Generalized proximity effect in metallic F/S/F heterostructures

We consider a microscopic theory of F/S/F trilayers with metallic or insulating ferromagnets. The trilayer with metallic ferromagnets is controlled by the formation of non local pair correlations among the two ferromagnets which do not exist with insulating ferromagnets. The difference between the insulating and ferromagnetic models can be understood from lowest order diagrams. Metallic ferromagnets are controlled by non local pair correlations and the superconducting gap is larger if the ferromagnetic electrodes have a parallel spin orientation. Insulating ferromagnets are controlled by pair breaking and the superconducting gap is smaller if the ferromagnetic electrodes have a parallel spin orientation. The same behavior is found in the presence of disorder in the microscopic phase variables and also in the presence of a partial spin polarization of the ferromagnets. The different behaviors of the metallic and insulating trilayers may be probed in experiments.