Using one of the methods of quantum nonequilibrium statistical physics we have investigated the spin transport transverse to the normal metal/ferromagnetic insulator interface in hybrid nanostructures. An approximation of the effective parameters, when each of the interacting subsystems (electron spin, magnon, and phonon) is characterized by its own effective temperature have been considered. The generalized Bloch equations which describe the spin-wave current propagation in the dielectric have been derived. Finally, two sides of the spin transport "coin" have been revealed: the diffusive nature of the magnon motion and magnon relaxation processes, responsible for the spin pumping and the spin-torque effect.

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 excited 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.

The formation of the two: injected and thermally excited, different in energies magnon subsystems and the influence of its interaction with phonons and between on drag effect under spin Seebeck effect conditions in the magnetic insulator part of the metal/ferromagnetic insulator/metal structure is studied. The analysis of the macroscopic momentum balance equations of the systems of interest conducted for different ratios of the drift velocities of the magnon and phonon currents show that the injected magnons relaxation on the thermal ones is possible to be dominant over its relaxation on phonons. This interaction will be the defining in the forming of the temperature dependence of the spin-wave current under spin Seebeck effect conditions, and inelastic part of the magnon-magnon interaction is the dominant spin relaxation mechanism.

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Using the non-equilibrium statistical operator method (NSO), we have investigated the spin transport through the interface in a semiconductor/ferromagnetic insulator hybrid structure. 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. We have constructed the macroscopic equations, describing the spinwave current caused by both resonantly excited spin system of conduction electrons and by an inhomogeneous thermal field in the ferromagnetic insulator.