriction along y, between the top of the notch and the top of the magnetic element at a spacing given by the pixel size. In Fig. 4.5, the orientation of magnetization is shown following the three line profiles indicated in the inset; one is at
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Figure 4.5: Three line profiles showing the rotation of magnetization with respect to the vertical direction.The sign convention is indicated in the inset (bottom left). The shape of the line profiles is shown in the inset (top right). They are parallel to the top edge of the magnetic element. The positions of the line profiles in the constriction are indicated by the colors and the symbols, respectively. The straight horizontal and dashed vertical lines illustrate the determination of the threshold angles θL and θR using the flexible threshold method.
the bottom, in the middle, and at the top of the constriction. In our convention the magnetization angle is positive to the left of the constriction and negative to the right. While parallel alignment at the top edge of the magnetic element is expected due to the shape anisotropy, there is in fact a non-parallel alignment with respect to the edge. This can be attributed to the fact that the mean inner potential has been subtracted, which can lead to a small gradient in the flux (see section 3.3). As a precaution, only line profiles within a certain distance to the upper edge were taken into account. This is to avoid that the edge profiles which show unexplainable behaviour have a influence on the resulting
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domain wall shape. The following methods used line profiles to determine the shape of the domain walls. 1: Fitting Method The idea of this method is to fit the line profiles with a function describing Bloch walls. For a Bloch wall it is possible to calculate the magnetization profile analytically which is not the case for Néel walls which only can be calculated numerically. Therefore the Bloch wall description is commonly applied to Néel-type walls although the spins do not rotate out-of-plane but in-plane. The Bloch wall Eq. 4.1 is applied to the line profiles x sinθ = tanh( ) λ
(4.2)
with θ the in-plane rotation angle of the magnetization and λ being a fitting parameter which gives the domain wall width by wDW = πλ. This method did not work for two reasons. First, the fitting procedure for many line profiles failed because of measurement artifacts and noise on the signal. The noise was reduced by averaging over several neighbouring line profiles, but still irregularities of the magnetic material could not be compensated. Second, the line profiles are expected to exhibit a plateau at the center of the wall where the magnetization points in y direction, perpendicular to the edge of the magnetic element. This indicates that transverse walls are not Bloch- or Néel-type walls and cannot be reproduced by a tanh-function. Fitting leads therefore to misleading values. An example is the line profile through the middle of the constriction in Fig. 4.5 (red circles). 2: Flexible Threshold Method The threshold between the domain wall and the surrounding domains is determined for each line profile separately; the maximum, the minimum, and the plateau of the line profile represent the orientation of magnetization outside (“DL ” and “DR ” in the inset of Fig. 4.5, respectively) and
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Figure 4.6: Illustration of the fixed threshold method. (a) A part of a flux line (red color) in a magnetic induction map is used to determine the threshold angle of the domain wall. (b) The isolated flux line to the right illustrates how the angles θ1 and θ2 are measured. From this θL can be calculated.
inside of the domain wall (“DW” in the inset of Fig. 4.5). The threshold is represented by the angles θL and θR being found between maximum and plateau and between minimum and plateau, respectively. From the positions of these angles (xL and xR for each profile), the shape of the domain wall can be reconstructed (Fig. 4.5). The advantage of this method is that it is a systematical procedure and no theoretical model needs to be employed. However, comparison of results obtained by this method with the electron holography image revealed discrepancies, e.g. the tilt direction for an asymmetric wall was not identical. This can have two reasons. First, for line profiles without plateau it is not clear how the angles should be chosen. Second, the chosen shape of the line profile is not suitable; in Fig. 4.7 it can be seen that the magnetic flux lines and the line profile are not parallel outside of the domain wall because of the influence of the notch on the spin structure due to shape anisotropy. This can introduce a systematic error explaining the discrepancies. The next method tries to address these problems.
3: Fixed Threshold Method The magnetic flux lines are assumed to represent the right shape for the line profiles. This gives a variable shape for the line profiles since the flux lines are not identical. Unfortunately, it is not possible to take line
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Figure 4.7: (a) The shape of a domain wall is reconstructed and transferred to the magnetic induction map by summing up the positions of threshold angles (red dots) for a large number of line profiles (yellow curved lines). (b) Threshold positions (xL , yL ) and (xR , yR ) (red dots) where θ(xL , yL ) = θL and θ(xR , yR ) = θR is fulfilled for each magnetization profile. The definition of θL and θR is described in the text. A 2-dimensional plot of the threshold positions reveals the triangular shape of the transverse wall from which the opening angle αDW can be determined.
profiles through each individual flux line in an automated and efficient way. Therefore, the further assumption was made that the shape of the flux lines within a certain region does not change significantly. This means that the threshold angles θL and θR are nearly constant. Consequently, the angles have to be determined only once. Fig. 4.6(b) shows a magnetic flux line extracted from a magnetic induction image (Fig. 4.6(a)). The angle of the straight parts of the magnetic flux line with respect to the vertical is measured giving the angles of the magnetization inside of the transverse wall (θ1 in the region indicated ”DW” in Fig. 4.6(a)) and outside in the domain (θ2 in region “DL ” or “DR ” respectively) of the domain wall. The threshold angle on the left side θL is calculated by θL = (θ1 + θ2 )/2. Using the magnetic flux line running from “DR ”, the threshold angle on the right side θR can be determined. The definition of the threshold angles θL and θR can be understood as follows (see Fig. 4.6): if a magnetic flux line is followed from inside of the domain wall (“DW”) to the outside of the domain wall (“DL ” for θL or “DR ” for θR , respectively) and the rotation of the magnetization is observed at the same time, then at θL (or θR ) the magnetization has rotated halfway starting from its initial orientation inside of the domain wall be-
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Figure 4.8: Distribution of transverse domain wall types in given ranges of wc ; symmetric (black), asymmetric tilted (white), asymmetric buckled (gray) type.
fore reaching its end position outside of the domain wall. The advantage of this definition is its compatibility with the threshold position detected by eye. The eye is most sensitive to the position of the biggest curvature of the flux line. This position corresponds approximately with the position of the threshold angle determined by this fixed threshold method and can be easily obtained from the line profiles (Fig. 4.7(a)). Summarizing again the positions of θL and θR , xL and xR for each line profile, gives a 2-dimensional plot of the shape of the domain wall (Fig. 4.7(b)). Comparison with results obtained by the electron holography images revealed good agreement for all types of domain walls in wide constrictions. Therefore this method was chosen to investigate the shape of domain walls in constrictions.
4.2.3
Domain Wall Type Distribution
With the help of the fixed threshold method described above the shape of the domain walls in constrictions of all sizes could be determined. The summary of this investigation is shown in Fig. 4.8. Here, the dependence of the percentage of each wall type on the constriction size range is shown. In line with the results in [NTM05], symmetric walls are only found in narrow constrictions and asymmetric walls prevail for
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Figure 4.9: (From [Lau06]) Domain wall width as a function of the ring width in permalloy. Red triangles represent both vortex walls and transverse walls, and blue circles the average values. The black line is a linear fit to the average values.
wider constrictions. Both tilted asymmetric and symmetric walls appear in the range of wc < 175 nm. The asymmetric tilted wall type is the result of an attempt to reduce the stray field energy. This is achieved by aligning the spins in direction of the sample edge. The second asymmetric wall type with the buckled shape (Fig. 4.4(c)) can be found for large constrictions, wc = 75 - 370 nm. Since in thick samples with large constrictions vortex walls become the most favorable domain wall type, buckled domain walls can be considered as an intermediate state at the onset of the transformation from a transverse wall to a vortex wall where the vortex core is not yet nucleated.
4.2.4
Domain Wall Width
Physical effects connected with domain walls, e.g. current-induced domain wall velocities and domain wall magnetoresistance, depend on the size of the domain wall. In a previous experiment, domain wall widths were determined in permalloy rings using PEEM [Lau06]. Because of the resolution limits, only ring widths down to 100 nm could be measured. In Fig. 4.9 the domain wall widths versus the ring width are shown. Both
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transverse and vortex walls were measured. The permalloy rings had thicknesses in the range of 3 - 30 nm. The domain wall width was determined from intensity profiles taken along the perimeter of the ring and averaged over the width of the ring. The details of this method are reported in Ref. [Lau06]. From the data points an average domain wall width was calculated which gives a linear dependence on the ring width. This means that a reduction of the lateral dimensions leads to a reduction of the domain wall width in line with theoretical predictions [Bru99]. In the following the domain wall width is determined for constriction widths bellow 100 nm to find out if the size of the domain walls can be further reduced. Here, a constriction with particular dimensions will give an indication of what happens in rings without notches with a line width with the same dimensions. First, the domain wall width of transverse walls has to be defined. As seen in Fig. 4.4(a-c), the magnetization profile varies significantly moving in the positive y-direction (see Fig. 4.3) from the tip of the notch towards the outside edge of the element and it is not obvious how the domain wall width should be defined. Traditionally the widths of 180◦ Bloch walls have been defined as λ from the tanh(x/λ) magnetization profile [HS98] and this definition is commonly applied to 180◦ Néel walls. Due to the more complicated spin structure of the head-to-head walls this is not applicable in our case. As already mentioned, the profiles of head-to-head walls exhibit a plateau at the center of the walls where the magnetization is pointing perpendicular to the wire. A conventional tanh−function cannot reproduce such line profiles which leads to wrong values for the wall widths. Rather it is found from the analysis of the domain wall types, that the opening angle αDW of the triangular transverse walls as shown in Fig. 4.4(a) constitutes a suitable quantity to characterize most domain walls. After determining αDW , an average domain wall width wDW can be calculated according to wDW = wc tan(αDW /2).
(4.3)
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Figure 4.10: Dependence of domain wall angle αDW on an averaged constriction width wc,avg obtained from (a) experiment and (b) Heisenberg simulation. (c+d) Domain wall width wDW calculated using the domain wall angles αDW from (a+b). In (b+d) the symbols refer to different element widths we (♦=120 nm, =200 nm, 4=300 nm, 5=400 nm).
This is the physically relevant parameter, for instance for electron transport across the wall. An increase of αDW from 85◦ for wc,avg = 50 nm to 100◦ for wc,avg = 300 nm is observed (Fig. 4.10(a)). By calculating wDW , this corresponds to an increase from 50 nm to 380 nm (Fig. 4.10(c)) averaged for all the walls in a certain range of wc . No significant influence of the element width we and the thickness of the material on αDW , and therefore wDW , could be found for the range of thicknesses (5-20 nm) and we (100-400 nm) considered.
4.2.5
Comparison with Heisenberg Simulation
In order to simulate the domain walls in constrictions an extended classical Heisenberg model was employed which can reproduce the changes
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in the spin structure at very short length scales as found in geometrically confined domain walls [Bru99]. In the conventional micromagnetic approach used in [NTM05], the exchange energy is approximated by ~ · m) (∇ ~ 2 (m ~ local magnetization), which is the first order Taylor expansion of the dot product and only valid for small angles between neighboring cells [KF03, Aha96]. In order to address this problem, C. Schieback from the Universität Konstanz performed simulations of domain walls in constrictions using an atomistic / semi-classical spin model approach. In this model the magnetic moments are located on a cubic lattice with nearest neighbors having ferromagnetic exchange coupling, a dipole-dipole interaction and coupling to an external magnetic field [SKN+ 07]. The exchange energy is calculated as the dot product of magnetic moments. The radius of curvature of the magnetic element was kept constant to 1 µm as in the experiments and the element width we was varied between 120 and 400 nm with a thickness of 4 nm. The domain wall configuration for constriction widths wc in the range 20 - 200 nm were simulated. The notch had a triangular shape with an angle of 70◦ in line with the experimental samples. The parameters of the Heisenberg simulations were deduced according to [Aha96] from the material parameters of permalloy; damping constant α = 0.02, exchange constant A = 13×10−12 J/m and saturation magnetization Ms = 800 × 103 A/m. A cell size of 2 nm and 4 nm was used with no significant difference in the results. In the experiment, domain walls are formed after reducing an external magnetic field from saturation in the y-direction (see Fig. 4.3) to zero. Since there is never a perfect alignment of the field to the constriction in the experiments, the field was tilted by 5.7◦ to the y-axis in the simulation. In the simulations, two types of transverse domain walls are found within the constriction as shown in Fig. 4.11: symmetric (Fig. 4.11(a)) and asymmetric transverse domain walls (Fig. 4.11(b)). The symmetric transverse domain wall is obtained in small constrictions, wc = 20 80 nm, and exhibits an elliptical shape also observed in [MD97]. For wider constrictions, wc ≥ 160 nm, an asymmetric spin structure is fa-
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Figure 4.11: Magnetization directions taken from computer simulations of (a) symmetrical and (b) asymmetrical transverse domain walls with thickness 4 nm; constriction width wc /element width we (a) 80 nm/400 nm and (b) 200 nm/400 nm. The color code in the inset of (a) and the arrows indicate the magnetization direction.
vored with the direction of the asymmetry (to the right in Fig 4.11(b)) governed by the initial field angle. For intermediate wc = 120 nm both types are found depending on we . The key energy contributions to the domain walls are the exchange energy, which favors large wall widths, and the stray field energy (shape anisotropy), which favors alignment of the spins parallel to the element edges. The increasing influence of the stray field energy results in smaller wDW for smaller constrictions. For symmetric walls, wDW is comparable with the experimental values for 0 < wc < 150 nm (Fig. 4.10(c+d)). However for wc > 150 nm, wDW extracted from the simulation increases to much larger values, since the exact tilt in experiment depends on irregularities such as edge roughness, which are inherently not well known and thus not taken into account into the simulation. In addition, the difficulty in determining the opening angle leads to the observed discrepancy of wDW for the highly asymmetric simulated walls in that range of wc (see Fig. 4.11(b)). The increase in the opening angle means that wDW according to Eq. 4.3 increases more than linearly with increasing wc . This is obvious in Fig. 4.10(d), but less so in Fig. 4.10(c), since in the experiment the increase in the angle is smaller than in the simulated data as discussed above. But even for the large constriction widths, the same qualitative trend as in the experimental data is observed.
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Conclusion
In this section, to our knowledge for the first time symmetric and asymmetric transverse walls are directly imaged in constrictions down to 30 nm using electron holography. The observed transverse wall types are in agreement with micromagnetic predictions and Heisenberg simulations. In the measurements it was found that, depending on the constriction width wc , the asymmetric walls could be subdivided into tilted and buckled walls, the latter being an intermediate state just before the appearance of a vortex. It was also confirmed that the domain wall width wDW depends strongly on the constriction width wc and decreases with decreasing wc . In agreement with simulations, the wall opening angle decreases with decreasing constriction width. This results in a faster than linear decrease of the wall width with wc which will facilitate the fabrication of very narrow domain walls. On such small length scales exciting physical effects are expected. In field-induced domain wall motion, the velocity of the domain walls depends critically on the spin structure [KJA+ 05]. Furthermore, for very narrow domain wall widths non-adiabatic contributions to the electron transport become significant [ZL04, TNMS05, XZS06]. This can lead to an increase in current-induced domain wall velocity and a decrease of critical current density which is important for applications. Finally, the domain wall magnetoresistance depends critically on the spin structure and therefore the width of the domain walls [LZ97, KRP01]. Direct imaging and characterization of domain walls in narrow constrictions carried out in this work will provide essential understanding of experimental results obtained by indirect measurement methods, e.g. magnetoresistance measurements.
