First-order phase transitions in ferromagnetic/superconducting/ferromagnetic trilayers

We study theoretically the proximity effect in ferromagnetic/superconducting/ferromagnetic trilayers at the nanoscopic scale in the dirty limit. We show using the Usadel equation scheme that the order of the normal-metal-superconductor phase transition in the superconducting layer strongly depends on the thickness d(f) of ferromagnetic (F) layers and on their relative orientation as well as on the interfaces transparency. In the parallel configuration for thin F layers and at high transparencies, the phase transition may become a first-order one. In the antiparallel case the transition always remains of second order. We calculate the order parameter Delta at T=0 as a function of F-layer thickness, analyze its behavior while decreasing transparency, and demonstrate that it can be either single valued or bivalued for an appropriate choice of parameters.