The modified Usadel equations for 3-d ferromagnet-superconductor multilayers

For the description of a transition ferromagnetic metal in a contact with the superconductor the modified Usadel equations are derived taking into account s-d scattering. They are used for the calculation of the Josephson current through a ferromagnetic sandwich with superconducting electrodes. It is shown that the critical current strongly depends on the mutual orientation of ferromagnetic layers magnetizations and oscillates as a function of the layers thickness. The oscillation period depends only on the exchange magnetic field meanwhile s-d scattering effectively destroys BCS correlation and suppresses the enhancement of the Josephson current.