C. van der Beek

Vortex pinning : a probe for nanoscale disorder in iron-‐based superconductors Kees van der Beek Laboratoire des Solides Irradiés, Ecole Polytechnique, PALAISEAU, France

ECRYS – Electronic Crystals – Cargèse, August 25th, 2011

1

Collaborators •  Sultan DEMIRDIŞ, Marcin KONCZYKOWSKI LSI, CNRS UMR 7642 & CEA/DSM/IRAMIS, Ecole Polytechnique, Palaiseau, France •  Yanina FASANO, René CEJAS, Hernan PASTORIZA Laboratorio de Bajas Temperaturas, InsLtuto Balseiro, Centro Atomico Bariloche, San Carlos de Bariloche, ArgenLna •  Dorothée COLSON, Florence ALBENQUE Service de Physique de l’Etat Condensé, CEA/DSM/IRAMIS, Gif sur YveSe, France • 

Shigeru KASAHARA, Takahito TERASHIMA Research Center for Low Temperature and Materials Sciences, Kyoto University, Japan

• 

Ryuji OKAZAKI, Takasada SHIBAUCHI, Yuji MATSUDA Department of Physics, Kyoto University, Kyoto, Japan


2

Iron-‐based superconductors Layered structure FeAs

FeSe

FeAs

LaFeAsO “1111”

BaFe2As2 “122”

PrFeAsO NdFeAsO SmFeAsO …

Ba(Fe,Co)2As2 BaFe2(As,P)2

Tc < 55 K

Tc < 42 K

FeSe

LiFeAs Tc < 20 K

Fe(Se,Te) Tc < 18K

From “To what extent pnictide superconductivity has been clarified: a progress report” Kenji Ishida, Yusuke Nakai, and Hideo Hosono, J. Phys. Soc. Japan 78, 062001 (2009).


3

IBS: Phase Diagram • Charge doped

• Isovalently doped

BaFe2(As1-‐xPx)2 Ba(Fe1-‐xCox)2As2

F. Rullier-Albenque, D. Colson, A. Forget, H. Alloul PRL 103, 057001 (2009)

S. Kasahara et al., Phys. Rev. B (2010)

• High sensi_vity to crystal structure details • Proximity to (an_-‐ferro)magne_sm ECRYS – Electronic Crystals – Cargèse, August 25th, 2011

4

IBS: Electronic structure / gap • Mul_band Superconduc_vity • New paradigm for High Tc s.c. H. Ding et al., EPL 83, 47001 (2008)

Photoemission


5


Photoemission

"Electron-‐like" sheets

"Hole-‐like" sheets

Μ

Μ

Γ

Μ


6


Photoemission

•  Proposal : AF coupling between "electron-‐like" and "hole-‐like" Fermi surface sheets "Electron-‐like" sheets

↓↑

-‐

-‐

↑↓


↑↓

-‐

Sign of the phase of the superconduc_ng ↑↓ wave func_on

D.J. Mazin et al., Phys. Rev. Lett. 101, 057003 (2008);

K. Kuroki et al., Phys. Rev Lett. 101, 087004 (2008);

K. Kuroki et al., Phys. Rev B. 79, 224511 (2008);

+

-‐

" s± " – coupling

↑↓


7


Photoemission


↓↑

-‐

-‐

↑↓


↑↓

-‐





+

-‐


↑↓ Role of disorder/impuri_es?


8


Photoemission


↓↑

-‐

-‐

↑↓


↑↓

-‐





+

-‐


↑↓ Role of disorder/impuri_es?

9 – Electronic Crystals – Cargèse, August 011 Interband scamering = dECRYS estruc_ve interference = harmful , 2 5th, I2ntraband scamering = benign

Gap symmetry

Materials with similar structure do not have the same ground state K. Hashimoto, M. Yamashita, S. Kasahara, Y. Senshu, N. Nakata, S. Tonegawa, K. Ikada, A. Serafin, A. Carrington, T. Terashima, H. Ikeda, T. Shibauchi, and Y. Matsuda, Phys. Rev. B 81, 220501 (2010).