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Pinning of Domain Walls Introduction
Control of the domain wall behavior, and in particular of the magnetic switching, can be achieved through pinning centers, which provide well-defined stable locations for domain walls and can be used to control the wall propagation [KVB+ 05, LDKRB01, GLC+ 02]. Pinning centers can result from imperfections in the material [GBC+ 03], which are inherently hard to control. Instead, artificially structured variations in the geometry of an element have been introduced to engineer such pinning [GLC+ 02, AXC04, HOK+ 05, KVR+ 03, KVW+ 04, ZP04]. In earlier work on narrow rings, it was observed indirectly by magnetoresistance (MR) measurements that constrictions create an attractive potential well for transverse walls, but vortex walls are repelled from a constriction [KVR+ 03, KVW+ 04]. While qualitatively the domain wall behavior could be determined using MR measurements, the details of the wall positions and in particular the nanoscale wall spin structure in magnetic elements with constrictions can not been elucidated by this measurement method. Electron holography is a more suitable measurement technique for this as has been shown in section 4.2 where the detailed spin structure of transverse domain walls was observed. The transverse walls were pinned inside of constrictions formed by notches due to their attractive potential on transverse walls. In this chapter, a characterization of the energy potential formed by a notch is presented which requires the determination of its width and amplitude. For applications it is the strength of the pinning, which corresponds to the depth of the potential well, that is critical for engineering of devices with reliable switching, thermal stability, etc. To determine the strength of the pinning, standard four-probe ac lock-in MR measurements can be carried out at 4 K (section 3.5). The presence or absence of a domain wall at a constriction can be sensed due to the anisotropic MR contribution of a domain wall (section 1.5.1). By applying a field while
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Figure 4.12: (From [KER+ 05]) SEM image of a 200 nm wide permalloy wavy line structure with a 70◦ notch forming a 140 nm constriction. The direction of the saturation field Hsat , used to position the domain wall at the notch, and the direction of the depinning field Hdepin , used to move the wall away from the notch, are indicated.
monitoring the resistance, the domain wall depinning fields are determined as a function of the constriction width (section 4.3.2). To find out how the strength of the pinning is correlated with the wall spin structure, the nanoscale spin structure and position of head-to-head and tail-to-tail domain walls in constrictions down to 35 nm width has to be determined. For this purpose electron holography is especially suited because of its high resolution (section 4.3.3). From the nanoscale wall configuration, the energy barrier to depin the wall from a constriction is quantitatively determined using simulations (section 4.3.4). A comparison with the experimentally measured depinning field reveals if the depinning field is a good measure for the energy barrier height. The results which are presented in this chapter have been published in Ref. [KER+ 05].
4.3.2
Magnetoresistance Measurement
In order to probe the pinning strength, the external magnetic field necessary to depin a domain wall from the constriction as a function of the constriction width is measured. 200 nm wide permalloy (Ni80 Fe20 ) ring
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Figure 4.13: (From [KER+ 05]) Experimental depinning field (left ordinate) vs constriction width in 200 nm wide permalloy ring structures with triangular 70◦ notches and a film thickness of 34 nm (black squares); numerical simulations (green up triangles). The calculated energy density differences show the same trend (red disks, right ordinate).
structures with constrictions and nonmagnetic contacts have been fabricated [KVW+ 04]. The thickness is chosen to be 34 nm for comparison with earlier experiments [KVR+ 03, KVW+ 04, KVB+ 04a]. The ring structure is first saturated with an in-plane field Hsat along the notch position in order to position the domain wall at the constriction and the field is then set to zero (see Fig. 4.12). Then, a perpendicular in-plane field Hdepin is applied, and the field necessary to depin the wall is determined (black squares in Fig. 4.13). The depinning field of the narrowest constrictions (335 Oe) is about six times the field needed to move a wall in a ring without a constriction (60 Oe), where the depinning field is governed by material imperfections and the edge roughness. Therefore, the geometrically induced pinning is by far stronger than the pinning due to natural imperfections, which means that the pinning strength can be tailored over a wide range of values by adjusting the notch geometry. The maximum depinning field is much lower than the field needed to nucleate a domain
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wall (600 Oe) [KVB+ 04b], so that indeed the depinning of a domain wall is probed and not the annihilation by a new wall, nucleated at a different position in the ring. In general, the depinning field increases with decreasing constriction width, indicating that walls in narrower constrictions are more strongly pinned. Qualitatively, this behavior is expected, since the energy of the domain wall scales with the size, so that smaller domain walls in narrower constrictions are energetically more favorable and thus more strongly pinned. From MR measurements and micromagnetic simulations, it could be concluded that transverse walls are attracted into constrictions and that vortex walls are repelled by the constriction [KVR+ 03, KVW+ 04]. In the following direct imaging of the spin structure helps to explain the different pinning mechanisms.
4.3.3
Spin Structure of Domain Walls
Magnetic induction mapping of domain walls using electron holography (section 3.3) was employed to reveal the details of the interaction of domain walls with constrictions. Wavy lines made of permalloy with 200 nm width and with constrictions were fabricated as described in section 2.3.2. In Fig. 4.14, high spatial-resolution magnetic induction maps of domain walls at various constrictions are presented, which were prepared by saturating the sample with a field Hsat along the notch position (as indicated in Fig. 4.12) and then relaxing the field to zero. For narrow constrictions (Figs. 4.14(a) and 4.14(b)) transverse walls can be discerned inside the constrictions, while for larger constrictions (Figs. 4.14(c)-4.14(g)) vortex walls are located at positions adjacent to the constrictions on the left- or right-hand side depending on slight geometrical asymmetries in the notch with respect to the applied field direction. The energy landscape around the notch can alrady be assumed as indicated in Fig. 4.15(a) for the transverse wall and 4.15(b) for the vortex wall. The sense of rotation can be directly correlated with the position with respect to the notch, which is not possible using MR measurements. The
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Figure 4.14: (From [KER+ 05]) High spatial-resolution electron holography images of sections of 27 nm thick, 200 nm wavy line structures with different constriction widths: (a) 35 nm, (b) 60 nm, (c) 100 nm, (d) 110 nm, (e) 140 nm, (f) 160 nm, and (g) 140 nm. The walls in constrictions (a) and (b) are transverse walls, (c) and (e) exhibit vortex head-to-head walls to the left and (d) and (f) vortex head-to-head walls to the right of the constriction; (e) and (g) show the same constriction with (e) a head-to-head and (g) a tail-to-tail vortex wall. The magnetization directions are indicated in (b), (e), (f), and (g) by white arrows. Areas where stray field occurs are denoted with black arrows in (e), (f) and (g). The color code indicating the magnetization direction is also shown.
head-to-head walls to the left of the constriction have counterclockwise sense of rotation (Figs. 4.14(c) and 4.14(e)), while the walls to the right of the notch have a clockwise sense of rotation (Figs. 4.14(d) and 4.14(f)). When the field is reversed to create tail-to-tail walls, the vortex wall sense of rotation is reversed. This can be seen by comparing the vortex walls to the left of the notch in Figs. 4.14(e) and 4.14(g), which show the same notch after applying opposite fields. This is a universal behavior, which is observed for all vortex walls at constrictions for all film thicknesses. To understand this behaviour, it has to be taken into account that a vortex wall has two positions where a stray field occurs. In Fig. 4.14, the po-
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Figure 4.15: Energy potential around a notch forming a constriction which depends on the domain wall spin structure. A transverse wall is attracted into the constriction (blue dashed line) and a vortex wall is pinned adjacent to the notch (red continuous line). The energy barrier 4E to overcome the pinning is indicated by the arrows for each wall type. For the vortex wall the energy barrier for depinning in direction of the constriction 4E2 and away from it 4E1 can be different.
sitions at which the stray field enters (Figs. 4.14(e) and 4.14(f)) or leaves (Fig. 4.14(g)) the vortex wall are marked by two black arrows. In order to minimize the stray field associated with the vortex wall, the lower of the two stray field areas is always located inside the notch, which determines the sense of rotation of the vortex wall. As a result, the wall is actually pinned in the location directly adjacent to the notch even though it is repelled from the constriction due to higher exchange energy costs in the constriction. This behavior explains the fact that in Fig. 4.13, a significant depinning field is also necessary to displace the vortex walls at wide constrictions. It should be mentioned that in the MR experiment, the vortex walls were pulled away from the notch by the magnetic field, not through the constriction [BKR+ 07].
4.3.4
Simulations
To fully understand our results for the experimental depinning fields, micromagnetic simulations have been carried out using the OOMMF pack-
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age [OOM]. The intrinsic parameters used are MS = 800 × 103 A/m, A = 13 × 10−12 J/m, and a cell size of 5 nm. Since the domain wall types which are obtained from OOMMF simulations (0 K) do not always correspond to the experimentally observed wall type [KVB+ 04a], the type of domain wall determined experimentally at a given constriction was inserted into the simulation as described in Ref. [KVW+ 04]. To obtain the theoretical depinning fields, the experiment was simulated by relaxing the experimentally observed domain wall type in the constriction at the notch position and then applying a perpendicular field until the wall depins. The simulated depinning fields (triangles in Fig. 4.13) reproduce the experiment (black squares in Fig. 4.13) very well. They are highest for the transverse walls inside the constriction (20-40 nm constriction width) and are lower and vary less for vortex walls adjacent to constrictions with different sizes (80 - 175 nm constriction width) due to the different pinning mechanisms of the two different wall spin structures. From this result it can be concluded that large depinning fields found by MR measurements are correlated with transverse walls found by imaging using electron holography. In the same way, lower depinning fields can be attributed to vortex walls. The nonzero depinning field without a notch (200 nm width) is due to the edge roughness induced by the cubic cell discretization. In order to understand the pinning further, the energetics that govern the domain wall pinning are discussed. To depin a wall, the depth of the energy well has to be overcome by the external field and as a simple model the depth is given by the energy difference of a wall inside the constriction and when it is moved outside, which are determined from the energy densities of the different walls at different positions, calculated using the OOMMF package as shown in Fig. 4.13 [KVR+ 03]. It can be seen that the energy density differences exhibit a very similar dependence on the constriction width as the depinning fields. This observation suggests that the experimentally obtained depinning fields are a measure of the energy barrier height (Fig. 4.15), because as a first approximation, the extra Zeeman energy for the domain wall due to the perpendicularly
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applied depinning field is proportional to the applied field strength.
4.3.5
Conclusions
In conclusion, the spin structure in constrictions was imaged using electron holography. Transverse walls were found in narrow constrictions and vortex walls adjacent to the notch. Using MR measurements, the domain wall depinning fields in constrictions down to 35 nm width could be systematically determined. Transverse walls were found to exhibit significantly higher depinning fields than vortex walls because of a different pinning mechanism. Transverse walls are pinned in the constriction because there the reduced domain wall size leads to a reduction of the total domain wall energy. For the vortex walls the pinning is governed by stray field minimization close to the notch. Simulations allow the calculation of the energy of domain walls being pinned by a constriction and being depinned. The measured depinning fields correlates with the difference of these energies and can therefore be used as an experimental measure for the energy barrier height. Since it is now possible to obtain the depth of the potential well (the strength of the pinning) as well as its width as described in Ref. [KVR+ 03], these measurements open the way to artificially engineer the potential landscape, as required for any application based on domain walls.
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Spin Structure of CrO2 Introduction
Improving the efficiency of the spin torque effect for current-induced domain wall motion is of importance for future applications. For research in this field, improving the efficiency opens up a way to verify the theoretical predictions as described in the following: Theoretically, the spin torque efficiency is governed by the generalized velocity u (eqn. 1.47 in chapter 1), 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. If this is true then using highly spinpolarized materials will reduce the critical current densities and higher wall velocities should be measured. CrO2 is such a material because it exhibits a high spin-polarization of 90 % [Kön06]. It is well-known that in addition to the material, the spin structure of domain walls which affects the velocity of the domain walls [KJA+ 05]. Therefore the spin structures in CrO2 thin film elements have to be investigated before carrying out current-pulse experiments. In this section, the possibilities are discussed to measure the spin structure of a patterned CrO2 thin film using photoemission electron microscopy (PEEM). PEEM is chosen because it is a non-intrusive measurement technique which means that the spin structure is not affected by the measurement. Besides this it provides a sufficient resolution. This makes PEEM the ideal candidate for direct measurement of the current-induced domain wall motion as has been shown for similar experiments using permalloy elements [KLH+ 06].
4.4.2
Imaging of a Single Layer of CrO2
60 nm-thick CrO2 continuous films were grown epitaxially on single-crystal TiO2 substrates by chemical-vapor deposition (section 2.2.2.2). The growth and characterization of the films was performed by C. König
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Figure 4.16: (a) X-ray absorption spectroscopy (XAS) spectrum of a continuous CrO2 film. (b) X-ray magnetic dichroic (XMCD) spectrum obtained by subtracting the intensity of the two circular polarization directions.
[Kön06]. To find the maximum XMCD contrast, an x-ray absorption spectroscopy (XAS) spectrum was taken. This means that the intensity in a certain region of the magnetic material is recorded for the circular polarization directions (helicity) of the x-rays in a certain energy range. From the difference of the intensities of both circulation directions, one obtains the x-ray magnetic dichroic (XMCD) spectrum. It is related to the different absorption depending on the orientation of the helicity with respect to the magnetization direction of the sample (section 3.1). The x-ray energy was set to various energies close to the peaks of the XMCD spectrum and XMCD images were taken. For all of the energies no magnetic contrast could be seen. Sputtering away the top layer of the CrO2 did not lead to any improvement. The lack of XMCD contrast could be due to several reasons. It could be due to damaging of the film caused by the sputtering process. A comparison of the measured XMCD spectrum with data from the literature revealed that although the spectra look similar, some small deviations are visible [GBG+ 02]. The measured XMCD signal of
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Figure 4.17: XMCD images taken at the Fe L3 -edge revealing the spin structure in the Py layer of the CrO2 /Py system after saturation in an external magnetic field applied in opposite directions along the easy axis. Inside the wire the magnetic contrast reverses. The schematics below the XMCD images illustrate the spin structure in the Py layer.
< 1 % is small compared to approx. 30 % which are obtained for an iron film of similar thickness [CIL+ 95] and such a small XMCD signal is difficult to detect. It is well-known that on the surface of the metastable CrO2 film a stable layer of Cr2 O3 forms [CXB+ 01, DTX+ 00]. Furthermore, it has been shown that the spin-polarization of a CrO2 film is drastically reduced with increasing Cr2 O3 thickness [JSY+ 01]. I seems more likely that a Cr2 O3 layer covers the CrO2 film which cannot be removed by sputtering. Imaging of the spin structure of the CrO2 film was therefore not possible.
4.4.3
Indirect Imaging using a Py layer
Indirect imaging of the CrO2 film was carried out via a 5 nm Py layer deposited in-situ on top of a 80 nm thick CrO2 film by C. König [Kön06]. The CrO2 /Py film was patterned using focused ion beam milling (FIB). The Py layer reflects the spin structure in the CrO2 layer if both layers are exchange coupled at the interface. This is attributed to the fact that the Py layer is much thinner than the CrO2 layer and therefore magnetically softer.
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Figure 4.18: XMCD images of a CrO2 wire for four different saturation procedures in the hard axis direction. The field was slightly but randomly tilted from the hard axis. A clear difference can be seen in the right part of the wire being black in (a, c) and white in (b, d). Furthermore the left part of the wire is either white (b) or exhibits a more complex, non-reproducible pattern (a, c, d).
In Fig. 4.17, XMCD images measured at the Fe L3 -edge are shown reflecting the spin structure in the Py layer. Beforehand a magnetic field was applied parallel to the easy axis of the CrO2 film as indicated by the arrow in Fig. 4.17(a). The typical head-to-head (or tail-to-tail) domain walls - transverse or vortex domain walls - are not observed [MD97, LBB+ 06a]. This is an indication that the spin structure in the Py layer is influenced by the CrO2 layer.
