Abstract
We present a phase diagram of a ferromagnetic superconductor (FS) in $T\ensuremath{-}h$ 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 $\mathrm{FS}/I/\mathrm{FS}$ 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.
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