Josephson current in ferromagnet-superconductor tunnel junctions

We present a phase diagram of a ferromagnetic superconductor (FS) in T-h plane with T the temperature and h the effective exchange field, in which a first-order phase-transition line separates the superconducting region from the normal-state region. The Josephson currents in an FS/I/FS junction (with I denoting thin insulating layers) are calculated as a function of the temperature, exchange field, and insulating barrier strength. It is found that the presence of h always suppresses the Josephson critical current at higher temperatures, or for weak barrier strength, or for a parallel configuration of the magnetic moments of two FS electrodes. The only exception that the critical current increases with h occurs if all three conditions are satisfied: at low temperatures, for strong barrier strength, and in an antiparallel configuration.