10

IBS : characterize the disorder defects nm-‐scale heterogeneity

vs

Intrinsic

impuri_es dopant atoms

Vortex pinning Extended defects pin differently than point-‐like defects


11

H

Crash-‐course on vor_ces π/2

Hc2

Etat state

normal Normal

π

3π/2 2ξ

j0

Mixed state

Etat mixte

λ

φ=0 2 Bc1 ns Bz(r)

j(r)

Hc1

Current density

Etat Meissner Meissner State

T

Tc


B (magn. flux density)

12

H


Hc2

Etat state

normal Normal

π

3π/2 2ξ

j0

Mixed state

Etat mixte

φ=0 2 Bc1 ns Bz(r)

λ j(r)

Hc1

Current density


T

Current-‐ voltage characteris_c F=j×B Lorentz force v = F/γ friction E=v×B Josephson relation

}

E = ρfj

where

Tc


E

flux flow

R

or V

ρf = B2/γ ECRYS – Electronic Crystals – Cargèse, August 25th, 2011

j or I 13

H


Hc2

Etat state

normal Normal

π

3π/2 2ξ

j0

Mixed state

Etat mixte

φ=0 2 Bc1 ns Bz(r)

λ j(r)

Hc1

Current density


T

Current-‐ voltage characteris_c F=j×B Lorentz force v = F/γ friction E=v×B Josephson relation

}

E = ρfj

where

ρf =

B2/γ

Tc


E

flux flow

R

or V

flux creep


jc = Fp/B

j or I 14

Bimer decora_on of vor_ces in Ba(Fe0.9Co0.1)2As2 Field coil

B = 0.5 mT

Fe filament

10 µm Single crystal Ba(Fe0.9Co0.1)2As2 (D. Colson, F. Albenque)

Ba(Fe1-‐xCox)2As2 crystal

Single crystal Bi2Sr2CaCu2O8+δ (Y. Fasano)

Cf Eskildsen et al. (BD,SANS); Vinikov et al. (BD);

Inosov et al. (MFM, SANS); Kalisky et al.;

Luan et al. (scanning SQUID)


15

Jc of iron-‐based superconductors 1. Magneto-‐op_cal visualiza_on of B Ba(Fe0.9Co0.1)2As2


16

Jc of iron-‐based superconductors 1. Magneto-‐op_cal visualiza_on of B Ba(Fe0.9Co0.1)2As2

2. Flux density profiles: jc at low B 500

T = 10 K

B ( mT )

400

µ0 jc = 2

dB

dx

300

200

100

0 0

200

400

600

x ( !m )

800

1000


17

Jc of iron-‐based superconductors 1. Magneto-‐op_cal visualiza_on of B Ba(Fe0.9Co0.1)2As2 + + + + + + + +

3. Hall probe array magnetometry: hysteresis loops of local B, jc at higher B

2 109

Ba(Fe Co As) 10

1-x

x

T[K]

2

4.2 6 8 10 12 14 16

x=5% crystal #2 H || c

500

T = 10 K

B ( mT )

400

µ0 jc = 2

dB

dx

300

200

5 108 0

0 -5 108

-5 -1 109 -1.5 109

-10 -2

100

1 109

-1

0 B(T)

1

2

-2 109

0 0

200

400

600

x ( !m )

800

1000


18

j ( Am-2 )

2. Flux density profiles: jc at low B

dB/dx ( G / !m )

5

1.5 109

Vortex pinning and the cri_cal current density Strong pinning

Sparse extended defects (ni ξ -‐3)

• • •

•

modify the core and modify the screening current distribu_on Total force Fp = direct sum Σi fp,i of elementary pinning forces fp,i

