Proximity effect in four-layered ferromagnet/superconductor nanostructures: decoupled superconductivity and hierarchy of critical temperatures

The four-layered nanostructure consisting of rather dirty superconducting (S) and ferromagnetic (F) metals is studied within the theory of the proximity effect taking detailed account of the boundary conditions. The F/S nanostructures with four and more F and S layers are shown to have considerably richer physics than the F/S/F trilayer and F/S superlattices. The dependence of the critical temperatures versus the F layers thicknesses is investigated. It is shown that the F/S/F$\prime $/S$\prime $ nanostructure can experience decoupled superconductivity. The latter manifests itself through a hierarchy of the critical temperature Tc, which can be different for different S and S$\prime $ layers. An optimal set of parameters is determined, for which the difference between the critical temperatures becomes significant, and the corresponding phase diagrams are constructed. A conceptual scheme of a new control device based on the F/S/F$\prime $/S$\prime $ nanostructure with superconducting and magnetic recording channels that can be controlled separately using a weak external magnetic field is proposed.