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Exchange coupling would mean that the thin Py spin structure reflects the much thicker and magnetically harder CrO2 spin structure. In remanence, after applying the magnetic field in an easy axis direction, a parallel alignment of the CrO2 magnetization in direction of the easy axis is expected [BKF+ 07]. The shape anisotropy supports an alignment parallel to the edges which are only slightly misaligned with respect to the easy axis direction. Therefore a unidirectional domain state without domain wall is expected in the nanowires. In Fig. 4.17(a), there is a centered white contrast surrounded on either side by an opposite contrast. If we assume that the CrO2 layer is in a single domain state, it seems that the coupling varies along the wire, i.e. giving either a ferromagnetic or an antiferromagnetic coupling (see schematics in Fig. 4.17(a)). On reversing the applied field direction, the contrast reverses (Fig. 4.17(b)) reflecting the differently coupled areas in Fig. 4.17(a). This indicates that the coupling is different to that initially expected. To shed more light on the reason for the observed contrast, the magnetic field was applied in the opposite easy axis direction. A magnetic contrast reversal in the Py layer of the wire can be observed. For the same reasons as before this can not be explained by an isolated Py layer or by exchange coupling between the layers. The coupling appears to be either parallel or antiparallel depending on the location. Coupling by RKKY exchange is a possible explanation. According to eqn. 1.56, if two magnetic layers are separated by a nonmagnetic spacer layer an oscillatory coupling between the layers is observed dependent on the layer thickness. Behaviour according to this was already found for Py/Cr multilayers where the coupling oscillated with the thickness of the Cr film [WWC+ 92, WDFH93]. Where such a Cr layer could possibly originate from is unclear but we suppose that CrO2 could be the source allthough a reduction of CrO2 to Cr seems rather unlikely. The interlayer exchange would give rise to either ferromagnetic or antiferromagnetic coupling dependent on the thickness of the Cr layer thickness which can differ across the film. This would explain the observed magnetic contrast even if the CrO2 layer is magnetized homogeneously in
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Figure 4.19: Schematic of a part of the CrO2 wire showing the individual crystallites and their magnetization direction. (a) A magnetic field HA is applied in hard axis direction. (b) The spin structure in remanence after relaxing the magnetic field to zero.
one direction (Fig. 4.17(a)) and also the magnetic contrast inversion if the magnetic field is applied in opposite direction (Fig. 4.17(b)). The experiment is repeated at a different location of the sample but now the magnetic field is applied in the hard axis direction. In Fig. 4.18 four XMCD images are shown with the saturating field applied at slightly different angle (±10◦ ) before the images were taken. The magnetic contrast, and therefore the spin structure in the Py, now looks quite different for each measurement in Fig. 4.17. Such different spin structures for a given applied field has been observed for a CrO2 wire using magnetic force microscopy (MFM) [BKF+ 07, KFL+ 07]. With the hard axis oriented parallel to the wire when the magnetic field was applied in the hard axis direction, an irregular pattern of stripe domains of alternating magnetization parallel to the easy axis was observed. It is likely that the complicate spin structure seen in Fig. 4.18 originates from the magnetocrystalline anisotropy of the single CrO2 crystallites [Kön06]. As the hard axis field is applied, the magnetization in each crystallite rotates so that it is at a small angle to the overall hard axis direction of the CrO2 film (Fig. 4.19(a)). Since angle tilt can be dif-
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Figure 4.20: XMCD contrast after saturating in opposite easy axis directions. One region (surrounded by a dashed line) does not show contrast reversal. For comparison other regions (surrounded by continuous lines) show contrast reversal.
ferent for each crystallite, at remanence, when the field has been reduced to zero, the magnetization of neighbouring crystallites can rotate in opposite directions and align along opposite easy axis directions giving rise to a head-to-head domain wall (Fig. 4.19(b)). The magnetic field itself was applied at slightly different orientations which explains why different spin structures have been observed. In Fig. 4.20, it can be seen that contrast reversal was not always observed if the sample was saturated in the easy axis directions. Although in the areas surrounded by continuous lines, contrast reversal occurred as observed in Fig. 4.17, in the area surrounded by dashed lines the contrast stayed the same. Possible explanations for a lack of contrast reversal are as follows: • Non-magnetic area: The area where no contrast reversal is observable is not magnetic anymore. This could be due to the ion-irradiation during patterning using FIB which locally damaged the film. However, it remains unclear why other locations remain unaffected. • Exchange bias in one direction: Multilayers consisting of a ferromagnetic and an antiferromagnetic layer can exhibit a shifted hys-
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teresis [MB56, MB57]. If the so-called exchange bias field associated with the shift of the hysteresis loop is large at remanence, the spins will be aligned in one direction regardless of the direction of the original magnetic saturation field. The 5 nm-thick Py represents the ferromagnet but the question of what could serve as the antiferromagnet remains unclear. The change in exchange coupling seen in Fig. 4.17 was explained to be due to a varying Cr interlayer thickness, where the origin of the Cr at the interface to the Py layer remains unclear. This could be accompanied by an oxidation of Ni to NiO which is known to be an antiferromagnet. A Py/NiO double layer was demonstrated to be an exchange bias system [PR02]. However, a NiO contribution to the XAS spectra was not measured for the investigated sample. The second possibility is the antiferromagnet Cr2 O3 which is created by the reduction of CrO2 . For Py and Cr2 O3 bilayers the exchange bias field (500 Oe) is very high [DRRB07]. The lack of contrast inversion in the indicated area of Fig. 4.20 is still unclear and requires further investigation. Assuming that exchange bias effects are the reason for the observations, the influence of the FIB patterning should also be taken into account. Ion irradiation is known to influence the exchange bias field and even to invert it depending on the irradiation dose [Bac04].
4.4.4
Conclusions
Different attempts were made to measure the spin structure of CrO2 using PEEM as a measurement technique. This would allow a detailed investigation of the spin structure of domain walls in patterned CrO2 films, an essential prerequisite for current-induced domain wall motion experiments. CrO2 is a promising candidate as a material for such experiments because of its high spin-polarization which is predicted to enhance spintorque effects, e.g. the domain wall velocity. PEEM is a suitable measurement technique for this because it is non-intrusive and provides a
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sufficient resolution. Unfortunately neither direct measurement nor indirect measurement of the CrO2 film was possible. For the latter a Py layer deposited on top of the CrO2 film was measured assuming that a direct exchange coupling between the layers exists. It was hoped that the spin structure of the soft-magnetic Py layer would reflect the CrO2 spin structure. Instead, contrast associated with an oscillatory coupling is observed which may be explained by RKKY coupling mediated by a Cr interlayer with a varying thickness. Furthermore contrast reversal does not take place everywhere if a saturating magnetic field is applied in opposite easy axis directions. Possible explanations are either damaging effects associated with the patterning process or an exchange bias interaction. For exchange bias, it remains unclear which material could serve as the antiferromagnet. Since the spin structure in CrO2 films could not be measured using PEEM, other measurement techniques have to be found in order to carry out current-induced domain wall motion experiments. The observed coupling effects are non-trivial and would require detailed spectroscopic analysis to understand the underlying causes.
Chapter 5 Antidots 5.1
Introduction
In the previous chapter, the spin structure of domain walls in isolated magnetic elements and the pinning of domain walls at artificially introduced constrictions has been investigated. In this chapter, the domain wall spin structure, behaviour and their interaction in arrays of crossed nanowires are studied. The arrays of orthogonal wires can also be thought of as arrays of non-magnetic inclusions, in this case holes, in thin films. Such arrays of holes, referred to as antidots, have previously been investigated by several authors but to a lesser extent than isolated magnetic elements [YJS+ 00, ABD97, WAW03, TBG+ 05, GGM+ 03, VGZ+ 02, CAB97]. By introducing antidot arrays in thin films, the magnetic properties such as the domain configuration, the magnetic anisotropies, and the magnetization reversal, can be modified. These modifications are a result of the stray field energy associated with the holes causing the neighbouring spins to align themselves with the hole edges. In section 5.3, photoemission electron microscopy (PEEM) is employed to observe the switching behavior of cobalt antidot arrays on application of an in-plane magnetic field and to determine the detailed magnetization reversal processes. Furthermore, PEEM allows the observa-
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. Figure 5.1: Schematic diagram of the antidot geometry with the position of the square antidot marked with the letter A. The expected XMCD contrast is included for a magnetization sensitivity direction (MSD) along y. The antidot columns are parallel to y and the rows parallel to x. The easy and hard axes are along the x and y directions. The magnetic field is applied parallel or at a small angle to y.
tion of the switching of the arrays via chains of domains which can be reproduced using micromagnetic simulations. In section 5.4, the different magnetic spin configurations around the antidots are determined by measurements and simulations. In section 5.5, it is described how chains of domains nucleate, propagate and get pinned. Finally, the question of how the reversal depends on the size of the antidot period is addressed in section 5.6.
5.2
Experimental details
The antidot array pattern was written with an electron beam writer in a polymethylmethacrylate resist (PMMA) on a silicon substrate. A polycrystalline cobalt film with a thickness of t = 10 nm and a 1 nm-thick aluminum capping layer was deposited by dc-magnetron sputtering at a base pressure of p = 2×10−6 mbar. Unwanted material was removed by a lift-off process and leaving a periodic array of holes.
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Figure 5.2: Hysteresis loops measured with longitudinal MOKE. The magnetic field was applied parallel to y; (a) for a 10-nm-thick continuous film and (b)-(d) for antidot arrays t = 10 nm.
The antidot arrays cover square areas with a sidelength of 10 - 20 µm. For MOKE measurements several arrays are close together. The periods, p, of the dots range from 2 µm down to 200 nm. The dot size is half the period and therefore equal to the antidot separation. In this case the stray field is large enough to give a checked domain configuration after saturation with an external magnetic field, HA , and relaxation. In Fig. 5.1 a schematic of the XMCD contrast is shown for HA previously applied in positive y direction and the magnetic sensitivity direction is also oriented along the y direction. The cobalt film has a small uniaxial anisotropy which leads to an easy and hard axis with directions indicated in Fig. 5.1. Measurements of the spin structure were carried out at the SIM beamline at the Swiss Light Source, Paul Scherrer Institut. For imaging of magnetic domains, x-ray magnetic circular dichroism (XMCD) was employed and the x-ray energy was tuned to the Co L3 -edge (section 3.1). Depending on a parallel or antiparallel orientation of the spins with the polarization vector (or MSD), the color in the images appears black or white and gray for a perpendicular orientation of the spins. By rotating the sample by 90◦ about the surface normal, the two XMCD images give full information about the magnetization of the sample. To observe the magnetization reversal in the PEEM, a field could be applied in situ.
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Figure 5.3: XMCD images taken with PEEM of domain chains in 10-nm-thick antidot arrays with p = (a) 1 µm, (b) 400 nm, (c) 240 nm.
Here a special magnetizing sample holder was used which allowed the application of in-plane magnetic fields up to 300 Oe. Current pulses provided even higher fields which were necessary to saturate the sample. The measurements were taken in the remanent state, i.e. after reducing the magnetic field to zero, because the low energy electrons in the PEEM are disturbed in the field.
5.3
Magnetization reversal
Hysteresis loops were measured using longitudinal MOKE for antidot arrays with different periods and the same thickness t = 10 nm (Fig. 5.2). The field was applied parallel to the antidot array columns in the y direction. First an unpatterned 100 µm square of cobalt of the same thickness was measured which can be regarded as a continuous film. It displayed a small uniaxial anisotropy with the easy axis along the x direction
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(anisotropy field of about 15 Oe) and the hard axis along the y direction (20 Oe). It turned out that the hysteresis loops of the antidot arrays do not differ if the field is applied in x or y direction and only depend on the period. From this can be conclude that the antidots themselves dominate the reversal behavior and not intrinsic anisotropy of the cobalt film. The hysteresis loops for different periods (Fig. 5.2(b-d)) have two features in common. After saturation there is a small decrease of the magnetization. Here the shape anisotropy causes the spins to align parallel to the edges of the dots to avoid stray fields. Therefore the spins neighbouring the holes in the rows rotate 90◦ and 45◦ if they are at the intersections of the antidot rows and the columns, respectively. The large change of the magnetization in the hysteresis loops represents the switching of the columns in direction of the field. The switching field and the field range of the first reversible process increase with decreasing antidot period. The antidot arrays reverse their magnetization by nucleation of oppositely oriented domains which spread out along the columns. This is the case for all periods observed ranging from 200 nm to 2 µm as can be seen in Fig. 5.3. Fig. 5.4 shows PEEM images during the magnetization reversal for the p = 1 µm antidot array. The magnetic sensitivity direction and the magnetic field are oriented along the y direction, so that the XMCD contrast is sensitive to reversal occurring in the columns. First a positive field pulse 195 Oe was applied to saturate the sample and a high remanence magnetic state was observed after reducing the field to 0 Oe (Fig. 5.4(a)). Next a magnetic field was applied in the opposite direction and afterwards an image taken in remanence. This was repeated several times for increasing field values to observe the development of the magnetization reversal. It is observed that once a domain is nucleated, a chain of domains propagates until the end is pinned. The length of the domain chain does not change if higher fields are applied. Instead new domain chains nucleate in other parts of the array. The majority of the switching events occurs between −85 and −110 Oe (Fig. 5.4(c-e)). Small domain chains with lengths of only few antidot periods remain up to −145 Oe (Fig. 5.4(g+h)).
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Figure 5.4: Magnetization reversal via domain chains observed with PEEM in a 10-nmthick antidot array with p = 1 µm. The array is first saturated with a positive field pulse > 195 Oe, and the resulting remanent states are given after decreasing the field to zero (a) and applying increasing negative field (b) to (i).
At −175 Oe the array is saturated ((Fig. 5.4(i)). With the magnetic sensitivity direction parallel to the magnetic field, it is not possible to see if there is a change of the magnetization in the rows. If the sample was 90◦ rotated about the surface normal the magnetic sensitivity direct was perpendicular to the magnetic field. It turned out that domain chain nucleation and propagation also occurs in the rows (Fig. 5.5). The switching field range is above -135 Oe which is higher than before. The presence of switching in the rows indicates that the magnetic field was slightly tilted to the y direction. To shed light on the reversal process, micromagnetic simulations were performed using the OOMMF package (http://math.nist.gov/oommf). The simulated structure was a 1.9×1.9 µm2 square with an array of square
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Figure 5.5: Magnetization reversal in the antidot array in Fig. 5.4 (t = 10 nm and p = 1 µm), with the magnetic field applied in the same direction as in Fig. 5.4 but with the magnetization sensitivity direction rotated 90◦ . Here we observed a reversal of the rows perpendicular to the applied field direction via domain chains along x.
antidots with p = 200 nm. The cell size was 5 × 5 nm2 . The material parameters for Co were; saturation magnetization, MS = 1400 × 103 A/m, exchange constant, A = 3 × 10−11 J/m, and uniaxial anisotropy constant, kU = 3.5 × 103 J/m3 . Since the magnetic field in the experiment has always a small tilt with respect to the y direction, a small offset angle of 5◦ with respect to the y direction was introduced in the simulation. First, the antidot array was saturated by a magnetic field of 500 Oe which was then reduced to zero. As in the experiment a negative field was then applied and reduced to zero to obtain the remanent state.
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Figure 5.6: Snapshots of a micromagnetic simulation of an antidot array with an area of 1.9 × 1.9 µm2 , with antidot size = antidot separation = 100 nm, and a film thickness of 10 nm. First, a positive field of 500 Oe was applied and then reduced to zero. The field was then increased in the negative sense in 50 Oe steps and remanent states captured after each increase in field. The applied field is at a small angle (5◦ ) to the hard axis resulting in a reversal of the rows along x. The arrows at HA = +550 Oe indicate magnetic defects (magnetization sensitivity direction along y), which corresponds to the ends of domain chains along x. The round frames at HA = −550 Oe indicate locations where the ends of orthogonal chains coincide and the oval frames at HA = −650 Oe indicate a row where several chains ends occur.
Fig. 5.6 shows the simulated remanent states of the antidot arrays and the value of the negative fields were increased in 50 Oe steps. Similar to the experiment, the reversal takes place by domain chain nucleation and propagation, which occurs at lower field for domain chains parallel to the columns compared to the rows. In the simulations it is often seen that the ends of domain chains along the columns coincide with the ends of domain chains along the rows. This
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. Figure 5.7: XMCD images taken with PEEM of a 40-nm-thick antidot array with p = 800 nm. (a) and (b) are the same array measured with orthogonal sensitivity directions, and (c) is the resulting two-dimensional color map determined from (a) and (b). The locations where the ends of orthogonal domains coincide are indicated with round frames.
is indicated by circles in Fig. 5.6 for a magnetic field HA = -550 Oe. Taking XMCD images with orthogonal sensitivity direction, many locations were found where the ends of two orthogonal domains coincide. Examples for coincident chain ends can be seen in Fig. 5.7. Looking at the simulation for a magnetic field HA = 500 Oe in Fig. 5.6, some magnetic irregularities become visible which are marked with arrows. At the corresponding positions of the perpendicular sensitivity direction, ends of domain chains are obtained. Similar magnetic defects are also seen in the XMCD images as black and white spots (Figs. 5.4(a) and (i)). Indeed, in the experiment it turns out that the positions of the magnetic defects, and therefore the ends of the x domain chains, often correspond to the position of the ends of the y domain chains which subsequently form.
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Figure 5.8: (a) Schematic diagrams of the different antidot configurations surrounding an antidot (A to D), at the antidot intersection (E to G) and at the end of a perpendicular domain chain (H and I). (b) Two-dimensional XMCD image taken with PEEM of an antidot array with p = 1 µm and t = 40 nm, which includes contrast corresponding to the four basic configurations and a location where orthogonal chain ends coincide as indicated by a round frame. (c) A color plot of a typical remanent state given by the micromagnetic simulations after application of a field of -450 Oe (field parallel to y, initial magnetic field: +1000 Oe with four 90◦ walls indicated by square frames and two 180◦ walls indicated by an oval frame.