Total force ~ 2nd moment of fp Fp = (np 〈fp2 〉/Vc)1/2

•

Vc = LcRc2

determined by

〈[u(Rc, 0) – u(0,0)] 2 〉1/2 = ξ

〈[u(0, Lc) – u(0,0)] 2 〉1/2 = ξ

• pins sufficiently effec_ve : Vc = Lca02 Yu. Ovchinnikov and B. Ivlev, PRB 43, 8024 (1991);

C.J. van der Beek et al PRB 66, 024523 (2002);

G. Blatter, V.B. Geshkenbein, J. Koopman, PRL 92, 067009 (2004).

Field-‐independent jc followed by e-B/B0

A.I. Larkin, Yu. Ovchinnikov, JETP 31, 784 (1970); J. Low. Temp. Phys. 34, 409 (1979). G. Blatter, M.V. Feigel'man, V.B. Geshkenbein, A.I. Larkin, and V.M. Vinokur, Rev. Mod. Phys. 66, 1125 (1994).


20

Jc of iron-‐based superconductors 1. Magneto-‐op_cal visualiza_on of B Ba(Fe0.9Co0.1)2As2 + + + + + + + +

3. Hall probe array magnetometry: hysteresis loops of local B, jc at higher B

2 109

Ba(Fe Co As) 10

1-x

x

T[K]

2

4.2 6 8 10 12 14 16


500

T = 10 K

B ( mT )

400

µ0 jc = 2

dB

dx

300

200

5 108 0

0 -5 108

-5 -1 109 -1.5 109

-10 -2

100

1 109

-1

0 B(T)

1

2

-2 109

0 0

200

400

600

x ( !m )

800

1000


21

j ( Am-2 )

2. Flux density profiles: jc at low B

dB/dx ( G / !m )

5

1.5 109

Jc of iron-‐based superconductors Ba(Fe0.925Co0.075)2As2 crystal #2.1 Critical current density vs applied magnetic field

jc(0; 5 K)

109

j ( Am-2 )

jc(0; 11 K)

0.5 2 109

Ba(Fe Co As)

jc(0; 17.5 K)

10

1-x

x

T[K]

2

4.2 6 8 10 12 14 16


5

8

5.0 K fit 3!108/B1/2 11.26 K fit 1!107/B1/2ı 17.5 K fit 2.8!07/B-1/2 0.01

1 109 5 108

0

0 -5 108

-5 -1 109

0.1

1

µ0Ha ( T )

-1.5 109

-10 -2

-1


0 B(T)

1

2

-2 109

22

j ( Am-2 )

dB/dx ( G / !m )

10

1.5 109

Jc of iron-‐based superconductors Ba(Fe0.925Co0.075)2As2 crystal #2.1 Critical current density vs applied magnetic field

Yu. Ovchinnikov and B. Ivlev, PRB 43, 8024 (1991);

C.J. van der Beek et al PRB 66, 024523 (2002);

G. Blatter, V.B. Geshkenbein, J. Koopman, PRL 92, 067009 (2004).

jc(0; 5 K)

109

j ( Am-2 )

jc(0; 11 K)

0.5 2 109

Ba(Fe Co As)

jc(0; 17.5 K)

10

1-x

x

T[K]

2

4.2 6 8 10 12 14 16


5

8


1 109 5 108

0

0 -5 108

-5 -1 109

0.1

1

µ0Ha ( T )

Extended point-‐like defects with niξ3 MP@

_I_1P L

S. Demirdiş et al cond-mat 1106.6065v1


38

Ba(Fe1-‐xCox)2As2 at low B : Pinning forces Hdec= 10 Oe

Tirr

Tdec

Tc

1P YRUWLFHV

D [

Tf

E [

[>MP@

  Pinning force distribu_on at Tf

|fi| ~ 5×10-6 N/m

_I_1P L

1P YRUWLFHV

NB Newton’s 3rd law: Interac_on force must be balanced by pinning force

F

G

[>MP@

_I_1P L

Average Pinning force per vortex S. Demirdiş et al cond-mat 1106.6065v1


39

Low B : Strong pinning by nm-‐scale disorder ε0 (T )

Spa_al inhomogeneity

ε0 ‒ Δε0

Tc

0.5 ε0

|fi| ~ 5×10-6 N/m

Average Pinning force per vortex

fp ~ 3×10-13 N

Pinning force of a single pin

Tc - δTc Distance between 2 pins ~ 60 nm

Nm-‐scale disorder



40



ε0 ‒ Δε0

Tc

0.5 ε0

|fi| ~ 5×10-6 N/m


fp ~ 3×10-13 N



Nm-‐scale disorder Cri_cal current density ?



