Analysis of proximity effects in S/N/F and F/S/F junctions
description
Transcript of 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.