5.4
Magnetic spin configurations
In this section the different spin configurations which surround the antidots are presented. If the simple assumptions is made that the spins neighbouring the border of the antidot align parallel and the spins in the intersections between columns and rows orient at 45◦ , 4 configurations
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are obtained (Fig. 5.8(a)): (A) circular, (B) cross, (C) C-state, and (D) leaf. These configurations are indeed found in the experiment as indicated in Fig. 5.8(b). By looking at the spin configuration in the intersection the magnetization reversal process can be understood further. There are 3 cases (Fig. 5.8(a)): (E) The magnetization is oriented at 45◦ which is the basic configuration. (F) A 180◦ domain wall oriented at 45◦ (oval frame in Fig. 5.8(c)). (G) Two 90◦ domain walls (square frames in Fig. 5.8(c)). Configuration F occurs when two orthogonal domain chains coincide. (indicated in the XMCD images of Figs. 5.7 and 5.8(b) by round frames). This configuration is a low energy flux closure state which supports pinning of the domain walls. It explains why the chain ends of orthogonal chains often coincide. Wider intersections i.e. larger antidot separations leads to more complex flux closure states. In the experiment occasionally it appears that domain chain ends do not coincide with orthogonal domain chain ends. This corresponds to configuration G in the simulation. The stray field contribution of the 90◦ domain walls is higher compared to the 180◦ domain wall which leads to a weaker pinning. After saturating the sample a S-shape wall configuration was found which marks the end of domain wall chains perpendicular to the field. After applying a field of +500 Oe in Fig. 5.6 (indicated by arrows) the Sshape wall configuration (H) in Fig. 5.8(a) is present. After application of a negative field, the S-shape walls transform into a 90◦ wall configuration I in Fig. 5.8(a), similar to configuration G but rotated. If two orthogonal domain chains coincide, configuration F forms.
5.5
Detailed reversal mechanism
Micromagnetic simulations were used to observe the processes that govern the nucleation, propagation and pinning of the domain chains. Fig. 5.9 shows a series of snapshots of a simulation. It shows how the spin configuration reaches its equilibrium state after applying a magnetic
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Figure 5.9: Details of the micromagnetic simulation shown in Fig. 5.6. Starting with the remanent state after an applied field of -450 Oe, (a-i) are snapshots of the development of the magnetic spins on application of a negative field of -500 Oe. Nucleation occurs by formation of diagonal domains (round frames), followed by propagation of the chain ends along the antidot array columns.
field. The round circles in Fig. 5.9(b) and (d) show locations where diagonal domains are nucleated. Domain propagation then occurs by expansion of the nucleated diagonal domains and advancement of the chain boundaries along the columns of the antidot array. The propagation of the domain chains can be blocked by three possible mechanisms: 1. intrinsic defects in the magnetic film (pores, surface roughness, and grain boundaries) 2. extrinsic defects due to patterning (the antidot themselves and edge
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roughness created by the patterning) 3. the magnetic configuration which is present, i.e. the presence of perpendicular chains in the antidot rows Without perpendicular domain chains during reversal, the first two mechanisms will cause the blocking of the propagating chain ends which will give the 90◦ wall configuration in G in Fig. 5.8(a). When perpendicular domains are present, there are two possible mechanisms responsible for restraining the propagating chain ends. 1. Pinning of the chain ends due to the formation of the flux closure 180◦ domain wall configuration F in Fig. 5.8(a) when orthogonal chain ends coincide. 2. Blocking of the chain ends propagating along y when they approach a perpendicular chain running along x. Here a 360◦ wall forms, as indicated at several locations by arrowheads in the simulation of the antidot array at equilibrium in an applied field in Fig. 5.10(a). The advancing chain ends are blocked due to the high exchange energy barrier associated with annihilation of 360◦ walls, also seen in small magnetic thin film elements [HNGP91]. On relaxation of the magnetic field, the chain ends relax back to the nearest pinning location forming either 90◦ or 180◦ walls, and often resulting in small domains (Fig. 5.4(g) and 5.4(h)). When several chain ends propagating along y approach the same perpendicular chain (a row in which the magnetic spin direction along x reverses), the blocking via formation of a 360◦ wall will result in the occurrence of several chain ends in the same row. In Fig. 5.10(a), several 360◦ walls form in the row indicated by the large arrow and on relaxation of the field, the chain ends recede to form a row of 90◦ indicated by the large arrow in Fig. 5.10(b). The alignment of chain ends in a row was not only observed in the micromagnetic simulations (see also region indicated by the oval frame
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Figure 5.10: Details of a micromagnetic simulation similar to that shown in Fig. 5.6, but with the applied field parallel to y. Starting with the remanent state after an applied field of 450 Oe, (a) is the equilibrium state on application of a negative field of 500 Oe and (b) is the remanent state after subsequent relaxation of the field to zero. The black arrowheads in (a) indicate locations where 360◦ walls form as the propagating chain ends approach a perpendicular chain, i.e., where there is a reversal of the magnetic spin direction in the rows. Several propagating chain ends approach a perpendicular chain forming a row of 360◦ walls indicated by the large arrow in (a). After relaxation of the field, they form a row of 90◦ walls indicated by the large arrow in (b). (c) XMCD image taken with PEEM of domain chains in a 10 nm thick antidot array with p = 240 nm. The array was first saturated with a negative field of 280 Oe, and then the remanent states observed after application of increasing positive fields. This shows the remanent state after an applied field of 245 Oe and in contrast to Fig. 5.3(c), the domain chains form in bands indicating the presence of perpendicular domain chains during reversal. (d) Schematics of the spin structure of the 360◦ wall indicated by a green circle in (a).
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in Fig. 5.6 at a field of -650 Oe) but also in the XMCD images (see rows indicated by arrows in Figs. 5.4(d) and 5.5(d)). It was already described above how the presence of perpendicular domain chains in the rows strongly influences the positions of the ends of chains forming in the columns during reversal in two ways: 1. The ends of the perpendicular chain ends provide pinning centers 2. Propagating domain chains can be blocked by perpendicular chains, resulting in the formation of chain ends in the same row. Indeed, in the simulations could be seen that when the applied field is sufficient to eliminate the perpendicular domain chains (i.e. under the same simulation conditions of Fig. 5.6, but starting with a positive field of 1000 Oe rather that 500 Oe), then the propagation of the chains is no longer blocked and the reversal along y occurs via a complete switching of the columns. In real systems, intrinsic material defects or edge roughness of the antidots can serve as pinning sites in the absence of perpendicular domain chains. The perpendicular chains are likely to be present during reversal along y when the x-component of the applied field is not sufficient to remove them, and in particular when the applied field is exactly parallel to y. Small differences in the applied field strengths and orientation can therefore lead to very different reversal behavior. For example, the striking formation of domain chains in bands in the XMCD image in Fig. 5.10(c) indicates the presence of perpendicular domain chains during reversal. In Fig. 5.3(c), virtually random positions of the chains were observed which implies that there are very few perpendicular chains present.
5.6
Size dependence of reversal
In Fig. 5.2 the hysteresis loops change with the period of the antidots. The switching field increases and the reversible region lengthens if the period
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is decreased. Pinning of the domain ends is important during magnetization reversal, i.e. the domain chains grow to a particular length where the chain ends are strongly pinned. This implies that the reversal of the columns, and therefore the switching field, is dominated by the energy barriers related to both domain nucleation and depinning of chain ends. When these barriers are overcome, the propagation of the chain boundaries occurs over several antidot periods until the next pinning center is reached, as observed in the TXM (transmission x-ray microscope) on increasing the applied field in small steps (5 - 10 Oe). It can also be inferred from the simulations that an additional higher energy barrier is related to the annihilation of the 360◦ walls and results in small domains remaining towards the end of the reversal (Figs. 5.4(g) and (h)). The exact height of these energy barriers is related to the extent of twisting of the magnetic spins (exchange energy contribution dominates) and collective rotation of magnetic spins (magnetostatic energy contribution is important) involved in a given reversal process. For example, for the annihilation of the 360◦ walls, it is the exchange energy contribution which mainly determines the height of the energy barrier. Both the exchange and magnetostatic contributions increase on reducing the antidot array period, i.e., decreasing the lateral dimensions resulting in the observed increase in the switching field. The initial reversible part of the hysteresis loops involves a coherent rotation of the magnetic spins in the rows away from the field direction along y to give the basic antidot configuration in Fig. 5.1. As the antidot period decreases, this process starts earlier (at higher positive fields) because the higher stray field energy assists the alignment of the spins with the antidot borders, and will end later (at higher negative fields) because the additional exchange energy at smaller lateral dimensions hinders the formation of the basic antidot configuration of Fig. 5.1.
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Conclusions
In conclusion, a detailed study of the magnetization reversal in cobalt antidot arrays was carried out with periods ranging from 2 µm down to 200 nm and with applied fields parallel to the array columns. The switching was found to occur first by a reversible rotation of the magnetic spins identified as a small change in the magnetization in the MOKE hysteresis loops. It is followed by nucleation and propagation of domain chains giving a large irreversible change in the magnetization. The reversal was observed to take place not only via growth of the chains in the columns but also in the rows. This could be reproduced by micromagnetic simulations that include a small angle between the applied field and the array columns. The propagating domain chains are pinned via two mechanisms. First, the position of the chain ends is strongly influenced by the presence of perpendicular chains during reversal. Orthogonal chain ends can form a stable domain wall configuration. Second, a propagating chain boundary approaching a perpendicular domain resulting in a 360◦ domain wall is able to block the propagation. The latter often results in the alignment of chain ends in rows. The chain domain configuration is therefore highly dependent on the field history, i.e., the applied field strength and orientation. Antidot arrays have the advantage compared to continuous films that the switching behaviour can be controlled. Another interesting feature of antidot arrays is the pinning mechanism of propagating domain chains which is due to magnetostatic pinning [HSKO06] rather than due to artificially fabricated constrictions (section 4.3). This opens up a possible application in field or current-induced domain wall propagation where the domain walls can be moved in a controlled way between different pinning sites. This is a precondition for new concepts of data storage, e.g. the racetrack memory device [Par].
Chapter 6 Effect of Current and Heating on Domain Walls 6.1
Introduction
Important aspects of current-induced domain wall motion in ferromagnetic nanowires like domain wall velocities [YON+ 04, KJA+ 05], critical current densities [GBC+ 03, VAA+ 04, KVB+ 05], and the deformation of the domain wall spin structure due to current [KJA+ 05, KLH+ 06] have been addressed in order to understand the details of the underlying theory and the physics involved. If the experimental effects have to be compared with theoretical predictions it is important to exclude that other influences could interfere with effects based on the spin torque. Oersted fields have been excluded as a possible origin for domain wall motion [KVB+ 03], which is supported by the observation that both head-tohead and tail-to-tail walls move in the same direction for a given current polarity [KJA+ 05]. Thermal excitations were reported to influence domain wall motion [LBB+ 06b] and can also originate from Ohmic heating. Therefore an important topic is to investigate if interactions of currents with domain walls is based purely on the spin torque effect or if thermal excitation also plays a role. To first understand thermal effects, the influence of heating with-
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out currents on the spin structure of domain walls is investigated ( section 6.2). Heating is expected to be sufficient to overcome the energy barriers separating different metastable domain wall spin structures which are stable and observable at room temperature. In section 6.3, an investigation of heating originating from current pulses for samples on silicon nitride (Si3 N4 ) membranes is described. The membranes do not conduct heat as well as a bulk material such as a silicon substrate and Si3 N4 has a low heat conductivity. Therefore the effects due to Joule heating are expected to be more pronounced than for the same experiments using silicon substrates. The Si3 N4 membranes allowed the use transmission electron microscopy (TEM) techniques for measurement. Electron holography and the Fresnel mode of Lorentz microscopy were employed, both providing high-resolution images of the spin structure. Finally, the heat conductance is improved by back-coating the Si3 N4 membranes with aluminum (Al) (section 6.4). This reduces heating effects and the different observations allow one to devise ways to separate unambiguously spin torque effects from heating. Parts of the results of this chapter have been published in [LBB+ 06a, HKK+ 07, JKB+ 07].
6.2
Temperature Effect on Spin Structure
In an earlier experiment [LBB+ 06a] the spin structure of arrays of polycrystalline Permalloy (Py) rings with thicknesses between 2.5 and 38 nm, widths between 110 and 1800 nm, and outer diameters between 1.64 and 10 µm was observed (fabrication described in section 2.3.1). The edge-toedge spacing between adjacent rings was more than twice the diameter to prevent dipolar interactions that would otherwise influence the domain wall type. To determine the spin structure of the domain walls, the rings were imaged using photoemission electron microscopy (PEEM, see section 3.1). Then the sample was heated up to a certain temperature by a filament in the sample holder and the spin structure was imaged.
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Figure 6.1: (From [LBB+ 06a]) 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) up to the transition temperature (c), at which a thermally activated transition to a vortex type occurs in both walls. (d) The vortex walls are retained after cooling down. The gray scale shows the magnetization direction.
For a 7 nm thick and 730 nm wide ring at a temperature of T = 20◦ C, transverse walls were formed during saturation in a magnetic field and relaxation (Fig. 6.1(a)). This geometry is close to the phase boundary between vortex and transverse walls for Py. Heating up to T = 260◦ C did not influence the spin structure of the domain walls, only the image contrast became weaker because imaging is more difficult at higher temperatures due to drift problems and decreasing magnetization (Fig. 6.1(b)). 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 changed to vortex walls (Fig. 6.1(c)). This spin structure could not be achieved only by applying a uniform magnetic field. The vortex wall was stable during cooling down and the XMCD signal was as strong as before the heating (Fig. 6.1(d)). From this experiment it could be concluded that both domain wall
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types are meta-stable spin configurations and therefore constitute local energy minima at room temperature which are separated by an energy barrier. The transverse wall state is attained first because of the magnetization process, even if the vortex state has a lower energy. By heating, the energy barrier to nucleate the vortex wall can be overcome, with a barrier height between 6.7 × 10−21 J and 8.0 × 10−21 J. This is a stochastic switching process with a distribution of energy barriers leading to slight variations of the transition temperature for domain walls in rings of the same size. Imperfections of the microstructure may also cause a variation of transition temperatures.
6.3
Current-induced Heating
Application of a current to observe spin-torque effects, e.g. domain wall motion, is also connected with a rise of the temperature in the sample due to Ohmic heating. This effect is more pronounced if very thin Si3 N4 membranes are required for transmission electron microscopy (TEM) because the heat transport is rather poor. First, the 50 nm-thick membrane does not conduct the heat as well as the bulk material such as a silicon wafer which is hundreds of micrometers thick. Second, the heat conductivity of Si3 N4 is one order of magnitude worse than e.g. silicon. Due to the large pulse length, the conductivity rather than the heat capacity dominates the thermal properties since thermalization takes place within a few nanoseconds. On the one hand, this allows one the investigation of the influence of heating on the spin structure. On the other hand, heating might render the observation of the current-induced spin torque effect using TEM techniques difficult. While off-axis electron holography (section 3.3), which requires time-consuming data processing, reveals detailed information about the spin structure, Fresnel imaging (section 3.2) is much easier but yields only indirect information; the type and the position of domain walls can be obtained and in contrast, one can conclude the direction of the vortex circulation (chirality). Samples consisting of
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Figure 6.2: (From [HKK+ 07]) (a),(d),(g) Schematic spin structures, (b),(e),(h) Fresnel images and (c),(f),(i) off-axis holograms of multivortex walls, whereby (i) is a simulated image. The red (solid) and blue (dotted) circles indicate positions of opposite-sign magnetic charge accumulation. The black and white contrast in the schematic drawings corresponds to overfocus Fresnel images and for simplicity the vortex cores are drawn in the center of the wire. The images show (a)-(c) a 2AP domain wall, (d)-(f) a 3AP domain wall and (g)-(i) a 2P domain wall. The contrast appearing at the sample edge is omitted in the schematic images.
four Py zigzag wires with 240 - 560 nm linewidth and 12 - 34 nm thickness were fabricated as described in section 2.3.4. Depending on the geometry of the wires, after initialization with an external magnetic field, vortex or transverse walls were observed. Then 10 µs long rectangular current pulses were applied because the wires cannot sustain the necessary current densities for longer periods of time without being damaged structurally. The observed changes of the spin structure are described in the following.
6.3.1
Transformation of the Spin Structure
When current pulses are injected, the temperature in the wire rises significantly due to the Joule heating [YSJ06]. When monitoring the resistance of the wire in a comparable setup, Togawa et al. [TKH+ 06] found evidence that Joule heating above the Curie temperature is possible. This
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large thermal energy due to the current pulses makes it possible to overcome even high energy barriers. Besides transformation of transverse walls into vortex walls as described in sections 6.2, more complicated domain wall types were observed; two vortices with antiparallel chirality (Fig. 6.2(a)-(c)), three vortices with alternating chirality (Fig. 6.2(d)-(f)), and two vortices with parallel chirality (Fig. 6.2 (g)-(i)). Other higher order vortex spin structures occurred less often. The more complicated structures allow an increase in the separation between same sign stray field sources (marked with circular frames in Fig. 6.2(a),(d),(g)) or allow flux closure through the initialization of opposite sign stray field sources, thus decreasing the stray field. At the same time an energy barrier to nucleate a vortex has to be overcome [LBB+ 06a]. After some current pulses with a certain strength (0.69 to 2.88 × 1011 A/m2 ) the vortex walls irreversibly transformed into more complicated spin structures, i.e. on applying further current pulses it did not revert back to the initial spin state. Thus the explanation for the multitude of observed domain wall types is as follows: besides the initial vortex state there are several energetically lower-lying multivortex states, which are separated from each other by energy barriers. Some of these states have the same energy for symmetry considerations, e.g. domain walls with reversed chiralities, but in general their energies vary. Due to the strong heating, transitions between the different states are possible and the energy barriers separating the different wall types lead to the fact that different spin structures can be observed at room temperature.