41


0.05 ε0


ε0 ‒ Δε0

Tc

0.5 ε0

|fi| ~ 5×10-6 N/m


fp ~ 3×10-13 N




4 109 3.5 109

Cri_cal current density ?

(a)

(b)

B = 30 mT

25

x = 0.075

jc ( Am-2 )

3 109

109

2.5 109

20

2 109

5K

1 109

Up ~ ∆ε0 = 0.05 ε0

108

5 108 0

Tc ( K )

1.5 109

11 K

x = 0.075 #2.1 x = 0.1 #1 0

5

10

17.5 K 15

T(K)

20

25

0.01

1 0.1 µ0Ha ( T ) et al S. Demirdiş

15

10

cond-mat 1106.6065v1

ECRYS –FIG. Electronic Crystals – Cargèse, August 25th, 2: (Color online) (a) Temperature of2011 the low-field critical current density in Ba(Fe0.925 Co0.075 )2 As2 crystal #2 and Ba(Fe0.9 Co0.1 )2 As2 crystal #1 . Error bars represent the dis-

42

5 6 108

#1 #2 #3


0.05 ε0


ε0 ‒ Δε0

Tc

0.5 ε0

|fi| ~ 5×10-6 N/m


fp ~ 3×10-13 N




4 109 3.5 109

Cri_cal current density ?

(a)

(b)

B = 30 mT

jc ( Am-2 )

3 109

109

2.5 109

25

x = 0.075

Gap maps

20

2 109

5K

1 109

Up ~ ∆ε0 = 0.05 ε0

108

5 108 0

Tc ( K )

1.5 109

11 K

x = 0.075 #2.1 x = 0.1 #1 0

5

10

17.5 K 15

T(K)

20

25

0.01

F. Massee

1 0.1 etµal., H (Phys. T ) Rev. 0 a

15

10

B 79, 220517 (2009)

ECRYS –FIG. Electronic Crystals – Cargèse, August 25th, 2: (Color online) (a) Temperature of2011 the low-field critical current density in Ba(Fe0.925 Co0.075 )2 As2 crystal #2 and Ba(Fe0.9 Co0.1 )2 As2 crystal #1 . Error bars represent the dis-

43

5 6 108

#1 #2 #3

Jc of iron-‐based superconductors Mesures locales du courant cri_que jc • 2 contribu_ons: Extended defects Small B Point-‐like impuri_es Larger B

jc(0; 5 K)

109

j ( Am-2 )

jc(0; 11 K)

jc(0; 17.5 K)

10

0.5

8

x

2

4.2 6 8 10 12 14 16


1.5 109 1 109 5 108

0

0 -5 108

-5 -1 109

0.1

1

µ0Ha ( T )

-1.5 109

-10 -2

-1


0 B(T)

1

2

-2 109

44

j ( Am-2 )


1-x

T[K]

5

dB/dx ( G / !m )

10

2 109

Ba(Fe Co As)

3 >> 1 High Mesures B : origin olf ocales weak ``collec_ve’’ p inning n ξ p j du courant cri_que

c

Two main clues:

• Magnitude of jc

he ohe

109

4

(b)

3 2

10

1 0 -1

-0.5

0

0.5

1

PrFeAsO1-y NdFeAsO0.9F0.1 Ba0.45K0.55Fe2As2

10

0.2

0.4

2

4.2 6 8 10 12 14 16


1.5 109 1 109 5 108

0

0 -5 108

-5

-1.5 109

-10

0.6

T / Tc

FIG. 3: tion jccoll

x

-1 109

Ba0.72K0.28Fe2As2 [35] Ba(Fe0.9Co0.1)2As2 [30]

