Magnetization-orientation dependence of the superconducting transition temperature calculated for F/S/F trilayer structures

We theoretically investigate the superconducting critical temperature T_c dependence on the relative orientation of the magnetizations in F/S/F trilayer structures, where F is a ferromagnet and S is a superconductor. The values of T_c are obtained from the linearized Usadel equations. We discuss the usual approximations employed to solve those equations and show that they are invalid in the parameter range of interest. We also compare approximate results of several authors. Adapting the numeric method used previously for F/S bilayers to the case of F/S/F trilayers, we find critical temperatures for parallel and antiparallel magnetic configurations with no approximations involved. Our results qualitatively explain experimental data and provide guidelines for optimizing the experimental systems.