6.3.2
Domain Wall Motion due to Heating
In addition to a change in the spin structure, thermally activated domain wall motion can occur. For this, pinning at edge roughness, which holds the domain walls in place, has to be overcome. Contrary to unidirectional movement due to the spin torque, this random motion is bidirectional. The threshold current densities for movement are lower than those re-
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ported for the spin torque effect [YON+ 04, KJA+ 05, KVB+ 05, KLH+ 06]. The measured current density is between 0.71 × 1011 A/m2 and 2.91 × 1011 A/m2 and is of the same magnitude as needed to switch between different spin configurations. This indicates that it is not a spin torque effect that is observed, but rather a thermally induced effect. Differences arise between samples with varying wire dimensions due to the better heat dissipation for a wire with a proportionally larger interface with the substrate [YSJ06]. Sometimes, especially for moving single vortex walls, the available energy is not sufficient to fully depin the domain wall. Then a wall is observed which as a whole is still pinned but the central intensity dot, marking the center of the vortex, moves from one position to the other. Because the outer parts of the wall are pinned by edge roughness while the vortex center is held in place by structural defects, e.g. holes, this yields information about the relative strengths of these two pinning mechanisms and pinning by edge roughness prevails. Another special case of thermally activated motion is a repeated jumping between two particular positions in the wire when injecting pulses. In this case the potential landscape for the domain wall is apparently a local multi-well potential, whereby the separating barrier is overcome by thermal excitations due to Joule heating by the current pulses.
6.3.3
Vortex Annihilation
Domain walls within a wire can interact as follows: when a new domain wall is nucleated in the neighborhood of an existing one, its chirality will prefer to be antiparallel to the one of its neighbor. If the walls consist of more than one vortex, the core which is closest to the other wall is affected by the interaction. A similar effect was observed in the thinnest wire when two vortex walls came close to each other. If they have opposite chirality, they will attract each other once depinned by current pulses. The motion is still random but has a strong unidirectional component. The walls will move towards each other until they finally annihilate. If
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Figure 6.3: (From [HKK+ 07]) (a) The spins in the domain between the vortex wall can rotate continuously, while in (b) they face an increasing exchange energy the closer the two walls are to each other.
by contrast two walls of parallel chirality come within a certain distance towards each other there is a repulsive force. Even for much higher pulses than usually needed to depin domain walls, there will be no further motion towards each other. This can be understood when taking into account the spin structure (Fig. 6.3). While for vortices with opposite chirality the magnetization between the two walls can continuously rotate because spins at both sides of the domain are parallel, this is not possible for vortex walls with the same sense of rotation. Here the magnetization cannot rotate continuously, but will face an increasing exchange energy, which will stabilize the configuration, prevent a further approach and hinder the ultimate annihilation.
6.3.4
Structural Changes by Heating
If pulses are injected which are 10 % or more above the current density usually needed to induce wall motion, even structural changes can be induced locally. The first observable consequence is the formation of a very long vortex chain (Fig. 6.4(c)). Second, in-focus images of the crystalline wire structure reveal a clear difference seen before and after the pulses (Fig. 6.4(a),(b)). The crystallites within the wire, which appear as dark spots in Fig. 6.4(b), have considerably grown in size. The usual size of
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Figure 6.4: (From [HKK+ 07]) In-focus image of (a) an as-grown wire and (b) the wire after the structural change. (c) Magnetic induction of the region pictured in (b). (d) Holographic magnetic image of the changed wire after remagnetization, (e) after one current pulse and (f) after another three pulses. The left image in (d),(e),(f) shows the same region pictured in (b),(d).
crystallites in Py is between 5 and 10 nm [VABR06], now they are found to be up to 20 times this size. Third, the magnetic structure change is permanent and not reversible by remagnetization. Figs. 6.4(d)-(f) show a pulse experiment after the structural change has happened. After remagnetization, an initial vortex wall is nucleated in the kink as before and the adjacent wire, where the vortex chain was observed, is single domain until the next kink (Fig. 6.4(d)). After one pulse with the usual depinning current density, the domain wall just moves out of the kink and out of the field of view (Fig. 6.4(e)). After another three pulses the wire has a similar spin structure as before remagnetizing (Fig. 6.4(c),(f)). Above all, the resistance of the total sample rises by about 6 % compared to the as-grown wire. The nucleation of chains of vortices can be explained if the sample is heated above the Curie temperature and becomes paramagnetic. Simulations have shown that a multivortex state is formed after cooling down (not shown). The strong heating leads to a recrystallization that changes the sizes of the crystallites and perhaps leads to oxidation and / or intermixing with the Au capping layer, which could explain the higher resis-
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Figure 6.5: (From [JKB+ 07]) Permalloy wire width: 580 nm, thickness: 12 nm. Pulses with a current density of 7 × 1011 A/m2 are applied. The Fresnel images are acquired in the alphabetical order with one 10 s pulse between the adjacent pictures. (a-d) High resolution images of the same vortex wall that have moved in the direction of the electron flow from position (a-d) as indicated above during five consecutive pulses. Here, no change of the vortex circulation direction is observed. (e-h) Back and forth movement of the vortex domain wall with changes of the vortex circulation direction (seen as contrast reversal) due to heating effects.
tance. There is an additional indication that the effects presented so far are truly of thermal origin. When increasing the pulse length, smaller current densities are needed to trigger the various effects. Thermal effects are statistical events and as such a longer period of heating and stronger pulses, i.e. more heating, increases the probability for them to take place. Thus for longer pulses, smaller current densities are sufficient to obtain the same probability for an event to take place.
6.4
Heat Conductance Improvement
To improve the heat flow through the sample, aluminum was deposited on the back side of the membrane because of its high heat conductivity
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of 237 W/Km compared to 18 W/Km for pure Si3 N4 [Lid01]. The idea is based on calculations which suggest that heat dissipation into the substrate dominates dissipation along the wire and into the contacts [YSJ06]. Due to the large pulse length the conductance rather than the heat capacity dominates the thermal properties since thermalization takes place within a few nanoseconds. For a sample with 580 nm wire width and 12 nm thickness, a current density of j = 7 × 1011 A/m2 is needed for domain wall movement.
This is higher than for a similar sample without aluminum
and is comparable to the critical current densities of similar Py structures on silicon wafers, which provide a more efficient heat dissipation [KJA+ 05, KVB+ 05, KLH+ 06]. The domain walls move predominantly in the direction of the electron flow, as shown in Figs. 6.5(a)-(d). Here four consecutive pulse injections move the walls similar distances with velocities between 0.05 and 0.3 ms , in line with observations of similar wires on Si [YON+ 04, KJA+ 05, KVB+ 05, KLH+ 06]. The conclusion from this is that observations of wall movements and transformations on Si3 N4 membranes without the aluminum backcoating at current densities far below what is reported on Si are due to thermal effects. Although the Al back-coating improves heat dissipation, the random movement can still occur. As visible in Figs. 6.5(e-h), the deterministic wall motion due to spin torque is still interjected by intervals with random thermal effects. As reported earlier, the vortex wall jumps randomly between two positions (section 6.3.2) and in addition, there are changes in the vortex circulation direction. Spin torque theory predicts that there are only transformations between transverse and vortex walls with a certain circulation direction. A statistical investigation of membranes without an aluminum coating shows that no motion in the electron flow direction was observed. In samples with an aluminum coating, it was found for 299 pulse injections that statistically significantly more wall movements occur in the electron flow direction 58.2 % than against it 41.8 % and this was observed to be independent of the wall type, head-to-head or tail-totail wall, so that the only symmetry breaking of the motion direction is
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due to the spin torque effect. This indicates that a superposition of heat and spin torque effect is observed [JKB+ 07]. Measurements of the resistance of the samples with an aluminum back layer as a function of the current density yield a resistance increase of 20 %, which corresponds to an increase in temperature of 150 K as determined from measurements in a cryostat, meaning that the temperature stays below the Curie temperature in contrast to the samples without the aluminum back layer. It can now be conclude that the main channel of heat dissipation is via the substrate. Thinner samples that have a larger interface with the substrate compared to the wire volume experience less heating. This trend was observed for all geometries. Therefore to prevent heating and to observe spin torque effects, for a constant cross section, thinner wires are better suited and even more cooling can be achieved by surrounding the wire with a good thermal conducting material. In this a non-conducting material such as Al2 O3 would be suitable to avoid shorting of the device. A set of indicators to distinguish current-induced domain wall motion effects due to spin torque from heating can be identified: i) the domain wall motion is in the direction of the electron flow, ii) the transformations occurring are compatible with those expected from theory and not only to energetically lower domain wall types, iii) the critical current densities and the velocities for nominally identical structures should be similar even if the substrate is changed, and iv) the temperature during current injection should stay far below TC .
6.5
Conclusions
In temperature-dependent XMCD-PEEM imaging, thermally activated switching from transverse walls to vortex walls was observed at elevated temperatures at a transition temperature between 260◦ C and 310◦ C which corresponds to an energy barrier between 6.7 × 10−21 J and 8.0 × 10−21 J. This gives direct experimental evidence for the fact that transverse and
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vortex walls are separated by an energy barrier which can be overcome thermally. Current pulses in poorly heat conducting samples can provide the necessary energy to overcome these barriers. In sufficiently thick and wide wires, where the vortex wall is not the energetically most favorable spin structure, a multitude of more complicated domain wall types can be observed. These spin structures are usually not accessible because they are separated from the initial state by high energy barriers. Current pulses can also trigger other effects which allow conclusions to be drawn on the potential landscape for the walls in the wire. Indications were provided that the pinning of vortex walls is predominantly due to edge defects and that high current pulses can lead to structural changes accompanied by changes in the spin configuration. The main cooling process was identified as heat diffusion through the Si3 N4 substrate. This was exploited by back coating the membrane with Al, which reduces local heating. Measurements on these samples revealed reduced heating and allowed the separation of spin torque from heating effects by analyzing the different wall motions and transformations which occur.
Chapter 7 Conclusions The major goals of this work were to determine the spin structure of domain walls in confined magnetic elements and to observe the behaviour of domain walls on the application of external magnetic fields and currents. These goals were achieved as detailed below: The spin structure of transverse walls in constrictions down to 30 nm was measured using electron holography. Symmetric, asymmetric tilted and asymmetric buckled transverse walls were found, the latter being an intermediate state just before the appearance of a vortex. It was confirmed that the domain wall width wDW decreases faster than linearly with decreasing constriction width wc , which will facilitate the fabrication of very narrow domain walls. The knowledge about the spin structure of such narrow domain walls is very useful for the interpretation of indirect measurement methods, e.g. magnetoresistance measurements. The knowledge about the spin structure facilitated the understanding of the depinning of domain walls from constrictions formed by a notch. Depinning fields were obtained by magnetoresistance measurements which could be directly related to the spin structure. Transverse walls were found to exhibit significantly higher depinning fields than vortex walls because of a different pinning mechanisms. Employing simulations, the energy barrier height of the potential of the constriction could be calculated. This opens the way to artificially engineer the potential landscape around a constriction, as required for any application
Conclusions
146
based on domain walls. An attempt was made to image the spin structure of a patterned CrO2 film using photoemission electron microscopy (PEEM) as a measurement technique. However, the material turned out to be too chemically unstable to observe a magnetic contrast. CrO2 is a promising candidate as a material for current-induced domain wall motion because of its high spin-polarization which is predicted to lead to more efficient spin-torque transfer which gives rise to, e.g. higher domain wall velocities. Also the approach of imaging the spin structure of a permalloy layer deposited on top of the CrO2 film, thus reflecting the spin structure of the CrO2 film if simple exchange coupling exists, was not successful. Instead, the coupling turned out to be more complicated than expected and RKKY coupling was suggested to explain the observations. Instead of isolated magnetic elements, crossed wires forming an array of holes in a thin cobalt film (antidots) were investigated. The switching behaviour occurs by propagation of chains of domains which are pinned by the surrounding spin structure. For this pinning the formation of domain walls plays a significant role and two mechanisms were observed. First, the ends of perpendicular chains of domains can stop the propagation. Second, a propagating chain boundary approaching a perpendicular domain results in a 360◦ domain wall which blocks further propagation. Pinning by the surrounding spin structure can serve as an alternative to pinning in constrictions and offers a further possibility to control switching behaviour. This could lead to applications in field or currentinduced domain wall propagation where moving of domain walls in a controlled way between different pinning sites is a precondition for new concepts of data storage, e.g. the racetrack memory device [Par]. Finally, the interaction of current with domain walls was addressed. The goal was to separate spin-torque effects from heating effects on the domain walls due to the current. From an earlier experiment it is already known that transverse walls can be transformed to vortex walls by heating above a certain temperature [LBB+ 06a]. With this in mind, poorly heat conducting membrane samples were chosen to study the combined
Conclusions
147
influence of current-pulses and heating. A variety of effects were observed including transformations into multi-vortex domain walls, domain wall jumping between two pinning sites, or structural changes of the magnetic material crystallites. To reduce the influence of heating, the conductance of the samples was improved by back-coating the membrane samples with aluminum. From this a set of indicators was derived to distinguish current-induced domain wall motion due to spin torque from heating effects. The significance of these results is that they can help to improve the physical understanding of the spin-torque effect and that new paths to possible applications have been shown. Smaller domain walls and high spin-polarized materials are predicted to increase the efficiency of the spin-torque, so increasing the domain wall velocity and lowering the critical current density. Experimental confirmation allows the verification of the theoretical predictions. For applications it is essential to avoid the domination of heating over spin-torque effects because heating can cause changes in the spin structure of domain walls and the movement of the domain walls would no longer be predictable. For devices it is of utmost importance to have full control over the domain wall movement by switching them between different pinning sites. Two possibilities to achieve this were shown in this thesis, one being constrictions and the other being pinning by the surrounding spin structure. For future studies, the developed fabrication processes can be applied to different materials and the spin structure of the resulting magnetic elements should be investigated. PEEM and electron holography are powerful tools to image the spin structure of a broad range of magnetic materials and in addition, both offer the possibility to observe the spin structure on application of current pulses. High spin-polarized materials, e.g. Fe3 O4 and CrO2 , are interesting materials for such experiments because they promise faster domain wall velocities and lower critical current densities. It turned out to be difficult to image CrO2 with PEEM, which means that this material is currently less suitable for current-induced domain
Conclusions
148
wall motion experiments. The spin structure of Fe3 O4 has already been successfully measured with PEEM, however patterning did not always result in good measurements. Therefore, the effort should be moved in improving the patterning process. Once the patterned Fe3 O4 films produce reproducible measurements, current-induced domain wall motion experiments should be carried out using PEEM. The results can then be compared with results obtained for 3d-metals. Since saturation magnetization and spin polarization govern the efficiency according to the existing theories, this would be a good possibility to test these theories. New patterning techniques will allow further reduction of the dimensions of the magnetic elements. Wires with a width of 30 nm or even below would allow the study of the behaviour of domain walls with the same size observed in constrictions in this work. If the wires are made of a spin valve multilayer, the position of the domain wall could be determined by measuring the giant magnetoresistance (GMR) signal [GLC+ 02, GBC+ 03] and the switching behaviour in an applied magnetic field or current could be observed.
Bibliography [ABD97]
A. O. Adeyeye, J. A. C. Bland, and C. Daboo. Magnetic Properties of Arrays of ”Holes” in Ni80 Fe20 Films. Appl. Phys. Lett. 70, 3164–3166, 1997.
[Aha96]
A. Aharoni. Introduction to the Theory of Ferromagnetism. Clarendon Press, Oxford, 1996.
[ASA+ 05]
T. Arnal, R. Soulimane, A. Aassime, M. Bibes, P. Lecoeur, A. M. Haghiri-Gosnet, B. Mercey, A. V. Khvalkovskii, A. K. Zvezdin, and K. A. Zvezdin. Magnetic Nanowires Patterned in the La2/3 Sr1/3 MnO3 Half-metal. Microelectron. Eng. 78-79, 201–205, 2005.
