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We theoretically investigate spin transport at the interface between theferromagnetic insulator(FI) and a superconductor(SC). Considering a simpleFI-SC interface model, we derive formulas for the spin current and spin-currentnoise induced by microwave irradiation (spin pumping) or the temperaturegradient (the spin Seebeck effect). We show how the superconducting coherencefactor affects the temperature dependence of the spin current. We alsocalculate the spin-current noise in thermal equilibrium and in non-equilibriumstates induced by the spin pumping, and compare them quantitatively for anyttrium-iron-garnet-NbN interface.

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