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)


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


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.


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)]


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


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).


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.


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)


T

c (K

)

dAu

(nm)

Nb(23nm)/Au



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)



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)


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


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), …].


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)


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


Triplet?

0 100 200

5

6

7

8

0 1 2 3 4 54

5

6

7

Tc

(K)

dAu

(nm)



Tc (

K)

dAu

(nm)

Nb(23nm)/Au



.

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


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


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


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


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


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.


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


Nb/CoFe

.34.0SFbFrom S/F,


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,


Quantitative analysis S/N/F

.4.0,15.1 NFb

SNb

.NFm

From S/N/F,

No need to introduce


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.


Pairing amplitudes

F N S


Triplet components

F N S


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)


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


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

Length scale of 2.1 nm.


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)


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


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.


is much smaller in experiment compared with theoretical calculation.

Why?

Pc

APc TT

Gu et al., PRL 2002

You et al., PRB 2004


Why?

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

S/F interfaces).


Triplet pairing components.

Tunneling conductance for FSF. Effects of triplet pairing components.

FF

S


Nb/SrRuO3

S

F M

S

FM

M M


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.

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

Documents

triplet pairing components

singlet pairing component

triplet components

odd frequency triplet

singlet component

spin triplet excitations

short length scale

s region