[AXC04]
D. A. Allwood, G. Xiong, and R. P. Cowburn. Domain Wall Diodes in Ferromagnetic Planar Nanowires. Appl. Phys. Lett. 85, 2848–2850, 2004.
[Bac04]
D. Backes. Herstellung und rasterkraftmikroskopische Untersuchung von topografisch strukturierten, magnetischen Schichtsystemen. Master’s thesis, Universität Kaiserslautern, 2004.
[Ber84]
L. Berger.
Exchange Interaction between Ferromagnetic
Domain-wall and Electric-current in Very Thin Metallic-Films. J. Appl. Phys. 55, 1954–1956, 1984. [Ber98]
G. Bertotti. Hysteresis in Magnetism. Academic Press, San Diego, CA, USA, 1998.
BIBLIOGRAPHY [Büh05]
150
W. Bührer. Interactions Between Spin Currents and Domain Walls. Master’s thesis, Universität Konstanz, 2005.
[BHD+ 06]
D. Backes, L. J. Heyderman, C. David, R. Schäublin, M. Kläui, H. Ehrke, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, T. Kasama, and R. E. Dunin-Borkowski. Fabrication of Curved-line Nanostructures on Membranes for Transmission Electron Microscopy Investigations of Domain Walls. Microelectron. Eng. 83, 1726–1729, 2006.
[BJZ98]
Y. B. Bazaliy, B. A. Jones, and S. C. Zhang.
Modifica-
tion of the Landau-Lifshitz Equation in the Presence of a Spinpolarized Current in Colossal- and Giant-magnetoresistive Materials. Phys. Rev. B 57, R3213–R3216, 1998. [BKF+ 07]
A. Biehler, M. Kläui, M. Fonin, C. König, G. Güntherodt, and U. Rüdiger. Domain Structures and the Influence of Current on Domains and Domain Walls in Highly Spin-polarized CrO2 Wire Elements. Phys. Rev. B 75, 184427, 2007.
[BKR+ 07]
D. Bedau, M. Kläui, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, G. Faini, L. Vila, and W. Wernsdorfer. Angular Dependence of the Depinning Field for Head-to-head Domain Walls at Constrictions. J. Appl. Phys. 101, 09F509, 2007.
[BNK+ 05]
G.S.D. Beach, C. Nistor, C. Knutson, M. Tsoi, and J.L. Erskine. Dynamics of Field-driven Domain-wall Propagation in Ferromagnetic Nanowires. Nature Mater. 4, 741, 2005.
[Bro63]
W.S. Brown. Micromagnetics. Wiley, New York, 1963.
[Bru99]
P. Bruno. Geometrically Constrained Magnetic Wall. Phys. Rev. Lett. 83, 2425–2428, 1999.
[BSK+ 07]
D. Backes, C. Schieback, M. Kläui, F. Junginger, H. Ehrke, P. Nielaba, U. Rüdiger, L.J. Heyderman, C.S. Chen, T. Kasama, R.E. Dunin-Borkowski, C.A.F. Vaz, and J.A.C.
BIBLIOGRAPHY
151
Bland. Transverse Domain Walls in Nanoconstrictions. Appl. Phys. Lett. 91, 2502, 2007. [CAB97]
R.P. Cowburn, A.O. Adeyeye, and J.A.C. Bland. Magnetic Switching and Uniaxial Anisotropy in Lithographically Defined Anti-dot Permalloy Arrays. J. Magn. Magn. Mat. 173, 193– 201, 1997.
[Cha67]
B.L. Chamberland. Crystal Growth of CrO2 . Mat. Res. Bull. 2, 827, 1967.
[CIL+ 95]
C. T. Chen, Y. U. Idzerda, H. J. Lin, N. V. Smith, G. Meigs, E. Chaban, G. H. Ho, E. Pellegrin, and F. Sette. Experimental Confirmation of the X-Ray Magnetic Circular-Dichroism SumRules for Iron and Cobalt. Phys. Rev. Lett. 75, 152–155, 1995.
[CvdBR+ 97] W. Clemens, H. A. M. van den Berg, G. Rupp, W. Schelter, M. Vieth, and J. Wecker. Contactless Potentiometer Based on Giant Magnetoresistance Sensors. J. Appl. Phys. 81, 4310– 4312, 1997. [CXB+ 01]
R. H. Cheng, B. Xu, C. N. Borca, A. Sokolov, C. S. Yang, L. Yuan, S. H. Liou, B. Doudin, and P. A. Dowben. Characterization of the Native Cr2 O3 Oxide Surface of CrO2 . Appl. Phys. Lett. 79, 3122–3124, 2001.
[DBMK+ 00]
R. E. Dunin-Borkowski, M. R. McCartney, B. Kardynal, S. S. P. Parkin, M. R. Scheinfein, and D. J. Smith. Offaxis Electron Holography of Patterned Magnetic Nanostructures. Journal Of Microscopy-Oxford 200, 187–205, 2000.
[DBMSP98]
R. E. Dunin-Borkowski, M. R. McCartney, D. J. Smith, and S. S. P. Parkin. Towards Quantitative Electron Holography of Magnetic Thin Films Using In-situ Magnetization Reversal. Ultramicroscopy 74, 61–73, 1998.
BIBLIOGRAPHY [Ded04]
152
Yu. S. Dedkov. Spin-Resolved Photoelectron Spectroscopy of Oxidic Half-Metallic Ferromagnets and Oxide/Ferromagnet Interfaces. PhD thesis, RWTH Aachen, 2004.
[DFK+ 02]
Y. S. Dedkov, M. Fonine, C. König, U. Rüdiger, G. Güntherodt, S. Senz, and D. Hesse. Room-temperature Observation of High-spin Polarization of Epitaxial CrO2 (100) Island Films at The Fermi Energy. Appl. Phys. Lett. 80, 4181–4183, 2002.
[dGMVEB83] R. A. de Groot, F. M. Mueller, P. G. Van Engen, and K. H. J. Buschow. New Class of Materials - Half-Metallic Ferromagnets. Phys. Rev. Lett. 50, 2024–2027, 1983. [DH99]
C. David and D. Hambach. Line Width Control Using a Defocused Low Voltage Electron Beam. Microelectron. Eng. 46, 219–222, 1999.
[DP02]
M. J. Donahue and D. G. Porter.
OOMMF User’s Guide,
2002. [DRRB07]
J. Dho, I. Rhee, H. C. Ri, and M. G. Blamire. Direction Dependent Giant Magnetoresistance of Spin Valves Using Epitaxial Cr2 O3 as the Pinning Layer. J. Magn. Magn. Mat. 310, 1892–1894, 2007.
[DTX+ 00]
J. B. Dai, J. K. Tang, H. P. Xu, L. Spinu, W. D. Wang, K. Y. Wang, A. Kumbhar, M. Li, and U. Diebold. Characterization of the Natural Barriers of Intergranular Tunnel Junctions: Cr2 O3 Surface Layers on CrO2 Nanoparticles. Appl. Phys. Lett. 77, 2840–2842, 2000.
[EGE+ 04]
W. F. Egelhoff, L. Gan, H. Ettedgui, Y. Kadmon, C. J. Powell, P. J. Chen, A. J. Shapiro, R. D. McMichael, J. J. Mallett, T. P. Moffat, M. D. Stiles, and E. B. Svedberg. Artifacts in Ballistic Magnetoresistance Measurements (invited). J. Appl. Phys. 95, 7554–7559, 2004.
BIBLIOGRAPHY [FDK+ 03]
153
M. Fonin, Yu. S. Dedkov, C. König, G. Güntherodt, U. Rüdiger, J. Mayer, D. Vyalikh, and S. Molodtsov. Room Temperature Spin Polarization of Epitaxial Halfmetallic Fe3 O4 (111) and CrO2 (100) Films. Adv. in Solid State Phys. 43, 487–504, 2003.
[FT65]
E. Feldtkeller and H. Thomas. Struktur und Energie von Blochlinien in dünnen ferromagnetischen Schichten.
Phys.
Kondens. Materie 4, 8–14, 1965. [GBC+ 03]
J. Grollier, P. Boulenc, V. Cros, A. Hamzic, A. Vaures, A. Fert, and G. Faini. Switching a Spin Valve Back and Forth by Current-induced Domain Wall Motion. Appl. Phys. Lett. 83, 509–511, 2003.
[GBG+ 02]
E. Goering, A. Bayer, S. Gold, G. Schütz, M. Rabe, U. Rüdiger, and G. Güntherodt. Strong Anisotropy of Projected 3d Moments in Epitaxial CrO2 Films. Phys. Rev. Lett. 88, 207203, 2002.
[GGM+ 03]
I. Guedes, M. Grimsditch, V. Metlushko, P. Vavassori, R. Camley, B. Ilic, P. Neuzil, and R. Kumar. Magnetization Reversal in a Fe Film with an Array of Elliptical Holes on a Square Lattice. Phys. Rev. B 67, 024428, 2003.
[Gil55]
T. L. Gilbert. Lagrangian Formulation of the Gyromagnetic Equation of the Magnetization Field. Phys. Rev. 100, 1243– 1243, 1955.
[GLC+ 02]
J. Grollier, D. Lacour, V. Cros, A. Hamzic, A. Vaures, A. Fert, D. Adam, and G. Faini. Switching the Magnetic Configuration of a Spin Valve by Current-induced Domain Wall Motion. J. Appl. Phys. 92, 4825–4827, 2002.
[GM04]
R. Gross and A. Marx. SS2004, 2004.
Spinelektronik - Vorlesungsskript
BIBLIOGRAPHY [GMZ99]
154
N. Garcia, M. Munoz, and Y. W. Zhao. Magnetoresistance in Excess of 200% in Ballistic Ni Nanocontacts at Room Temperature and 100 Oe. Phys. Rev. Lett. 82, 2923–2926, 1999.
[Har06]
C. Hartung. Growth and Characterization of Highly SpinPolarized Oxide Systems. Master’s thesis, Universität Konstanz, 2006.
[HC03]
S. Z. Hua and H. D. Chopra. 100,000% Ballistic Magnetoresistance in Stable Ni Nanocontacts at Room Temperature. Phys. Rev. B 67, 060401, 2003.
[Hey91]
L.J. Heyderman. Magnetic Properties of Coupled Permalloy Thin Films. PhD thesis, University of Bristol, 1991.
[Hüf03]
S. Hüfner.
Photoelectron Spectroscopy.
Springer-Verlag,
Berlin Heidelberg New York, 2003. [Hin02]
D. Hinzke. Computersimulationen zur Dynamik magnetischer Nanostrukturen. PhD thesis, Gerhard-Mercator-Universität Duisburg, 2002.
[HKK+ 07]
E.M. Hempe, M. Kläui, T. Kasama, D. Backes, F. Junginger, S. Krzyk, L. J. Heyderman, R. Dunin-Borkowski, and U. Rüdiger. Domain Walls, Domain Wall Transformations and Structural Changes in Permalloy Nanowires when Subjected to Current Pulses. Phys. Stat. Sol. A 204, 3922, 2007.
[HKS+ 05]
L. Heyderman, M. Kläui, R. Schäublin, U. Rüdiger, C.A.F. Vaz, J.A.C. Bland, and C. David. Fabrication of Magnetic Ring Structures for Lorentz Electron Microscopy. J. Magn. Magn. Mat. 290, 86–89, 2005.
[HLZ06]
J. He, Z. Li, and S. Zhang. Effects of Current on Vortex and Transverse Domain Walls. J. Appl. Phys. 99, 08G509, 2006.
BIBLIOGRAPHY [HNGP91]
155
L. J. Heyderman, H. Niedoba, H. O. Gupta, and I. B. Puchalska. 360◦ and 0◦ Walls in Multilayer Permalloy Films. J. Magn. Magn. Mat. 96, 125–136, 1991.
[HOK+ 05]
A. Himeno, T. Okuno, S. Kasai, T. Ono, S. Nasu, K. Mibu, and T. Shinjo. Propagation of a Magnetic Domain Wall in Magnetic Wires with Asymmetric Notches. J. Appl. Phys. 97, 066101, 2005.
[HS98]
A. Hubert and R. Schäfer. Magnetic Domains - The Analysis of Magnetic Microstructures. Springer-Verlag, Berlin Heidelberg New York, 1998.
[HSKO06]
M. Hara, J. Shibata, T. Kimura, and Y. Otani. Control of Domain Wall Pinning by a Switchable Magnetic Gate. Appl. Phys. Lett. 89, 192504, 2006.
[IL99]
H. Ibach and H. Lüth. Festkörperphysik. Springer-Verlag, Berlin Heidelberg New York, 1999.
[INS79]
S. Ishibashi, T. Namikawa, and M. Satou. Epitaxial-growth of Ferromagnetic CrO2 Films in Air. Mat. Res. Bull. 14, 51–57, 1979.
[JBdBdV96]
M. T. Johnson, P. J. H. Bloemen, F. J. A. den Broeder, and J. J. de Vries. Magnetic Anisotropy in Metallic Multilayers. Reports On Progress In Physics 59, 1409–1458, 1996.
[JKB+ 07]
F. Junginger, M. Kläui, D. Backes, U. Rüdiger, T. Kasama, R. E. Dunin-Borkowski, L.J. Heyderman, C.A.F. Vaz, and J.A.C. Bland. Spin Torque and Heating Effects in Currentinduced Domain Wall Motion Probed by Transmission Electron Microscopy. Appl. Phys. Lett. 90, 2506, 2007.
[JSY+ 01]
Y. Ji, G. J. Strijkers, F. Y. Yang, C. L. Chien, J. M. Byers, A. Anguelouch, G. Xiao, and A. Gupta. Determination of
BIBLIOGRAPHY
156
the Spin Polarization of Half-metallic CrO2 by Point Contact Andreev Reflection. Phys. Rev. Lett. 86, 5585–5588, 2001. [Kas56]
T. Kasuya. A Theory of Metallic Ferromagnetism and Antiferromagnetism on Zeners Model. Progress Of Theoretical Physics 16, 45–57, 1956.
[Ker77]
J. Kerr. On the Rotation of the Plane of Polarization by Reflection from the Pole of a Magnet. Phil. Mag. 3, 321–343, 1877.
[KER+ 05]
M. Kläui, H. Ehrke, U. Rüdiger, T. Kasama, R. E. DuninBorkowski, D. Backes, L. J. Heyderman, C. A. F. Vaz, J. A. C. Bland, G. Faini, E. Cambril, and W. Wernsdorfer. Direct Observation of Domain-wall Pinning at Nanoscale Constrictions. Appl. Phys. Lett. 87, 102509, 2005.
[KF03]
H. Kronmüller and M. Fähnle. Micromagnetism and the Microstructure of Ferromagnetic Solids. Cambridge University Press, 2003.
[KFL+ 07]
C. König, M. Fonin, M. Laufenberg, A. Biehler, W. Bührer, M. Kläui, U. Rüdiger, and G. Güntherodt.
Micromag-
netism and Magnetotransport Properties of Micron-sized Epitaxial CrO2 Wires. Phys. Rev. B 75, 144428, 2007. [Kik56]
R. Kikuchi. On The Minimum of Magnetization Reversal Time. J. Appl. Phys. 27, 1352–1357, 1956.
[KJA+ 05]
M. Kläui, P. O. Jubert, R. Allenspach, A. Bischof, J. A. C. Bland, G. Faini, U. Rüdiger, C. A. F. Vaz, L. Vila, and C. Vouille. Direct Observation of Domain-wall Configurations Transformed by Spin Currents. Phys. Rev. Lett. 95, 026601, 2005.
[Klä03]
M. Kläui. Nanomagnetism of High-symmetry Magnetic Structures. PhD thesis, University of Cambridge, 2003.
BIBLIOGRAPHY [KLH+ 06]
157
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.
[Kön06]
C. König. Nanomagnetismus von epitaktischen Fe(110)- und CrO2 (100)-Strukturen im Hinblick auf potentielle spinelektronische Anwendungen. Phd thesis, RWTH Aachen, 2006.
[KPSW03]
S. Khmelevskyi, K. Palotás, L. Szunyogh, and P. Weinberger. Ab Initio Calculation of the Anisotropic Magnetoresistance in Ni1−c Fec Bulk Alloys. Phys. Rev. B 68, 012402, 2003.
[KRP01]
A.D. Kent, U. Rüdiger, and S.S.P. Parkin. Domain Wall Resestivity in Epitaxial Thin Film Microstructures. J. Phys.: Cond. Matter 13, R461, 2001.
