analysis of proximity effects in s/n/f and f/s/f junctions

Analysis of proximity effects in S/N/F and F/S/F junctions

Han-Yong Choi Na-Young Lee / SKKU

Hyeonjin Doh / Toronto

Kookrin Char / SNU

KIAS workshop

2005. 10. 25 ~ 10. 29.

SKKU condensed-matter theory group

Superconductivity (S) vs. Ferromagnetism (F)

SKKU condensed-matter theory group

Proximity effect

0 10 20 30 40 50 604

5

6

7

8

9

Nb Nb/CoFe(10nm) Nb/Ni(10nm) Nb/CuNi(10nm)

Tc (

K)

dNb

(nm)

F

NS

.~

.or.vs

SS

FNc

d

ddT

SKKU condensed-matter theory group

Plan

I. Introduction to proximity effect.S/N, S/F.

II. S/N/F. Issues of SNU data.

III. Usadel equation. Odd triplet pairing.Results.

IV. F/S/F.V. Summary and outlook.

SKKU condensed-matter theory group

Tc/T

c,S

dPb (nm)

dCu (nm)

I. Introduction

S N

.3

1,

2,

2F

SS

NN vD

T

D

T

D

For ,cTT

S/N bilayers: 1960’s. [de Gennes, Rev. Mod. Phys. (’64)]

Cu ~ 40 nm

[Werthamer, Phys.Rev. (’63)]

SKKU condensed-matter theory group

S/F bilayers: 1980’s & 90’s

0 2 4 6 8 104

5

6

7

8

Nb(26nm)/CoFe

Tc (

K)

dCoFe

(nm)

fit results

S=8.3nm,

S=14.6cm,

f=14.4nm,

f=14.4cm,

TCurie

=1152K

b=0.28, R

bA=0.6 x 10-11cm2

Re{ }

S F0-state

-state

Min Tc vs. dF

SKKU condensed-matter theory group

Origin of oscillations

x

,2/qk

,2/qk

,k

,k

h

S

F

U K 2h

S F

.,/

Re

./, /

)/sin(~cos

./

)/sin(cos,

cos,2

02

8/3/)1(

00

0coscos

0

0cos

2/2/

mm

m

ixi

Fmm

mx

k

hixx

m

mk

hix

Fqkqk

x

e

hvx

xeeedc

x

xedc

k

hqh

m

F

F

dirty limit (oscillation suppressed).

SKKU condensed-matter theory group

II. S/N/F trilayers

Experiments: “surprises” two more length scales.

Tc

dN

SN

SNF

0

S N F

Expectations: only one length scale in N.

SKKU condensed-matter theory group

1. Short length

0 100 200

5

6

7

8

0 1 2 3 4 54

5

6

7

Tc

(K)

dAu

(nm)

Nb(26nm)/Au/CoFe(10nm)

Nb(22nm)/Au/CoFe(10nm)

T

c (K

)

dAu

(nm)

Nb(23nm)/Au

Nb(23nm)/Au/CoFe(10nm)

SKKU condensed-matter theory group

2. Intermediate length

0 100 200

-0.3

-0.2

-0.1

0.0

20 40 60 80 100 120

-0.1

0.0

Tc (

K)

dAu

(nm)

Nb(16nm) Nb(17nm) Nb(18nm)

Tc -

Tc,

lim (

K)

dAu

(nm)

Nb(23nm)/Au/CoFe(10nm)

SKKU condensed-matter theory group

Au & Cu

0 100 2004

5

6

7

8

Nb24.3nm/Au Nb24.3nm/Au/CoFe10nm

Nb24.3nm/Cu Nb24.3nm/Cu/CoFe10nm

Tc

(K)

dAu

(nm)

SKKU condensed-matter theory group

Another way of looking atthe short length

Which has the highest Tc?

superconductor

normal metal

ferromagnetic metal

dS = 26 nmdS = 23 nm

dF = 10 nm dF = 10 nmdN = 3 nm

dS = 23 nm

dF = 10 nm

SKKU condensed-matter theory group

How to understand?

1. Obvious/mundane explanation.

Bad interfaces. higher interface resistance higher Tc.

But, interface resistance bet metals are similar.

Oscillations in Tc vs. dF. 2. More exotic explanation.

From new physics like triplet pairing?