0

1-x

T[K]

5

# charges / u.c.

8

2 109

Ba(Fe Co As)

dB/dx ( G / !m )

,

jccoll ( Am-2 )

(a)

0.8

1

-2

-1

ECRYS – Electronic Crystals – Cargèse, August 25th, 2011 (Color online) (a) Collective pinning contribuin the charge-doped compounds PrFeAsO1−y ,

0 B(T)

1

2

-2 109

45

j ( Am-2 )

of y,

jccoll ( 109 Am-2 )

C.J. van der Beek et al., PRL 105, 267002 (2010)

α

4) ny. r2 mi va of nt in

3

• Temperature dependence of jc


c

Two main clues:

• Magnitude of jc • Temperature dependence of jc

•  Local varia_ons of Tc •  Charge redistribu_on •  Reduc_on of the pairing poten_al V

fp = (Bc2/µ0) Dv3/ξ ~ ε0 (Dv/ξ)3

p p

p

G. Blatter, M.V. Feigel'man, V.B. Geshkenbein, A.I. Larkin, and V.M.Vinokur, Rev. Mod. Phys. 66, 1125 (1994).


46


c

Two main clues:

• Magnitude of jc • Temperature dependence of jc

•  Local varia_ons of Tc •  Charge redistribu_on •  Reduc_on of the pairing poten_al V

•  Quasipar_cle scamering (δl or δκ) •  ξeff = (ξ0l)1/2

fp = (Bc2/µ0) Dv3/ξ ~ ε0 (Dv/ξ)3

p p

p

G. Blatter, M.V. Feigel'man, V.B. Geshkenbein, A.I. Larkin, and V.M.Vinokur, Rev. Mod. Phys. 66, 1125 (1994).

E.V. Thuneberg, J. Kürkijärvi, D. Rainer, PRL 48, 1853 (1982).


47

High B : origin of weak pinning Mesures locales du c``collec_ve’’ ourant cri_que j c

Two main clues:

• Magnitude of jc : pinning by dopant atoms reproduce this for the correct nd 3

• T-‐dependence of jc : reproduced by pinning due to quasi-‐par_cle scamering

he ohe

3 2

10

1 0 -1

-0.5

0

0.5

1

PrFeAsO1-y NdFeAsO0.9F0.1 Ba0.45K0.55Fe2As2

10

0.2

0.4

2

4.2 6 8 10 12 14 16


1.5 109 1 109 5 108

0

0 -5 108

-5

-1.5 109

-10

0.6

T / Tc

FIG. 3: tion jccoll

x

-1 109

Ba0.72K0.28Fe2As2 [35] Ba(Fe0.9Co0.1)2As2 [30]

0

1-x

T[K]

5

# charges / u.c.

8

2 109

Ba(Fe Co As)

dB/dx ( G / !m )

109

4

p

(b)

0.8

1

-2

-1

ECRYS – Electronic Crystals – Cargèse, August 25th, 2011 (Color online) (a) Collective pinning contribuin the charge-doped compounds PrFeAsO1−y ,

0 B(T)

1

2

-2 109

48

j ( Am-2 )

of y,

,

jccoll ( Am-2 )

(a)

α

4) ny. r2 mi va of nt in

jccoll ( 109 Am-2 )


