We have developed the theory of spin transport transverse to the interface in metal/ferromagnetic insulator hybrid structures under the spin Seebeck effect conditions. We have calculated the deviation of the conduction electrons spin temperature from equilibrium under conditions of saturation of resonance interaction between the electrons and a sound wave field. We have demonstrated that the conduction electrons spin subsystem, when ex-cited under the above conditions, generates a spin-wave current in a nonconducting ferromagnetic of the metal/ferromagnetic insulator hybrid structure being in a nonuniform temperature field. In addition, the spin-wave current generation in the ferromagnetic has a resonance nature. We have analyzed the approximation of effective parameters, when each of the considered subsystems (conduction electrons, magnons, and phonons) is characterized by its effective temperature.

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