1. Interplay of Magnetic and Superconducting Proximity effect in F/S hybrid structures Thierry Champel Collaborators: Tomas Löfwander Matthias Eschrig Institut für Theoretische Festkörperphysik Grenoble 16/03/2006

2. PLAN S/F PROXIMITY EFFECT RESULTS Characteristic features Motivation S/F bilayer with a rotating exchange field F/S/F trilayer with noncollinear moments 1/ 2/ 3/F/S/F/S/F pentalayer with noncollinear moments Study of triplet correlations within:

3. SUPERCONDUCTOR/FERROMAGNET HYBRID NANOSTRUCTURES Systems under study: FS Singlet Cooper pairing Zeeman splitting CONTEXT: SPINTRONICS Possibility for a new physics with interesting applications

4. S/F PROXIMITY EFFECT Proximity effect: Penetration of Pairing correlations into non- superconducting areas In F: center of mass momentum of Cooper pair: 2q Spatial modulation of the pair amplitude in F if J=0 fSfS Dependence on impurities, interface quality, domain state of F,... leakage of pairs = influence on T C change of sign = influence on j C in Josephson junctions nanoscale

5. Some characteristic features

6. S/F PROXIMITY EFFECT : SOME CHARACTERISTIC FEATURES Tagirov, PRL 1999 Buzdin et al., EPL 1999 Nonmonotonic behavior of T c (d f ) Superconducting switch Transparency + - FS dFdF for recent th. developments see e.g. Fominov et al., PRB 2002 Th: Buzdin et al. (1991) F S dFdF F dFdF dSdS or Th:

7. S/F PROXIMITY EFFECT : SOME CHARACTERISTIC FEATURES Ryazanov et al, PRL (2001) Kontos et al, PRL (2002) Guichard et al, PRL (2003) Bauer et al, PRL (2004)   junctions Critical current I c of Cu 0.47 Ni 0.53 junctions as a function of the F layer thickness From Ryazanov et al. (2005) Taken in Buzdin, RMP 77, 935 (2005) FSS 2d F Th: Buzdin et al. (1982) Exp:

8. MOTIVATION : ROLE OF INHOMOGENEITY OF EXCHANGE FIELD? Theoretical motivation S/F wire with a local inhomogeneity of J F/S/F trilayer with noncollinear F moments Bergeret et al., PRL 2001 Volkov et al., PRL 2003 As a result of inhomogeneity: Production of triplet components which penetrate far in F QUESTIONS: Why do we have triplet correlations? Under which conditions are long-range triplet components produced? Signatures and consequences on physical quantities?

9. Triplet correlations

10. S/F PROXIMITY EFFECT : THEORETICAL ASPECTS Quasi-classical approximation METHODS Quasi-classical equations of superconductivity for the Nambu-Gorkov Green functions main difficulties: System of coupled nonlinear differential eqs. Coupling with the self-consistent gap eq. Inhomogeneous superconductivity + consideration of the diffusive limit

11. S/F PROXIMITY EFFECT : COEXISTENCE OF SINGLET/TRIPLET CORRELATIONS Pair states singlet triplet Order parameter: triplet vector Linearized Usadel equation within this basis Coexistence of singlet/triplet correlations Role of inhomogeneity of J T. C. and M. Eschrig, PRB 71, 220506(R) (2005 ) T. C. and M. Eschrig, PRB 72, 054523 (2005)

12. S/F PROXIMITY EFFECT : COEXISTENCE OF SINGLET/TRIPLET CORRELATIONS Sup.Fer. S=1 S=0 S=0, S z =0 S z =+1 S z =-1 Energy of pair states: FS Picture for a fixed exchange field

13. Singlet component: Correlator: Pauli principle: Order parameter: So, f t dropped out of the gap equation. But it isn’t zero… Triplet vector: Symmetry Properties of triplet correlations S/F PROXIMITY EFFECT : COEXISTENCE OF SINGLET/TRIPLET CORRELATIONS PECULIARITY OF THE DIFFUSIVE LIMIT

14. S/F PROXIMITY EFFECT : LOCAL DENSITY OF STATES AND SPIN MAGNETIZATION Spin structure of the Green function g Normalization condition T. C. and M. Eschrig, PRB 72, 054523 (2005) local density of states spin magnetization

15. Spin-dependent local DOS Spin magnetization Superconductivity dependent on moment orientation Physical consequences of the presence of triplet correlations: TRIPLET CORRELATIONS IN S/F HYBRID STRUCTURES To resume: Signatures at the quantitative level on physical quantities?

16. S/F bilayer with spiral magnetic order

17. EFFECT OF INHOMOGENEITY OF EXCHANGE FIELD: STUDY OF A S/F BILAYER Within this model, only short-range triplet correlations (S Z =0) are produced T. C. and M. Eschrig, PRB 71, 220506(R) (2005 ) Spatial dependence of pair correlationsEffect of inhomogeneity of J on T c (d f ) Enhancement of T c with Q TCTC

18. EFFECT OF INHOMOGENEITY OF EXCHANGE FIELD : MAGNETIC SPIRAL ORDER superconducting switch operated by controlling the domain state in F jCjC TCTC Destruction of π phase by inhomogeneity S/F/S junctions unpublished (2006)

19. F/S/F trilayer with noncollinear moments

20. STUDY OF A F/S/F TRILAYER : LOCAL INDUCED MAGNETIZATION Spatial dependence of the induced magnetization T. Löfwander, T. C., et al., PRL 95, 187003 (2005) or x F F S collinear moments MM

21. STUDY OF A F/S/F TRILAYER : PAIR CORRELATIONS AND MAGNETIZATION Spatial dependences of: the induced local magnetizationthe pair correlations (a)-(c): projections (b)-(d): angles relative to z-axis x FFS y z perpendicular moments T. Löfwander, T. C., et al., PRL (2005) MM

22. angle relative to z-axis for B B applied in yz plane norm. state STUDY OF A F/S/F TRILAYER : TOTAL INDUCED MAGNETIZATION AND TORQUE Integrated magnetization : screening effect sup. state x F F S y z Changes in torque between normal and superconducting states

23. F/S/F/S/F pentalayer

24. T. C. et al., unpublished (2006) SWITCHING BETWEEN THE 0 AND π STATES IN F-S-F-S-F PENTALAYERS Switching between the 0 and π states by controlling the moment orientations in F switching region π state 0 state TCTC

25. CONCLUSION The coexistence near the S/F interface of singlet components with triplet components is the hallmark of the S/F proximity effect Consequences: Sensitivity of superconductivity on moment direction Spin-dependent density of states Spin magnetization Concrete examples: S/F bilayer within spiral order model F/S/F trilayer Superconducting switch controlled by domain state Torque variation by cooling down the trilayer F/S/F/S/F pentalayer Switching between the 0 and π states by acting on the moment orientation Future directions:Influence on transport properties?