Inhomogeneous exchange fields are predicted to induce enhanced superconductivity by spin triplet excitations. [Rusanov et al, PRL (2004), Bergeret et al, PRL (2001), …].

SKKU condensed-matter theory group

Nb/Au/Co60Fe40

0 1 2 3 4 5 6 7 8

0.90

0.95

1.00Nb(24nm)/Au(10nm)/CoFe(d nm)

Tc /

Tc(d

CoF

e=0

)

dCoFe

(nm)

bNF

=0.5

0 1 2 3 4 5 6 7 8 96.4

6.6

6.8

7.0

7.2

7.4

7.6

Nb(24nm)/Au/CoFe(d nm)

Au = 5 nm Au = 10 nm Au = 30 nm

Tc (

K)

dCoFe

(nm)

SKKU condensed-matter theory group

Two options to understand the short length scale (~ 2 nm)

SKKU condensed-matter theory group

Triplet?

0 100 200

5

6

7

8

0 1 2 3 4 54

5

6

7

Tc

(K)

dAu

(nm)

Nb(26nm)/Au/CoFe(10nm)

Nb(22nm)/Au/CoFe(10nm)

Tc (

K)

dAu

(nm)

Nb(23nm)/Au

Nb(23nm)/Au/CoFe(10nm)

SKKU condensed-matter theory group

.

000

000

000

0

ˆ,

0

0

0

)(

)(,

),(

),(

),(

),(

),(,2

.2

1,

2

1,

2

1,

2

1

2

y

x

z

yxz

ty

tx

tz

s

c

tytxtzs

h

h

h

hhh

H

x

x

ixf

ixf

ixf

ixf

ixFT

D

ffi

ffffffffff

III. Usadel formalism

tytxtzs

tzstytxys iffff

ffiffiffF

ˆ

Usadel equation

.),,(),(),,(),,(),,( 21 k

nnn ikxFixfikRFtrRFtrrF

.),(),(),,( 22112121 trtrttrrF

,ˆ)sgn()(),(2

22 FHixFixF

xTc

S N F

x

z

O

SKKU condensed-matter theory group

Boundary conditions

Boundary modeled by

Boundary conditions.

.

000

00

000

00

ˆ,ˆ

.ˆ.2

,0),(),(.1

NFb

NFb

NFm

NFb

NFm

NFb

NFSNb

SN

NNSN

NS

NNSS

i

i

Fx

FF

ixFx

ixFx

).()( 0 xVVVVxV zzyyxx

S N F

x

z

O

.),()(

2ln)(0

0

nns

n

c ixfx

TT

Tx

Self-consistency relation

SKKU condensed-matter theory group

Antisymmetry requirement (at t1=t2): F changes sign under

Odd triplet pairing?

.),,(),(),,(),,(),,( 21 k

nnn ikxFixfikRFtrRFtrrF

.),(),(),,( 22112121 trtrttrrF

.,, 21 rr

).,(),( nn ixfixf

For

.0),(1

),,(1

)0,0,( n

nn k

n ixfikxFrxF

Odd frequency triplet pairing.

.0)0,0,().0,,()0,,(, rxFrxFrxF

SKKU condensed-matter theory group

Solution: by extending the Green’s function method of Fominov et al, PRB 2002.

SKKU condensed-matter theory group

Solution

The basic idea is to solve the homogeneous equations with appropriate boundary conditions to obtain a single equation for the singlet pairing component ,

and the boundary conditions in terms of

and

within the S region. The obtained differential equation is then solved by

constructing Green’s function following standard procedure, say, in Arfken.

),( ixf s

),( ixfx s

),( ixf s

.0 Sdx

SKKU condensed-matter theory group

Triplet pairing in S/N/F

S = conventional s-wave singlet superconductor.

Tc determined by the singlet pairing component. Triplet pairing components are induced in addition to

the singlet component (via spin-flip scatterings). Triplet components are s-wave (even in k), and odd in

frequency. Long length scale. Triplet components change Tc indirectly by changing

singlet component via boundary conditions.

SKKU condensed-matter theory group

Procedures for understandingTc vs. dN of Nb/Au/CoFe.

