arXiv2006
We study the Josephson effect in clean heterojunctions that consist of superconductors connected through two metallic ferromagnets with insulating interfaces. We solve the scattering problem based on the Bogoliubov--de Gennes equation for any relative orientation of in-plane magnetizations, arbitrary transparency of interfaces, and mismatch of Fermi wave vectors. Both spin singlet and triplet superconducting correlations are taken into account, and the Josephson current is calculated as a function of the ferromagnetic layers thicknesses and of the angle $α$ between their magnetizations. We find that the critical Josephson current $I_c$ is a monotonic function of $α$ when the junction is far enough from $0-π$ transitions. This holds when ferromagnets are relatively weak. For stronger ferromagnets, variation of $α$ induces switching between 0 and $π$ states and $I_c(α)$ is non-monotonic function, displaying characteristic dips at the transitions. However, the non-monotonicity is the effect of a weaker influence of the exchange potential in the case of non-parallel magnetizations. No substantial impact of spin-triplet superconducting correlations on the Josephson current has been found in the clean limit. Experimental control of the critical current and $0-π$ transitions by varying the angle between magnetizations is suggested.