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

Abstract

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 α between magnetization in a ferromagnetic bilayer of thickness d is analyzed. For various orientations of the superconducting electrodes, we calculate a (d, α) phase diagram and discuss the possibility of achieving not only the coexistence of two stable states 0 and π but also the coexistence of three stable states 0, π and π/2, by varying the angle between magnetizations.We also observe areas of coexistence of stable and metastable states.