Critical current in SFIFS junctions

Quantitative theory of the Josephson effect in SFIFS junctions (S denotes bulk superconductor, F — metallic ferromagnet, I — insulating barrier) is presented in the dirty limit. Fully self-consistent numerical procedure is employed to solve the Usadel equations at arbitrary values of the F-layers thicknesses, magnetizations, and interface parameters. In the case of antiparallel ferromagnets magnetizations the effect of the critical current $I_c$ enhancement by the exchange energy $H$ is observed, while in the case of parallel magnetizations the junction exhibits the transition to the $\pi$-state. In the limit of thin F-layers, we study these peculiarities of the critical current analytically and explain them qualitatively; the scenario of the $0$-$\pi$ transition in our case differs from those studied before. The effect of switching between $0$ and $\pi$ states by changing the F-layers mutual orientation is demonstrated.