Some remarks on the phase diagram of magnetic-superconducting-magnetic proximity sandwiches

We study the phase diagram of a sandwich in which superconductivity is induced by the proximity effect from a superconducting film into two normal or superconducting films containing magnetic impurities which can be magnetically ordered. We describe the M-S-M sandwich with a two order parameter mean field theory: the Ginzburg-Landau equations and the corresponding free energy functional reduce the study of this inhomogeneous system to a problem of nonlinear functional anlysis. Simultaneous use of bifurcation theory and the direct method of the calculus of variations gives qualitative but sufficiently complete information for drawing the phase diagram. The existence of a mixed phase with the coexistence of both superconductivity and magnetism is proved in a restricted region of the phase diagram for any value of the coupling constant between the two order parameters.