Current-phase relation in SFS Josephson junctions in the presence of s-d scattering

The analytical equations for the current-phase relation (CPR) coefficients for Josephson junctions with a ferromagnetic interlayer in the model where the scattering from s- to d-band is considered to be the main type scattering of charge carrier in a ferromagnet are obtained. It is shown that the magnitude of the coefficients oscillates and decays with an increase of the interlayer thickness. Both the oscillation period and the decay length for the first and the second harmonics differ by two times. The temperature dependence of the critical current demonstrating 0-π temperature transitions is obtained. The possibility of design a flux qubit based on such Josephson junctions is demonstrated.