General boundary conditions for quasiclassical theory of superconductivity in the diffusive limit: application to strongly spin-polarized systems

Boundary conditions in quasiclassical theory of superconductivity are of crucial importance for describing proximity effects in heterostructures between differentmaterials. Although they have been derived for the ballistic case in full generality, corresponding boundary conditions for the diffusive limit, described byUsadel theory, have been lacking for interfaces involving strongly spin-polarized materials, e.g. half-metallic ferromagnets. Given the current intense research in the emergingfield of superconducting spintronics, the formulation of appropriate boundary conditions for theUsadel theory of diffusive superconductors in contact with strongly spin-polarized ferromagnets for arbitrary transmission probability and arbitrary spin-dependent interface scattering phases has been a burning open question.Herewe close this gap and derive the full boundary conditions for quasiclassical Green functions in the diffusive limit, valid for any value of spin polarization, transmission probability, and spin-mixing angles (spin-dependent scattering phase shifts). Our formulation allows also for complex spin textures across the interface and for channel off-diagonal scattering (a necessary ingredient when the numbers of channels on the two sides of the interface differ). As an example we derive expressions for the proximity effect in diffusive systems involving half-metallic ferromagnets. In a superconductor/half-metal/superconductor Josephson junctionwefind 0 φ -junction behavior under certain interface conditions.