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

Results

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:

• 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

Conclusions