  We show that the spin pumping from ferromagnetic insulator into the adjacent
metallic spin sink can be strongly stimulated by the superconducting
correlations.
  The key physical mechanism responsible for this effect is the presence of
quasiparticle surface states at the ferromagnetic insulator/superconductor
interface. We consider the minimal model when these states appear because of
the suppressed pairing constant within the interfacial normal layer. For thin
normal layers we obtain a strongly peaked temperature dependence of the Gilbert
damping coefficient which has been recently observed in such systems. For
thicker normal layers the Gilbert damping monotonically increases down to the
temperatures much smaller than the critical one. The suggested model paves the
way to controlling the temperature dependence of the spin pumping by
fabricating hybrid normal metal/superconductor spin sinks.
