Phase diagrams of ferromagnet-superconductor multilayers with misaligned exchange fields

Abstract

We study the influence of misalignment of the ferromagnetic exchange field on the equilibrium properties of hybrid structures, composed of superconducting (S) and ferromagnetic (F) parts. In particular, we study numerically the superconducting critical temperature ${T}_{c}$ in F-S-F trilayers and in F-S-F-S-F Josephson junctions as a function of the misalignment angle $\ensuremath{\theta}$ of the ferromagnetic magnetization. We discuss the corresponding phase diagrams for these hybrid structures. For the Josephson junctions, a transition between the zero-phase and the $\ensuremath{\pi}$-phase ground states as a function of $\ensuremath{\theta}$ takes place under certain conditions. Within the quasiclassical Green's function technique in the diffusive limit, we introduce a fast and effective method for calculating ${T}_{c}$ in such multilayer structures.