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.

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