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D . Ivanov 1 , Ya . Fominov 2 , M . Skvortsov 2 , P . Ostrovsky 3,2

Effective spin-flip scattering in diffusive superconducting proximity systems with magnetic disorder. D . Ivanov 1 , Ya . Fominov 2 , M . Skvortsov 2 , P . Ostrovsky 3,2 1 EPFL, Lausanne , Switzerland 2 Landau Institute , Chernogolovka , Russia 3 Forschungszentrum Karlsruhe, Germany

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D . Ivanov 1 , Ya . Fominov 2 , M . Skvortsov 2 , P . Ostrovsky 3,2

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  1. Effective spin-flip scattering in diffusive superconducting proximity systemswith magnetic disorder D. Ivanov1,Ya. Fominov2, M. Skvortsov2, P. Ostrovsky3,2 1EPFL, Lausanne, Switzerland 2Landau Institute, Chernogolovka, Russia 3Forschungszentrum Karlsruhe, Germany Phys. Rev. B 80, 134501 (2009) I.F. Schegolev Memorial Conference “Low-Dimensional Metallic and Superconducting Systems” 11–16 October 2009, Chernogolovka, Russia

  2. Magnetic (spin-flip) scattering and superconductivity Abrikosov and Gor’kov (1960): pointlike magnetic impurities Usadel equation (diffusive limitfor potential scattering + weaker spin-flip scattering): G– normal Green function F– anomalous Green function (superconductivity) • Effects of spin-flip scattering: • suppression of the critical temperatureTc • gapless superconductivity • etc.

  3. Motivation: SF junctions Ryazanov, Oboznov, Rusanov, Veretennikov, Golubov, Aarts (2001): experimental observation ofthe π-junction state in SFSsystems with weak ferromagnets Kontos, Aprili, Lesueur, Genêt, Stephanidis, Boursier (2002): Interpretation in terms ofmonodomainferromagnet:

  4. Motivation: spin-flip scattering in SF junctions Oboznov, Bol’ginov, Feofanov, Ryazanov, Buzdin (2006): Explanation: homogeneous exchange fieldh + spin-flip scatteringΓsf Simplifying assumption: easy-axis magnetic disorderδhz·σz • Questions: • Would we effectively getΓsfif the magnetic disorder is not pointlike? • All directions in the magnetic disorder? • Triplet superconducting component in this case?

  5. Problem formulation Total exchange field: a slow (compared toaandl), independent of disorder realization L decays on the scalea • Thouless energy (inverse diffusion time through the ferromagnet) • - «domain» Thouless energy Assumptions: i.e. the «domains» are small enough so that the triplet component is small

  6. Previous results for Γsf • Ivanov, Fominov (2006) • ∫F(r) dr = 0 Abrikosov and Gor’kov (1960) • Bulaevskii, Buzdin, Panjukov, Kulić (1983) • easy-axis magnetic disorder New results: 1) calculation of effectiveΓsfat arbitrarya 2) allowance for all directions of the disordered exchange field

  7. Results

  8. Diagrams Regimes of magnetic scattering at variousa: • local magnetic scattering • non-local magnetic scattering × • potential scattering (like in the standard diagrammatic technique) • magnetic scattering

  9. Sigma model Averaging overδh: integrating out fluctuations around the saddle point local: nonlocal: Comparison of the two contributions:

  10. Usadel equation • Pauli matrices in the Nambu-Gor’kov space • Pauli matrices in the spin space • 44 matrix in the Nambu-Gor’kov  spin space : slow (compared toaandl), realization-independent linear response toδh • slow (compared to a andl), realization-independent • zeroth order over • second order: As a result:

  11. Conclusions • At • (where) • the effect of inhomogeneous magnetization effectively reducesto the spin-flip scattering • Expressions for the effective spin-flip rateΓsf • at arbitrary correlation length of the magnetization

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