1. 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 ~

2. Superconductivity (S) vs. Ferromagnetism (F)
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Proximity effect F N S
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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.
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5. I. Introduction
S/N bilayers: 1960’s. [de Gennes, Rev. Mod. Phys. (’64)]
Tc/Tc,S
dPb (nm)
dCu (nm) S N Y
xCu ~ 40 nm
[Werthamer, Phys.Rev. (’63)]
For
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S/F bilayers: 1980’s & 90’s S F
0-state
p-state
Min Tc vs. dF
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7. Origin of oscillationsU K 2h S F x h S F
dirty limit (oscillation suppressed).
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II. S/N/F trilayers
Expectations: only one length scale in N. S N F Y Tc dN SN
SNF
Experiments: “surprises” two more length scales.
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1. Short length
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2. Intermediate length
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Au & Cu
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12. Another way of looking at the short length
superconductor
normal metal
ferromagnetic metal
dN = 3 nm
dS = 23 nm
dF = 10 nm
dF = 10 nm
dF = 10 nm
dS = 23 nm
dS = 26 nm
Which has the highest Tc?
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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), …].
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Nb/Au/Co60Fe40
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15. Two options to understand the short length scale (~ 2 nm)
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Triplet?
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III. Usadel formalism
S N F x z O
Usadel equation
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18. Self-consistency relation
Boundary conditions
Self-consistency relation
S N F x z O
Boundary modeled by
Boundary conditions.
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Odd triplet pairing?
Antisymmetry requirement (at t1=t2): F changes sign under
For
Odd frequency triplet pairing.
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Solution: by extending the Green’s function method of Fominov et al, PRB 2002.
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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.
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22. 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.
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23. Procedures for understanding Tc 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
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Nb/CoFe
From S/F,
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Nb/Au
From S/N,
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26. Quantitative analysis S/N/F
From S/N/F,
No need to introduce
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Usadel calculations.
By solving the Usadel equation,
because S/N/F still has two interfaces (mathematically) in the limit dN 0.
Short length scale of ~ 2-3 nm:
The length scale over which electrons feel the interface.
Not the physical material length.
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Pairing amplitudes
F N S
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Triplet components
F N S
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2. Intermediate length
Could never match the experimental observations of more than one length scales.
Intermediate length not understood.
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31. Yamazaki et al.: Nb/Au/Fe (MBE)
Length scale of 2.1 nm.
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Nb/Au/Co60Fe40
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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.
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IV. F/S/F
Parallel & antiparallel
F S F
F S F
because the F effect is canceled in antiparallel junctions.
Proximity switch device.
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Gu et al., PRL 2002
You et al., PRB 2004
is much smaller in experiment compared with theoretical calculation.
Why?
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Why?
Two F’s are not identical.
Triplet components (induced by spin flip scatterings at S/F interfaces).
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37. Triplet pairing components.
Tunneling conductance for FSF.
Effects of triplet pairing components. F S
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Nb/SrRuO3 S F M S F M
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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.
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