Scattering by magnetic and spin-orbit impurities and the Josephson current in superconductor-ferromagnet-superconductor junctions

We analyze the Josephson current in a junction consisting of two superconductors (S) and a ferromagnetic layer (F) for arbitrary impurity concentration. In addition to non-magnetic impurities, we consider also magnetic ones and spin-orbit scattering. In the limit of weak proximity effect we solve the linearized Eilenberger equation and derive an analytical expression for the Josephson critical current valid in a broad range of parameters. This expression enables us to obtain not only known results in the dirty and clean limits but also in a intermediate region of the impurity concentration, which may be very important for comparison with experimental data.