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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. Superconductivity (S) vs. Ferromagnetism (F). N. S. F. Proximity effect. Plan.

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

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  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 2005. 10. 25 ~ 10. 29.

  2. Superconductivity (S) vs. Ferromagnetism (F) SKKU condensed-matter theory group

  3. N S F Proximity effect SKKU condensed-matter theory group

  4. 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

  5. dPb (nm) Tc/Tc,S S N Y dCu (nm) I. Introduction S/N bilayers: 1960’s. [de Gennes, Rev. Mod. Phys. (’64)] xCu ~ 40 nm [Werthamer, Phys.Rev. (’63)] For SKKU condensed-matter theory group

  6. F S 0-state p-state Min Tc vs. dF S/F bilayers: 1980’s & 90’s SKKU condensed-matter theory group

  7. S F S F h x 2h K U Origin of oscillations dirty limit (oscillation suppressed). SKKU condensed-matter theory group

  8. S N F SN Y Tc SNF 0 dN II. S/N/F trilayers • Expectations: only one length scale in N. • Experiments: “surprises” two more length scales. SKKU condensed-matter theory group

  9. 1. Short length SKKU condensed-matter theory group

  10. 2. Intermediate length SKKU condensed-matter theory group

  11. Au & Cu SKKU condensed-matter theory group

  12. dF = 10 nm dN = 3 nm dS = 23 nm Another way of looking atthe short length superconductor • Which has the highestTc? normal metal ferromagnetic metal dF = 10 nm dF = 10 nm dS = 23 nm dS = 26 nm SKKU condensed-matter theory group

  13. 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

  14. Nb/Au/Co60Fe40 SKKU condensed-matter theory group

  15. Two options to understand the short length scale (~ 2 nm) SKKU condensed-matter theory group

  16. Triplet? SKKU condensed-matter theory group

  17. z x O S N F III. Usadel formalism Usadel equation SKKU condensed-matter theory group

  18. z x O S N F Boundary conditions Self-consistency relation • Boundary modeled by • Boundary conditions. SKKU condensed-matter theory group

  19. Odd triplet pairing? • Antisymmetry requirement (at t1=t2): F changes sign under For Odd frequency triplet pairing. SKKU condensed-matter theory group

  20. Solution: by extending the Green’s function method of Fominov et al, PRB 2002. SKKU condensed-matter theory group

  21. 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. SKKU condensed-matter theory group

  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. SKKU condensed-matter theory group

  23. 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 SKKU condensed-matter theory group

  24. Nb/CoFe From S/F, SKKU condensed-matter theory group

  25. Nb/Au From S/N, SKKU condensed-matter theory group

  26. Quantitative analysis S/N/F From S/N/F, No need to introduce SKKU condensed-matter theory group

  27. 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. SKKU condensed-matter theory group

  28. Pairing amplitudes F N S SKKU condensed-matter theory group

  29. Triplet components F N S SKKU condensed-matter theory group

  30. 2. Intermediate length • Could never match the experimental observations of more than one length scales. • Intermediate length not understood. SKKU condensed-matter theory group

  31. Yamazaki et al.: Nb/Au/Fe (MBE) Length scale of 2.1 nm. SKKU condensed-matter theory group

  32. Nb/Au/Co60Fe40 SKKU condensed-matter theory group

  33. 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. SKKU condensed-matter theory group

  34. F S F F S F IV. F/S/F • Parallel & antiparallel because the F effect is canceled in antiparallel junctions. Proximity switch device. SKKU condensed-matter theory group

  35. Gu et al., PRL 2002 You et al., PRB 2004 • is much smaller in experiment compared with theoretical calculation. • Why? SKKU condensed-matter theory group

  36. Why? • Two F’s are not identical. • Triplet components (induced by spin flip scatterings at S/F interfaces). SKKU condensed-matter theory group

  37. F F S Triplet pairing components. • Tunneling conductance for FSF. • Effects of triplet pairing components. SKKU condensed-matter theory group

  38. S S M M F F M M Nb/SrRuO3 SKKU condensed-matter theory group

  39. 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. SKKU condensed-matter theory group

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