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 the Josephson effect in arbitrarily oriented d-wave superconductors connected through two ferromagnets with noncollinear magnetizations, by solving the scattering problem. The critical Josephson current is calculated for various parameters of the junction. The mutual influence of d-wave superconducting electrodes' orientation and angle alpha between magnetization in a ferromagnetic bilayer of thickness d is analyzed. For various orientations of the superconducting electrodes, we calculate a (d, alpha) phase diagram and discuss the possibility of achieving not only the coexistence of two stable states 0 and pi but also the coexistence of three stable states 0,pi and pi/2, by varying the angle between magnetizations. We also observe areas of coexistence of stable and metastable states.