The dc Josephson current in double ferromagnet-superconductor tunnel junctions

Using Bogoliubov-de Gennes equations, we obtain the self-consistent equation in a ferromagnetic superconductor. Taking into account the rough interface scattering effects, within Bogoliubov-de Gennes equations and Furusaki-Tsukada formula we calculate the dc Josephson current in the double ferromagnet-superconductor tunnel junctions. It is found that de Josephson currents in FS/I/FS are suppressed by the ferromagnetic exchange interaction for weak barrier strength and weak rough interface scattering strength. The only exception that the dc Josephson currents increase with the ferromagnetic exchange interaction occurs if all three conditions are satisfied: at low temperature, for strong barrier strength or strong rough interface scattering strength, and in an antiparallel configuration.