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Interplay of spin-discriminated Andreev bound states forming the 0-$π$ transition in Superconductor-Ferromagnet-Superconductor Junctions

The Josephson current in S-F-S junctions is described by taking into account different reflection (transmission) amplitudes for quasiparticles with spin up and down. We show that the 0-$π$ transition in the junctions can take place at some temperature only for sufficiently strong spin-activity of the interface. In particular, Andreev interface bound state energies in one spin channel have to be all negative, while in the other one positive. Only one spin channel contributes then to the zero-temperature Josephson current. At the temperature of the 0-$π$ transition two spin channels substantially compensate each other and can result in a pronounced minimum in the critical current in tunnel junctions. The minimal critical current is quadratic in small transparency and contains first and second harmonics of one and the same order.