  We theoretically investigate spin transport at the interface between the
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 non-equilibrium
states induced by the spin pumping, and compare them quantitatively for an
yttrium-iron-garnet-NbN interface.
