$\pi-0$ transition in superconductor-ferromagnetic-superconductor junctions

Superconductor-ferromagnetic-superconductor (SFS) Josephson junctions are known to exhibit a transition between $\pi$ and $0$ states. In this note we find the $\pi-0$ phase diagram of an SFS junction depending on the transparency of an intermediate insulating layer (I). We show that in general, the Josephson critical current is nonzero at the $\pi-0$ transition temperature. Contributions to the current from the two spin channels nearly compensate each other and the first harmonic of the Josephson current as a function of phase difference is suppressed. However, higher harmonics give a nonzero contribution to the supercurrent.