Superconducting decay length in a ferromagnetic metal

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.