Spin-orbit coupling as a source of long-range triplet proximity effect in superconductor-ferromagnet hybrid structures

Abstract

We investigate the proximity effect in diffusive superconducting hybrid structures with a spin-orbit (SO) coupling. Our study is focused on the singlet-triplet conversion and the generation of long-range superconducting correlations in ferromagnetic elements. We derive the quasiclassical equations for the Green's functions including the SO coupling terms in form of a background SU(2) field. With the help of these equations, we first present an interesting complete analogy between the spin diffusion process in normal metals and the generation of the triplet components of the condensate in a diffusive superconducting structure in the presence of SO coupling. From this analogy it turns out naturally that the SO coupling is an additional source of the long-range triplet component (LRTC) besides the magnetic inhomogeneities studied in the past. This analogy opens a range of possibilities for the generation and manipulation of the triplet condensate in hybrid structures. In particular we demonstrate that a normal metal with SO coupling can be used as source of LRTC if attached to a superconductor-ferromagnet bilayer. We also demonstrate an explicit connection between an inhomogeneous exchange field and SO coupling mechanisms for the generation of the LRTC and establish the conditions for the appearance of the LRTC in different geometries. Our work gives a global description of the singlet-triplet conversion in hybrid structures in terms of generic spin fields and our results are particularly important for the understanding of the physics underlying spintronic devices with superconductors.