Influence of d-wave superconductor orientation on Josephson current and phase difference in junctions with inhomogeneous ferromagnet

Utilizing a microscopic Bogoliubov-de Gennes approach we study Josephson effect in arbitrarily oriented d-wave superconductors connected through two ferromagnets with noncollinear magnetizations, by solving scattering problem. The critical Josephson current is calculated for various parameters of the junction. Mutual influence of d-wave superconducting electrodes orientation and angle α between magnetization in ferromagnetic bilayer of thickness d is analyzed. For various orientation of superconducting electrodes, we calculate (d,α) phase diagram, and discuss the possibility to achieve except coexistence of two stable states 0 and π, also coexistence of three stable states 0, π and π∕2, by varying the angle between magnetizations. We observe also areas of coexistence of stable and metastable states.