An Effective Action approach to inhomogeneous superconductors: Application to F/S/F spin valves

The interplay between magnetism and superconductivity can be studied in simple systems such as ferromagnetic-superconductor-ferromagnetic tri-layers. Many recent experiments [1] measured a critical temperature dependence of the superconductor as a function of the relative orientations of the surrounding ferromagnetic layers. This layered system gives rise to an in-homogenous gap equation for the superconductor due to the polarization at the ferromagnetic-superconductor interfaces irrespective of the orientation of the magnetization in-plane or out-of-plane. Real space formulations are therefore better suited to study this kind of systems. We show that an Effective Action formulation similar to the one proposed by Weinberg [2] is very advantageous in this respect as was shown in normal-ferromagnetic-normal systems in [3]. \newline \newline [1] Yu. Rusanov, S. Habraken and J. Aarts, Phys. Rev. B 73, 060505(R) (2006); A. Singh, C. Sugers and H. v. Lohneysen, Phys. Rev. B 75, 024513 (2007); T. Ambrose (unpublished). \newline [2] S. Weinberg, Nucl. Phys. B 413, 567 (1994). \newline [3] A. Rebei and M. Simionato, Phys. Rev. B 71, 174415 (2005).