Effects of spin-orbit interaction on superconductor – ferromagnet heterostructures: spontaneous electric and spin surface currents

We find proximity-induced spontaneous spin and electric surface currents, at all temperatures below the superconducting $T_c$, in an isotropic $s$-wave superconductor deposited with a thin ferromagnetic metal layer with spin-orbit interaction. The currents are carried by Andreev surface states and generated as a joint effect of the spin-orbit interaction and the exchange field. The background spin current arises in the thin layer due to different local spin polarizations of electrons and holes, which have almost opposite velocities in each of the surface states. The spontaneous surface electric current in the superconductor originates in asymmetry of Andreev states with respect to sign reversal of the momentum component parallel to the surface. Conditions for electric and spin currents to show up in the system, significantly differ from each other.