Superconducting decay length in a ferromagnetic metal

TL;DR

This paper presents a theoretical analysis of the superconducting decay length in ferromagnetic metals, focusing on how it depends on exchange energy and scattering processes, with implications for SFS Josephson junctions.

Contribution

It develops a comprehensive theory for the decay length in ferromagnets, including criteria for its applicability in different scattering regimes, advancing understanding of superconducting proximity effects.

Findings

Calculated real and imaginary parts of decay length as functions of exchange energy and scattering rates.

Provided criteria for the applicability of decay length expressions in dirty and clean limits.

Clarified the spatial scales of decay and oscillation of the critical current in SFS junctions.

Abstract

The complex decay length xi characterizing penetration of superconducting correlations into a ferromagnet due to the proximity effect is studied theoretically in the frame of the linearized Eilenberger equations. The real part xi_1 and imaginary part xi_2 of the decay length are calculated as functions of exchange energy and the rates of ordinary, spin flip and spin orbit electronic scattering in a ferromagnet. The lengths xi_1,2 determine the spatial scales of, respectively, decay and oscillation of a critical current in SFS Josephson junctions in the limit of large distance between superconducting electrodes. The developed theory provides the criteria of applicability of the expressions for xi_1 and xi_2 in the dirty and the clean limits which are commonly used in the analysis of SF hybrid structures.