The main goal of the present work is the description of the dynamics of spin current and induced magnetization inside a superconducting film S that is in contact with a ferromagnetic insulator layer FI. Spin current and induced magnetization are calculated not only at the interface of the S/FI hybrid structure, but also inside the superconducting film. The new and interesting predicted effect is the frequency dependence of the induced magnetization with a maximum appearing at high temperatures. It is also shown that the increase of the magnetization precession frequency can drastically change the spin distribution of quasiparticles at the S/FI interface.

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