[KSG+ 87]
K. P. Kamper, W. Schmitt, G. Güntherodt, R. J. Gambino, and R. Ruf. CrO2 - A New Half-metallic Ferromagnet. Phys. Rev. Lett. 59, 2788–2791, 1987.
[KSS+ 03]
S. O. Kim, H. H. Solak, M. P. Stoykovich, N. J. Ferrier, J. J. de Pablo, and P. F. Nealey. Epitaxial Self-assembly of Block Copolymers on Lithographically Defined Nanopatterned Substrates. Nature 424, 411–414, 2003.
[Kuc05]
W. Kuch. Imaging Magnetic Microspectroscopy. In H. Hopster and H.P. Oepen, editors, Magnetic Microscopy of Nanostructures, chapter 1. Springer-Verlag, Berlin Heidelberg New York, 2005.
[KVB+ 02]
M. Kläui, C. A. F. Vaz, J. A. C. Bland, W. Wernsdorfer, G. Faini, and E. Cambril. Controlled Magnetic Switching in Single Narrow Rings Probed by Magnetoresistance Measurements. Appl. Phys. Lett. 81, 108–110, 2002.
BIBLIOGRAPHY [KVB+ 03]
158
M. Kläui, C.A.F. Vaz, J.A.C. Bland, W. Wernsdorfer, G. Faini, E. Cambril, and L.J. Heyderman. Domain Wall Motion Induced by Spin Polarized Currents in Ferromagnetic Ring Structures. Appl. Phys. Lett. 83, 105–107, 2003.
[KVB+ 04a]
M. Kläui, C.A.F. Vaz, J.A.C. Bland, L.J. Heyderman, F. Nolting, A. Pavlovska, E. Bauer, S. Cherifi, S. Heun, and A. Locatelli. Head-to-head Domain-wall Phase Diagram in Mesoscopic Ring Magnets. Appl. Phys. Lett. 85, 5637–5639, 2004.
[KVB+ 04b]
M. Kläui, C.A.F. Vaz, J.A.C. Bland, E.H.C.P. Sinnecker, A.P. Guimaraes, W. Wernsdorfer, G. Faini, E. Cambril, L.J. Heyderman, and C. David. Switching Processes and Switching Reproducibility in Ferromagnetic Ring Structures. Appl. Phys. Lett. 84, 951–953, 2004.
[KVB+ 05]
M. Kläui, C.A.F. Vaz, J.A.C. Bland, W. Wernsdorfer, G. Faini, E. Cambril, L.J. Heyderman, F. Nolting, and U. Rüdiger. Controlled and Reproducible Domain Wall Displacement by Current Pulses Injected into Ferromagnetic Ring Structures. Phys. Rev. Lett. 94, 106601, 2005.
[KVR+ 03]
M. Kläui, C.A.F. Vaz, J. Rothman, J.A.C. Bland, W. Wernsdorfer, G. Faini, and E. Cambril. Domain Wall Pinning in Narrow Ferromagnetic Ring Structures Probed by Magnetoresistance Measurements. Phys. Rev. Lett. 90, 097202, 2003.
[KVW+ 04]
M. Kläui, C.A.F. Vaz, W. Wernsdorfer, E. Bauer, S. Cherifi, S. Heun, A. Locatelli, G. Faini, E. Cambril, L.J. Heyderman, and J.A.C. Bland. Domain Wall Behaviour at Constrictions in Ferromagnetic Ring Structures. Physica B 343, 343–349, 2004.
[Lau06]
M. Laufenberg. Interactions Between Current and Domain Wall Spin Structures. PhD thesis, Universität Konstanz, 2006.
BIBLIOGRAPHY [LBB+ 06a]
159
M. Laufenberg, D. Backes, W. Buhrer, D. Bedau, M. Kläui, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, L. J. Heyderman, F. Nolting, S. Cherifi, A. Locatelli, R. Belkhou, S. Heun, and E. Bauer. Observation of Thermally Activated Domain Wall Transformations. Appl. Phys. Lett. 88, 052507, 2006.
[LBB+ 06b]
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 Dependence of the Spin Torque Effect in Current-induced Domain Wall Motion. Phys. Rev. Lett. 97, 046602, 2006.
[LDKRB01]
L. Lopez-Diaz, M. Kläui, J. Rothman, and J. A. C. Bland. Precessional Switching in Narrow Ring Nanomagnets. Physica B 306, 211–215, 2001.
[Lid01]
D. R. Lide. Handbook of Chemistry and Physics, volume 12. CRC, Boca Raton, FL, 2001.
[Lil50]
B.A. Lilley. Energies and Widths of Domain Boundaries in Ferromagnetics. Phil. Mag. 41, 792–813, 1950.
[LL35]
L. D. Landau and E. Lifshitz. On the Theory of the Dispersion of Magnetic Permeability in Ferromagnetic Bodies. Phys. Z. Sowjetunion 8, 153–169, 1935.
[LZ97]
P. M. Levy and S. Zhang. Resistivity due to Domain Wall Scattering. Phys. Rev. Lett. 79, 5110, 1997.
[LZ04a]
Z. Li and S. Zhang. Domain-wall Dynamics and Spin-wave Excitations with Spin-transfer Torques. Phys. Rev. Lett. 92, 207203, 2004.
[LZ04b]
Z. Li and S. Zhang. Domain-wall Dynamics Driven by Adiabatic Spin-transfer Torques. Phys. Rev. B 70, 024417, 2004.
[Mar05]
C. H. Marrows. Spin-polarised Currents and Magnetic Domain Walls. Adv. Phys. 54, 585–713, 2005.
BIBLIOGRAPHY [MB56]
160
W. H. Meiklejohn and C. P. Bean. New Magnetic Anisotropy. Phys. Rev. 102, 1413–1414, 1956.
[MB57]
W. H. Meiklejohn and C. P. Bean. New Magnetic Anisotropy. Phys. Rev. 105, 904–913, 1957.
[MD55]
G. Möllenstedt and H. Düker. Fresnelscher Interferenzversuch mit einem Biprisma für Elektronenwellen.
Naturwis-
senschaften 42, 41–41, 1955. [MD97]
R. D. McMichael and M. J. Donahue. Head to Head Domain Wall Structures in Thin Magnetic Strips. IEEE Trans. Magn. 33, 4167–4169, 1997.
[MDBS05]
M.R. McCartney, R.E. Dunin-Borkowski, and D.J. Smith. Electron Holography of Magnetic Nanostructures. In H. Hopster and H.P. Oepen, editors, Magnetic Microscopy of Nanostructures, chapter 5. Springer-Verlag, Berlin Heidelberg New York, 2005.
[MMK+ ]
T. A. Moore, P. Möhrke, M. Kläui, D. Backes, L. J. Heyderman, S. Krzyk, K. Kirsch, R. Mattheis, and U. Rüdiger. Single Shot Measurement of Current- and Field-induced Domain Wall Motion in a Permalloy Nanowire. Presentation FE-08 at 52nd MMM Conference, Tampa, Florida, 2007.
[Née55]
L. Néel. Énergie des parois de Bloch dans les couches minces. C. R. Acad. Sci. Paris 241, 533–536, 1955.
[NTM03]
Y. Nakatani, A. Thiaville, and J. Miltat. Faster Magnetic Walls in Rough Wires. Nature Materials 2, 521–523, 2003.
[NTM05]
Y. Nakatani, A. Thiaville, and J. Miltat. Head-to-head Domain Walls in Soft Nano-strips: a Refined Phase Diagram. J. Magn. Magn. Mat. 290, 750–753, 2005.
BIBLIOGRAPHY [NYN+ 98]
161
H. Namatsu, T. Yamaguchi, M. Nagase, K. Yamazaki, and K. Kurihara. Nano-patterning of a Hydrogen Silsesquioxane Resist with Reduced Linewidth Fluctuations. Microelectron. Eng. 42, 331–334, 1998.
[OOM]
The
OOMMF
software
is
available
at
http://math.nist.gov/oommf. [Par]
S. S. P. Parkin/IBM US Patent 10/984,055 (2005).
[PLC05]
A.K. Petford-Long and J.N. Chapman.
Lorentz Mi-
croscopy. In H. Hopster and H.P. Oepen, editors, Magnetic Microscopy of Nanostructures, chapter 4. Springer-Verlag, Berlin Heidelberg New York, 2005. [PR02]
A. Paetzold and K. Roll. Thermally Activated Self-alignment of Exchange Coupling in NiO/NiFe Bilayers. J. Appl. Phys. 91, 7748–7750, 2002.
[QFP+ 01]
C. Quitmann, U. Flechsig, L. Patthey, T. Schmidt, G. Ingold, M. Howells, M. Janousch, and R. Abela. A Beamline for Time Resolved Photoelectron Microscopy on Magnetic Materials at the Swiss Light Source. Surface Science 480, 173–179, 2001.
[RCDJDJ95]
T.G.S.M. Rijks, R. Coehoorn, M. J. M. De Jong, and W. J. M. De Jonge. Semiclassical Calculations of the Anisotropic Magnetoresistance of NiFe-Based Thin-Films, Wires, and Multilayers. Phys. Rev. B 51, 283–291, 1995.
[RK54]
M. A. Ruderman and C. Kittel. Indirect Exchange Coupling of Nuclear Magnetic Moments by Conduction Electrons. Phys. Rev. 96, 99–102, 1954.
[RYZ+ 98]
U. Rüdiger, J. Yu, S. Zhang, A. D. Kent, and S. S. P. Parkin. Negative Domain Wall Contribution to the Resistivity of Microfabricated Fe Wires. Phys. Rev. Lett. 80, 5639–5642, 1998.
BIBLIOGRAPHY [SBO+ 98]
162
R. J. Soulen, J. M. Byers, M. S. Osofsky, B. Nadgorny, T. Ambrose, S. F. Cheng, P. R. Broussard, C. T. Tanaka, J. Nowak, J. S. Moodera, A. Barry, and J. M. D. Coey. Measuring the Spin Polarization of a Metal with a Superconducting Point Contact. Science 282, 85–88, 1998.
[Sch86]
K. Schwarz. CrO2 Predicted as a Half-metallic Ferromagnet. J. Phys. F: Met. Phys. 16, L211, 1986.
[SDG+ 02]
H. H. Solak, C. David, J. Gobrecht, L. Wang, and F. Cerrina. Multiple-beam Interference Lithography with Electron Beam Written Gratings. J. Vac. Sci. Techn. B 20, 2844–2848, 2002.
[Ser06]
R. F. Service. Data Storage - Is the Terabit Within Reach? Science 314, 1868–1870, 2006.
[SKN+ 07]
C. Schieback, M. Kläui, U. Nowak, U. Rüdiger, and P. Nielaba. Numerical Investigation of Spin-torque Using the Heisenberg Model. Eur. Phys. J. B 59, 429–433, 2007.
[Slo96]
J. C. Slonczewski.
Current-driven Excitation of Magnetic
Multilayers. J. Magn. Magn. Mat. 159, L1–L7, 1996. [Smi51]
J. Smit. Magnetoresistance of Ferromagnetic Metals and Alloys at Low Temperatures. Physica 17, 612–627, 1951.
[SS06]
J. Stöhr and H.C. Siegmann. Magnetism: From Fundamentals to Nanoscale Dynamics. Springer Series in Solid-State Sciences. Springer-Verlag, Berlin Heidelberg New York, 2006.
[SWH+ 93]
J. Stöhr, Y. Wu, B. D. Hermsmeier, M. G. Samant, G. R. Harp, S. Koranda, D. Dunham, and B. P. Tonner. ElementSpecific Magnetic Microscopy with Circularly Polarized XRays. Science 259, 658–661, 1993.
BIBLIOGRAPHY [TBG+ 05]
163
J. M. Torres Bruna, J. Bartolomé, L. M. García Vinuesa, F. Garcia Sanchez, J. M. Gonzalez, and O. A. ChubykaloFesenko. A Micromagnetic Study of the Hysteretic Behavior of Antidot Fe Films. J. Magn. Magn. Mat. 290, 149–152, 2005.
[TF97]
G. Tatara and H. Fukuyama. Resistivity due to a Domain Wall in Ferromagnetic Metal. Phys. Rev. Lett. 78, 3773–3776, 1997.
[TH88]
B.P. Tonner and G.R. Harp. Photoelectron Microscopy with Synchrotron Radiation. Rev. Sci. Instr. 59, 853–858, 1988.
[Tho57]
W. Thomson. On the Electro-dynamic Qualities of Metals: Effects of Magnetization on the Electric Conductivity of Nickel and of Iron. Proc. Roy. Soc. London 8, 546–550, 1857.
[TK04]
G. Tatara and H. Kohno. Theory of Current-driven Domain Wall Motion: Spin Transfer Versus Momentum Transfer. Phys. Rev. Lett. 92, 086601, 2004.
[TKH+ 06]
Y. Togawa, T. Kimura, K. Harada, T. Akashi, T. Matsuda, A. Tonomura, and Y. Otani. Current-excited Magnetization Dynamics in Narrow Ferromagnetic Wires. Japanese J. Appl. Phys. 45, L683–L685, 2006.
[TM71]
P. M. Tedrow and R. Meservey. Spin-dependent Tunneling into Ferromagnetic Nickel. Phys. Rev. Lett. 7, 192, 1971.
[TM73]
P. M. Tedrow and R. Meservey. Spin Polarization of Electrons Tunneling from Films of Fe, Co, Ni, and Gd. Phys. Rev. B 7, 318, 1973.
[TNMS05]
A. Thiaville, Y. Nakatani, J. Miltat, and Y. Suzuki. Micromagnetic Understanding of Current-driven Domain Wall Motion in Patterned Nanowires. Europhys. Lett. 69, 990–996, 2005.
BIBLIOGRAPHY [TNMV04]
164
A. Thiaville, Y. Nakatani, J. Miltat, and N. Vernier. Domain Wall Motion by Spin-polarized Current: a Micromagnetic Study. J. Appl. Phys. 95, 7049–7051, 2004.
[TTK+ 06]
G. Tatara, T. Takayama, H. Kohno, J. Shibata, Y. Nakatani, and H. Fukuyama. Threshold Current of Domain Wall Motion Under Extrinsic Pinning, Beta-term and Non-adiabaticity. Journal of The Physical Society of Japan 75, 064708, 2006.
[TWK+ 06]
C. Thirion, W. Wernsdorfer, M. Kläui, C. A. F. Vaz, P. Lewis, H. Ahmed, J. A. C. Bland, and D. Mailly. Anisotropy Engineering in Co Nanodiscs Fabricated Using Prepatterned Silicon Pillars. Nanotechnology 17, 1960–1963, 2006.
[TZMG99]
G. Tatara, Y. W. Zhao, M. Munoz, and N. Garcia. Domain Wall Scattering Explains 300% Ballistic Magnetoconductance of Nanocontacts. Phys. Rev. Lett. 83, 2030–2033, 1999.
[UPLB98]
S. K. Upadhyay, A. Palanisami, R. N. Louie, and R. A. Buhrman.
Probing Ferromagnets with Andreev Reflection.
Phys. Rev. Lett. 81, 3247–3250, 1998. [VAA+ 04]
N. Vernier, D. A. Allwood, D. Atkinson, M. D. Cooke, and R. P. Cowburn. Domain Wall Propagation in Magnetic Nanowires by Spin-polarized Current Injection. Europhys. Lett. 65, 526–532, 2004.
[VABR06]
C. A. F. Vaz, C. Athanasiou, J. A. C. Bland, and G. Rowlands. Energetics of Magnetic Ring and Disk Elements: Uniform Versus Vortex State. Phys. Rev. B 73, 054411, 2006.
[VGZ+ 02]
P. Vavassori, G. Gubbiotti, G. Zangari, C. T. Yu, H. Yin, H. Jiang, and G. J. Mankey. Lattice Symmetry and Magnetization Reversal in Micron-size Antidot Arrays in Permalloy Film. J. Appl. Phys. 91, 7992–7994, 2002.
BIBLIOGRAPHY
165
[vHWH+ 93] R. von Helmolt, J. Wecker, B. Holzapfel, L. Schultz, and Samwer K. Giant Negative Magnetoresistance in Perovskitelike La2/3 Ba1/3 M nOx Ferromagnetic Films. Phys. Rev. Lett. 71, 2331–2333, 1993. [WAB03]
M. J. Word, I. Adesida, and P. R. Berger. Nanometer-period Gratings in Hydrogen Silsesquioxane Fabricated by Electron Beam Lithography. J. Vac. Sci. Techn. B 21, L12–L15, 2003.
[WAW03]
C. C. Wang, A. O. Adeyeye, and Y. H. Wu. Magnetic Properties of Asymmetric Antirectangular Ni80 Fe20 arrays. J. Appl. Phys. 94, 6644–6648, 2003.