Scattering parameters from jc of IBS compound

impurity

PrFeAsO0.9 (vacancy) NdFeAsO0.9F0.1 (F) Ba(Fe0.9Co0.1)2As2 ( Co ) Ba0.72K0.28Fe2As2 ( K ) Ba0.6K0.4Fe2As2 (K) Ba0.45K0.55Fe2As2 ( K ) kF ~ 0.3 Å-1

np (nm-3) 1.5 1.5 2 2.8 4 5.5

sin δ0 = 2-1/2 kFDv

Dv (Å) 1.46 0.9 0.9 0.7 0.8 0.7

0.3(2) 0.2 0.17 0.1(4) 0.2 0.2

l ( nm ) 10 25 20 23 10 12



49

Scattering parameters from jc of IBS compound

impurity

PrFeAsO0.9 (vacancy) NdFeAsO0.9F0.1 (F) Ba(Fe0.9Co0.1)2As2 ( Co ) Ba0.72K0.28Fe2As2 ( K ) Ba0.6K0.4Fe2As2 (K) Ba0.45K0.55Fe2As2 ( K )

np (nm-3) 1.5 1.5 2 2.8 4 5.5

Dv (Å)

sin δ0 = 2-1/2 kFDv

1.46 0.9 0.9 0.7 0.8 0.7

0.3(2) 0.2 0.17 0.1(4) 0.2 0.2

l ( nm ) 10 25 20 23 10 12

Kontani and S. Onari, Phys. Rev. Lett. 104, 157001 (2010).

δTc ~ 100 – 200 %

V. Mishra et al., Phys. Rev. B 79, 094512(2009).

δTc ~ 50 %

Tc/Tc0

kF ~ 0.3 Å-1

Γ = [nd/πNn(0)] sin δ0


50

Summary •  Two contribu_ons to flux pinning in IBS •  Strong pinning (extended defects) niξ3 > 1 -‐  QP scamering in the vortex core -‐  Extract scamering parameters, problema_c for s± C.J. van der Beek et al., PRL 105, 267002 (2010); PRB 81, 174517 (2010). S. Demirdiş et al cond-mat 1106.6065v1 ECRYS – Electronic Crystals – Cargèse, August 25th, 2011

51

Hystere_c magne_za_on loops for different IBS 1 Ba0.45K0.55Fe2As2 10

10

0.5

jccoll+jcs(0) -2

j ( Am )

NdFeAsO0.9F0.1 BaFe2(As0.67P0.33)2 Hon(PrFeAsO)

0

108

-0.5

-1

109

c

Bs / Bs( 0 )

PrFeAsO1-y

jccoll+jc

jcs(0)


-2

-1.5

-1

-0.5

0

0.5

1

1.5

107

2

µ0Ha ( T )


FIG. 1: (Color online) Normalized hysteresis loops of the

52

FIG. 2: (Color on

the sur-

2 Cri_cal current density for different IBS

10

10

jccoll+jcs(0)

0.5

(Ba,K)Fe2As2

jccoll

-2

j ( Am )

jccoll+jcs(0)

jc

109

c

Hon 0.5 s

108

jc (0)

Ba(Fe,Co)2As2

jccoll

NdFeAs(O,F)

BaFe2(As1-xPx)2

Ba0.45K0.55Fe2As2 Ba0.6K0.4Fe2As2 [36 ]

10

Hon

jccoll

PrFeAsO1-y NdFeAsO0.9F0.1

7

PrFeAsO1-‐y

coll

Ba(Fe0.9Co0.1)2As2 [34 ]

0.01

x=0.23 x=0.33 x=0.49

0.1

B(T)

BaFe2(As,P)2 1 C.J. van der Beek et al., PRL 105, 267002 (2010)

ECRYS – Electronic – Cargèse, August 25th, FIG. 2: (Color online) Critical currentCrystals density as function of2011 magnetic flux density for PrFeAsO1−y (✷), NdFeAsO0.9 F0.1 (◦), Ba(Fe Co ) As (�) [35], Ba K Fe As ( , �), and

53

PrFeAsO1-‐y

µ0 jc = 2

dB

dx


54

Local measurement of jc PrFeAsO1-‐y

Hall probe arrays µ0 jc = 2

dB

dx

Magneto-‐op_cal visualisa_on ECRYS – Electronic Crystals – Cargèse, August 25th, 2011

55

Local measurement of jc Low field

• two contribu_ons: -‐  -‐ 

Extended defects Point-‐like Impuri_es

Higher field


56