D . Ivanov 1 , Ya . Fominov 2 , M . Skvortsov 2 , P . Ostrovsky 3,2
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Transcript of 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. Ivanov1, Ya. Fominov2, M. Skvortsov2, P. Ostrovsky3,2
1 EPFL, Lausanne, Switzerland2 Landau Institute, Chernogolovka, Russia3 Forschungszentrum 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
Magnetic (spin-flip) scattering and superconductivity
Abrikosov and Gor’kov (1960):pointlike magnetic impurities
Effects of spin-flip scattering:
• suppression of the critical temperature Tc
• gapless superconductivity• etc.
Usadel equation(diffusive limit for potential scattering + weaker spin-flip scattering):
G – normal Green functionF – anomalous Green function (superconductivity)
Motivation: SF junctions
Ryazanov, Oboznov, Rusanov, Veretennikov, Golubov, Aarts (2001):experimental observation of the π-junction statein 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:
decays on the scale a
Assumptions:
i.e. the «domains» are small enoughso that the triplet component is small
- Thouless energy (inverse diffusion time through the ferromagnet)
- «domain» Thouless energy
S
L
slow (compared to a and l ),independent of disorder realization
L
a
Previous results for Γsf
Abrikosov andGor’kov (1960)
Bulaevskii, Buzdin, Panjukov, Kulić (1983)• easy-axis magnetic disorder
Ivanov, Fominov (2006)• ∫F(r) dr = 0
New results:1) calculation of effective Γsf at arbitrary a 2) allowance for all directions of the disordered exchange field
Diagrams
Regimes of magnetic scattering at various a :
×- potential scattering (like in the standard diagrammatic technique)
- magnetic scattering
- local magnetic scattering
- non-local magnetic scattering
Sigma model
Averaging over δh :
integrating out fluctuations around the saddle point
local: nonlocal:Comparison of thetwo 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: