Superconducting decay length in a ferromagnetic metal

The complex decay length ξ characterizing the penetration of superconducting correlations into a ferromagnet due to the proximity effect is studied theoretically in the framework of the linearized Eilenberger equations. The real part ξ1 and imaginary part ξ2 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 ξ1,2 determine the spatial scales of, respectively, the decay and oscillation of a critical current in SFS Josephson junctions in the limit of a large distance between superconducting electrodes. The developed theory provides the criteria of applicability of the expressions for ξ1 and ξ2 in the dirty and clean limits, which are commonly used in the analysis of SF hybrid structures.