Microscopic theory of spin transport at the interface between a superconductor and a ferromagnetic insulator

We theoretically investigate spin transport at the interface between a ferromagnetic insulator (FI) and a superconductor (SC). Considering a simple FI-SC interface model, we derive formulas for the spin current and spin-current noise induced by microwave irradiation (spin pumping) or the temperature gradient (the spin Seebeck effect). We show how the superconducting coherence factor affects the temperature dependence of the spin current. We also calculate the spin-current noise in thermal equilibrium and in nonequilibrium states induced by the spin pumping and compare them quantitatively for an yttrium iron garnet-NbN interface.