[WDFH93]
M. L. Watson, W. D. Doyle, H. Fujiwara, and S. Hossain. The Absence of Giant Magnetoresistance on Antiferromagnetically Coupled NiFe/Cr Multilayers. J. Appl. Phys. 73, 5518– 5520, 1993.
[Wer01]
W. Wernsdorfer. Classical and Quantum Magnetization Reversal Studied in Nanometer-sized Particles and Clusters. In Advances In Chemical Physics, volume 118 of Advances In Chemical Physics, pages 99–190. 2001.
[Wie02]
R. Wieser. Computersimulationen von Domänenwänden in ferromagnetischen Drähten, 2002.
[WWC+ 92]
J. S. S. Whiting, M. L. Watson, A. Chambers, J. C. S. Levy, D. Mercier, I. B. Puchalska, and H. Niedoba. Magnetic and Theoretical-Studies of NiFe Layers Coupled through a Chromium Interlayer. J. Magn. Magn. Mat. 115, 174–176, 1992.
[XZS06]
J. A. Xiao, A. Zangwill, and M. D. Stiles. Spin-transfer Torque for Continuously Variable Magnetization. Phys. Rev. B 73, 054428, 2006.
BIBLIOGRAPHY [YCL+ 01]
166
F. Y. Yang, C. L. Chien, X. W. Li, G. Xiao, and A. Gupta. Critical Behavior of Epitaxial Half-metallic Ferromagnetic CrO2 Films. Phys. Rev. B 6309, 092403, 2001.
[YJS+ 00]
C. T. Yu, H. Jiang, L. Shen, P. J. Flanders, and G. J. Mankey. The Magnetic Anisotropy and Domain Structure of Permalloy Antidot Arrays. J. Appl. Phys. 87, 6322–6324, 2000.
[YON+ 04]
A. Yamaguchi, T. Ono, S. Nasu, K. Miyake, K. Mibu, and T. Shinjo. Real-space Observation of Current-driven Domain Wall Motion in Submicron Magnetic Wires. Phys. Rev. Lett. 92, 077205, 2004.
[Yos57]
K. Yosida. Magnetic Properties of Cu-Mn Alloys. Phys. Rev. 1, 893–898, 1957.
[YSJ06]
C. Y. You, I. M. Sung, and B. K. Joe.
Analytic Expres-
sion for the Temperature of the Current-heated Nanowire for the Current-induced Domain Wall Motion. Appl. Phys. Lett. 89, 222513, 2006. [ZFP+ 05]
G. M. Zhang, C. F. Fan, L. Q. Pan, F. P. Wang, P. Wu, H. Qiu, Y. S. Gu, and Y. Zhang. Magnetic and Transport Properties of Magnetite Thin Films. J. Magn. Magn. Mat. 293, 737–745, 2005.
[ZL04]
S. Zhang and Z. Li. Roles of Nonequilibrium Conduction Electrons on the Magnetization Dynamics of Ferromagnets. Phys. Rev. Lett. 93, 127204, 2004.
[ZP04]
A. J. Zambano and W. P. Pratt. Detecting Domain-wall Trapping and Motion at a Constriction in Narrow Ferromagnetic Wires Using Perpendicular-current Giant Magnetoresistance. Appl. Phys. Lett. 85, 1562–1564, 2004.
Publication List Journal Papers • L. Heyne, D. Backes, T. Moore, S. Krzyk, M. Kläui, U. Rüdiger, L. J. Heyderman, A. Fraile Rodriguez, F. Nolting, T. O. Mentes, A. Locatelli, K. Kirsch, R. Mattheis, Relationship between Nonadiabaticity and Damping in Permalloy Studied by Current Induced Spin Structure Transformations, Phys. Rev. Lett. 100, 066603, 2008. • D. Backes, C. Schieback, M. Kläui, F. Junginger, H. Ehrke, P. Nielaba, U. Rüdiger, L. J. Heyderman, C. S. Chen, T. Kasama, R. E. DuninBorkowski, C. A. F. Vaz and J. A. C. Bland, Transverse Domain Walls in Nanoconstrictions, Appl. Phys. Lett. 91, 112502, 2007. • F. Junginger, M. Kläui, D. Backes, U. Rüdiger, T. Kasama, R. E. Dunin-Borkowski, L. J. Heyderman, C. A. F. Vaz, and J. A. C. Bland, Spin Torque and Heating Effects in Current-induced Domain Wall Motion Probed by Transmission Electron Microscopy, Appl. Phys. Lett. 90, 132506, 2007. • E.-M. Hempe, M. Kläui, T. Kasama, D. Backes, F. Junginger, S. Krzyk, L. J. Heyderman, R. Dunin-Borkowski, U. Rüdiger, Domain Walls, Domain Wall Transformations and Structural Changes in Permalloy Nanowires when Subjected to Current Pulses, phys. stat. sol.
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(a) 204, 3922, 2007. • 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, 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, 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. Locatelli, R. Belkhou, S. Heun, E. Bauer, Observation of Thermally Activated Domain Wall Transformations, Appl. Phys. Lett. 88, 052507, 2006. • I. Neudecker, M. Kläui, K. Perzlmaier, D. Backes, L. J. Heyderman, C. A. F. Vaz, J. A. C. Bland, U. Rüdiger, C. H. Back, Spatially Resolved Dynamic Eigenmode Spectrum of Co Rings, Phys. Rev. Lett. 96, 057207, 2006. • L. J. Heyderman, F. Nolting, D. Backes, S. Czekaj, L. Lopez-Diaz, M. Kläui, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, R. J. Matelon, U. G. Volkmann, P. Fischer, Magnetization Reversal in Cobalt Antidot Arrays, Phys. Rev. B 73, 214429, 2006. • D. Backes, L. J. Heyderman, C. David, R. Schäublin, M. Kläui, H. Ehrke, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, T. Kasama, and R. E. Dunin-Borkowski, Fabrication of Curved-line Nanostructures on Membranes for Transmis-
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sion Electron Microscopy Investigations of Domain Walls, Microelectr. Eng. 83, 1726, 2006. • M. Kläui, H. Ehrke, U. Rüdiger, T. Kasama, R. E. Dunin-Borkowski, D. Backes, L. J. Heyderman, C. A. F. Vaz, J. A. C. Bland, G. Faini, E. Cambril, and W. Wernsdorfer, Direct Observation of Domain-wall Pinning at Nanoscale Constrictions, Appl. Phys. Lett. 87, 102509, 2005. • F. Junginger, M. Kläui, D. Backes, S. Krzyk, U. Rüdiger, T. Kasama, R. E. Dunin-Borkowski, J. Feinberg, R. Harrison, L. J. Heyderman, Quantitative Determination of Vortex Core Dimensions in Head-to-head Domain Walls using Off-axis Electron Holography, submitted to Applied Physics Letters • L. Heyne, M. Kläui, D. Backes, T. A. Moore, J. G. Kimling, U. Rüdiger, L. J. Heyderman, A. Fraile-Rodriguez, F. Nolting, K. Kirsch, R. Mattheis, Direct Imaging of Current-induced Domain Wall Motion in CoFeB Structures, accepted by J. Appl. Phys.
Review Article • C. A. F. Vaz, T. J. Hayward, J. Llandro, F. Schackert, D. Morecroft, J. A. C. Bland, M. Kläui, M. Laufenberg, D. Backes, U. Rüdiger, F. J. Castano, C. A. Ross, L. J. Heyderman, F. Nolting, A. Locatelli, G. Faini, S. Cherifi, W. Wernsdorfer, Direct Observation of Domain-wall Pinning at Nanoscale Constrictions, J. Phys.: Condens. Matter 19, 255507, 2007. • 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. DuninBorkowski, A. Pavlovska, and E. Bauer,
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Domain Wall Spin Structures in 3d Metal Ferromagnetic Nanostructures, Adv. in Solid State Phys. 46, 281-293, 2008.
Conference Contributions • D. Backes, C. Schieback, L. J. Heyderman, C. David, M. Kläui, F. Junginger, H. Ehrke, P. Nielaba, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, C. S. Chen, T. Kasama, R. E. Dunin-Borkowski, Geometrically Confined Domain Walls and the Interaction with Currents Observed by TEM, WUN-SPIN07 2007 York England, Best Poster Award. • D. Backes, L. J. Heyderman, C. David, M. Kläui, F. Junginger, H. Ehrke, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, C. Chen, T. Kasama, R. E. Dunin-Borkowski, Head-to-Head Domain Wall Investigations by TEM methods, DPGFrühjahrstagung 2007 Regensburg, Poster contribution. • D. Backes, L. J. Heyderman, M. Kläui, H. Ehrke, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, T. Kasama, R. E. Dunin-Borkowski, Spin-structure
Investigations
by
Electron
Holography,
DPG-
Frühjahrstagung 2006 Dresden, Poster contribution. • D. Backes, L. J. Heyderman, C. David, F. Nolting, M. Kläui, M. Laufenberg, L. Heyne, D. Bedau, W. Bührer, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, S. Cherifi, A. Locatelli, R. Belkhou, T. O. Mentes, L. Aballe, S. Heun, Domain Wall Transformation and Propagation Observed by Photoemission Electron Microscopy, SLS users´ meeting 2006 PSI Villigen, Poster contribution. • D. Backes, L. J. Heyderman, C. David, F. Nolting, M. Kläui, M. Laufenberg, H. Ehrke, D. Bedau, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, T. Kasama, R. E. Dunin-Borkowski, S. Cherifi, A. Locatelli, S. Heun,
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Spin-structure Investigations by Photoemission Electron Microscopy and Electron Holography, Microscopy Conference 2005 Davos, Poster contribution. • D. Backes, L. J. Heyderman, C. David, A. Fraile-Rodríguez, F. Nolting, M. Kläui, M. Laufenberg, L. Heyne, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, S. Cherifi, A. Locatelli, T. O. Mentes, and L. Aballe, Interaction of Currents and Domain Walls in Nanowires, SLS Symposium on Nanostructures 2007 PSI Villigen, Oral contribution. • D. Backes, L. J. Heyderman, C. David, M. Kläui, F. Junginger, H. Ehrke, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, T. Kasama, R. E. Dunin-Borkowski, Fabrication of Magnetic Nanostructures on Membranes for Electron Holography Investigations of Domain Walls, International Microprocesses and Nanotechnology Conference (MNC) 2006 Kamakura, Japan, Oral contribution (Invited). • D. Backes, L. J. Heyderman, C. David, R. Schäublin, M. Kläui, H. Ehrke, U. Rüdiger, C. A. F. Vaz, J. A. C. Bland, T. Kasama, R. E. Dunin-Borkowski, Fabrication of Ferromagnetic Nanostructures on Membranes for Transmission Electron Microscopy Investigations of Domain Walls, MNE 2005 Wien, Oral contribution (Young Author´s Award). •
Acknowledgement / Danksagung Bei der Durchführung dieser Arbeit wurde ich auf verschiedenste Weise unterstützt. Im folgenden möchte ich die Hilfeleistenden gebührend würdigen. Prof. Ulrich Rüdiger danke ich für die Aufnahme in seinen Lehrstuhl an der Universität Konstanz. Dadurch ermöglichte er mir erst, an forderster Front zu forschen und darüberhinaus eine Doktorarbeit anzufertigen. Seine Anregungen und seine Hilfe bei organisatorischen Angelegenheiten waren eine große Erleichterung. Prof. Jens Gobrecht danke ich für die Aufnahme in das Labor für Mikro- und Nanotechnologie am Paul Scherrer Institut in der Schweiz und für die schöne Zeit, die ich dort verbringen durfte. Seine sehr menschliche Art hat sich auf das ganze Labor übertragen. Weiterhin bedanke ich mich für die Übernahme des Zweitgutachtens. Dr. Laura Heyderman und Dr. Mathias Kläui möchte ich für die tolle Betreuung recht herzlich danken. Durch ihre Kooperation war es mir möglich, einen Teil der Arbeit am Paul-Scherrer-Institut in der Schweiz und den anderen Teil an der Universität Konstanz zu leisten. Dadurch konnte ich gleichzeitig die Vorteile eines Forschungsinstituts und einer Universität nutzen. Laura danke ich im speziellen dafür, dass sie mich in die verschiedenen Strukturierungstechniken eingeführt hat. Dies erstreckte sich nicht bloß auf Faktenwissen, sondern sie versuchte mir ihre extrem professionelle Arbeitsweise zu vermitteln. Mathias danke ich für die intensive Betreuung der Arbeit. Durch ihn habe ich viel sowohl über die Physik als auch über die experimentel-
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len Details gelernt. Weiterhin war es mir durch die Teilnahme an vielen Strahlzeiten möglich, Erfahrungen mit Synchrotronmeßtechniken zu sammeln. Durch seine Energie und sein Organisationsgeschick wurde das gesamte Projekt wesentlich vorangetrieben. Den jetzigen und früheren Mitgliedern des Lehrstuhles Prof. Rüdiger danke ich herzlich für die Aufnahme. Besonders bedanken möchte ich mich bei Stephen Krzyk und Dr.
Mikhail Fonin für die Dünn-
filmbeschichtung und bei Tom Moore und Philipp Möhrke für die Hilfe bei Kerr-Mikroskopiemessungen. Friederike Stuckenbrock danke ich für ihre Unterstützung bei organisatorischen Angelegenheiten. Lutz Heyne, Dr. Markus Laufenberg, Dr. Tom Moore und Dr. Mathias Kläui waren meine Mitstreiter bei den ELETTRA-Strahlezeiten in Triest. Ihnen danke ich für ihre Kollegialität und ihren Einsatz während dieser arbeitsintensiven und nervenaufreibenden Zeit. Dr. Rafal Dunin-Borkowski von der University of Cambridge möchte ich für die Möglichkeit danken, Elektronenholografie-Messungen in seinem Labor anzustellen.
Henri Ehrke, Friederike Junginger und
Eva-Maria Hempe danke ich für die exzellenten ElektronenholografieAufnahmen, die sie während ihres Praxissemesters dort angefertigt haben, und Dr. Takeshi Kasama für deren Betreuung und Einweisung vor Ort. Frithjof Nolting und Arantxa Fraile-Rodriguez von der SIM-Beamline an der SLS danke ich für die professionelle Unterstützung während den zahlreichen Strahlzeiten dort. Allen Mitgliedern der SIM-Beamline danke ich für die Möglichkeit, an Seminaren und ähnlichem teilnehmen zu können, um einen umfassenderen Einblick in die Synchrotronforschung erhalten zu können. Desweiteren danke ich für die Einladungen zu den Unterwasser-Workshops, die sehr ergiebig waren. Dem Team der Nanospectroscopy-Beamline an der ELETTRA in Trieste mit Dr. Andrea Locatelli, Dr. Tevik Onur Mentes und Dr. Miguel Angel Nino danke ich für die exzellente Unterstützung. Meinen jetzigen und ehemaligen Mitgliedern der Nanomag-Gruppe am Labor für Mikro- und Nanotechnologie mit Dr. Laura Heyderman,
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Dr. Slawomir Czekaj, Dr. Feng Luo, Elena Mengotti und Anja Weber danke ich für ihre Kollegialität und den Spaß bei der Arbeit. Den Mitgliedern des Labors für Mikro- und Nanotechnologie danke ich für all die Hilfe, die sie mir in den letzten drei Jahren zukommen ließen. Besonders bedanken möchte ich mich bei Eugen Deckhardt, der der den LION im Zaum hielt, und bei Anja Weber für die Bedampfungen und vieles mehr. Edith Meisel danke ich für die Unterstützung in organisatorischen Belangen. Bei allen möchte ich mich für das sehr kollegiale Betriebsklima bedanken. Ganz besonders vermissen werde ich meine Mitbewohner der Villa, die während der letzten drei Jahre mein zweites Zuhause war. So viele haben schon ausziehen müssen, was jammerschade war. Nun trifft es mich selber. Natürlich hat meine Familie einen großen Anteil am Zustandekommen dieser Arbeit, obwohl sie nicht fachlich involviert war. Meine Freundin Miryam half mir sehr durch ihre Loyalität auch in Zeiten, in denen ich sicher nicht leicht zu ertragen war. Durch ihren Zuspruch verlor ich nie die Zuversicht, diese Arbeit zum Abschluss bringen zu können. Meine Eltern Hedi und Werner haben mich durch ihre Fürsorge über viele Jahre unterstützt. Noch wichtiger, sie haben mir die Gewissheit gegeben, etwas nicht alltägliches tun zu dürfen. Ohne sie wäre ich nicht am Ziel angekommen.
