Analysis of proximity effects in SNF and FSF junctions

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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.

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Superconductivity (S) vs. Ferromagnetism (F)
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Proximity effect
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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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I. Introduction
S/N bilayers 1960s. de Gennes, Rev. Mod. Phys.
(64)
xCu 40 nm
Werthamer, Phys.Rev. (63)
For
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S/F bilayers 1980s 90s
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Origin of oscillations
dirty limit (oscillation suppressed).
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II. S/N/F trilayers

• Expectations only one length scale in N.

• 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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Another way of looking atthe short length
superconductor
normal metal
ferromagnetic metal
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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Two options to understand the short length scale
( 2 nm)
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Triplet?
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III. Usadel formalism
Usadel equation
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Boundary conditions
Self-consistency relation

• Boundary modeled by
• Boundary conditions.

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Odd triplet pairing?

• Antisymmetry requirement (at t1t2) F changes
  sign under

For
Odd frequency triplet pairing.
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Solution by extending the Greens 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 Greens function following
  standard procedure, say, in Arfken.

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Solution
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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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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

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Perfect interfaces
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Effects of
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Nb/CoFe
From S/F,
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Nb/Au
From S/N,
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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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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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Nb/Al/CoFe
is needed.
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IV. F/S/F

• Parallel antiparallel

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 Fs are not identical.
• Triplet components (induced by spin flip
  scatterings at S/F interfaces).

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Triplet pairing components.

• Tunneling conductance for FSF.
• Effects of triplet pairing components.

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Nb/SrRuO3
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Nb/SrRuO3
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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
  Fs of F/S/F is reduced by triplet components.
• Search for the odd-frequency triplet pairing in
  artificial junctions of S, N, and F.