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Effective spin-flip scattering in diffusive superconducting proximity systems with magnetic disorder D. Ivanov1, Ya. Fominov2, M. Skvortsov2, P. Ostrovsky3,2 EPFL, Lausanne, Switzerland 2 Landau Institute, Chernogolovka, Russia 3 Forschungszentrum Karlsruhe, Germany 1 Phys. Rev. B 80, 134501 (2009) I.F. Schegolev Memorial Conference “Low-Dimensional Metallic and Superconducting Systems” 11–16 October 2009, Chernogolovka, Russia Magnetic (spin-flip) scattering and superconductivity Abrikosov and Gor’kov (1960): pointlike magnetic impurities Usadel equation (diffusive limit for potential scattering + weaker spin-flip scattering): G – normal Green function F – anomalous Green function (superconductivity) Effects of spin-flip scattering: • suppression of the critical temperature Tc • gapless superconductivity • etc. Motivation: SF junctions Ryazanov, Oboznov, Rusanov, Veretennikov, Golubov, Aarts (2001): experimental observation of the π-junction state in SFS systems with weak ferromagnets Kontos, Aprili, Lesueur, Genêt, Stephanidis, Boursier (2002): Interpretation in terms of monodomain ferromagnet: Motivation: spin-flip scattering in SF junctions Oboznov, Bol’ginov, Feofanov, Ryazanov, Buzdin (2006): Explanation: homogeneous exchange field h + spin-flip scattering Γsf Simplifying assumption: easy-axis magnetic disorder δhz·σz Questions: • Would we effectively get Γsf if the magnetic disorder is not pointlike? • All directions in the magnetic disorder? • Triplet superconducting component in this case? Problem formulation Total exchange field: S slow (compared to a and l ), independent of disorder realization a LL decays on the scale a - 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 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 effective Γsf at arbitrary a 2) allowance for all directions of the disordered exchange field Results Diagrams Regimes of magnetic scattering at various a : - local magnetic scattering - non-local magnetic scattering × - potential scattering (like in the standard diagrammatic technique) - magnetic scattering Sigma model Averaging over δh : integrating out fluctuations around the saddle point local: nonlocal: Comparison of the two contributions: Usadel equation - Pauli matrices in the Nambu-Gor’kov space - Pauli matrices in the spin space - 44 matrix in the Nambu-Gor’kov spin space : slow (compared to a and l ), realization-independent linear response to δh slow (compared to a and l ), realization-independent • zeroth order over • second order: As a result: Conclusions • At (where ) the effect of inhomogeneous magnetization effectively reduces to the spin-flip scattering • Expressions for the effective spin-flip rate Γsf at arbitrary correlation length of the magnetization