Parameters of Usadel equation:

(for i = S, N, F), Tc0.

hex, (interface)

1. Fit S/F (Nb/CoFe): hex, Tc0.

2. Fit S/N (Nb/Au):

3. Fit S/N/F (Nb/Au/CoFe) to determine

,, ii

.,, NFm

NFb

SNb

., NFm

NFb

.SNb

,ˆ)sgn()(),(2

22 FHixFixF

xTc

SKKU condensed-matter theory group

Nb/CoFe

.34.0SFbFrom S/F,

SKKU condensed-matter theory group

Nb/Au

0 100 200

6.5

7.0

7.5

8.0

T

c (K

)

dAu

(nm)

Nb(23nm)/Au

Nb

~7.0nm, Nb

=15.2cm

Au

~85nm, Au

=2.3cm,

b~1.15, R

bA~2.24 x 10-11cm2

.15.1SNbFrom S/N,

SKKU condensed-matter theory group

Quantitative analysis S/N/F

.4.0,15.1 NFb

SNb

.NFm

From S/N/F,

No need to introduce

SKKU condensed-matter theory group

Usadel calculations.

By solving the Usadel equation,

because S/N/F still has two interfaces (mathematically) in the limit dN 0.

S/FS/N/Flim0

Nd

Short length scale of ~ 2-3 nm: The length scale over which electrons feel the interface. Not the physical material length.

SKKU condensed-matter theory group

Pairing amplitudes

F N S

SKKU condensed-matter theory group

Triplet components

F N S

SKKU condensed-matter theory group

2. Intermediate length

0 100 200

-0.3

-0.2

-0.1

0.0

20 40 60 80 100 120

-0.1

0.0

Tc (

K)

dAu

(nm)

Nb(16nm) Nb(17nm) Nb(18nm)

Tc -

Tc,

lim (

K)

dAu

(nm)

Nb(23nm)/Au/CoFe(10nm)

Could never match the experimental observations of more than one length scales. Intermediate length not understood.

SKKU condensed-matter theory group

Yamazaki et al.: Nb/Au/Fe (MBE)

Length scale of 2.1 nm.

SKKU condensed-matter theory group

Nb/Au/Co60Fe40

0 1 2 3 4 5 6 7 8

0.90

0.95

1.00Nb(24nm)/Au(10nm)/CoFe(d nm)

Tc /

Tc(d

CoF

e=0

)

dCoFe

(nm)

bNF

=0.5

0 1 2 3 4 5 6 7 8 96.4

6.6

6.8

7.0

7.2

7.4

7.6

Nb(24nm)/Au/CoFe(d nm)

Au = 5 nm Au = 10 nm Au = 30 nm

Tc (

K)

dCoFe

(nm)

SKKU condensed-matter theory group

Results for S/N/F

It seems that it is the interface resistance that caused the Tc jump (short length scale) on Tc vs. dN for Nb/Au/CoFe.

S/F : S/N/F :

for continuity. Intermediate length of ~ 20 nm not understood. Oscillations in Tc vs. dF not understood.

.34.0SFb

.4.0,15.1 NFb

SNb

NFb

NFSNb

SFb

b

SKKU condensed-matter theory group

because the F effect is canceled in antiparallel junctions.

IV. F/S/F

Parallel & antiparallel

APc

Pc TT

F S F F S F

Proximity switch device.

SKKU condensed-matter theory group

is much smaller in experiment compared with theoretical calculation.

Why?

Pc

APc TT

Gu et al., PRL 2002

You et al., PRB 2004

SKKU condensed-matter theory group

Why?

Two F’s are not identical. Triplet components (induced by spin flip scatterings at

S/F interfaces).

SKKU condensed-matter theory group

Triplet pairing components.

Tunneling conductance for FSF. Effects of triplet pairing components.

FF

S

SKKU condensed-matter theory group

Nb/SrRuO3

S

F M

S

FM

M M

SKKU condensed-matter theory group

V. Summary & Outlook

No need for triplet pairing components for Nb/Au/CoFe.

It is the interface resistance that caused the Tc

jump. Short length scale of ~ 2 nm: the length scale over which electrons feel the interface. Not the physical material length.

Not understood: intermediate length of ~ 20 nm, Tc vs. dF of S/N/F.

Tc difference between parallel and antiparallel F’s of F/S/F is reduced by triplet components.

Search for the odd-frequency triplet pairing in artificial junctions of S, N, and F.