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In the framework of the kinetic approach based on the Boltzmann equation forthe phonon distribution function, we analyze phonon heat transfer in aheterostructure containing a layer of a normal metal ($ N $) and a layer of aferromagnetic insulator ($ F $). Two realistic methods for creating atemperature gradient in such a heterostructure are considered: by heating ofthe $N$-layer by an electric current and by placing the $N/F$-bilayer betweenmassive dielectrics with different temperatures. The electron temperature $ T_e$ in the $ N $-layer and the magnon temperature $ T_m $ in the $ F $-layer arecalculated. The difference in these temperatures determines the voltage $V_{ISHE} $ on the $ N $-layer in the Seebeck spin effect regime. The dependenceof $ V_{ISHE} $ on the bath temperature and on the thickness of the $ N $ and $F $ layers is compared with the available experimental data.

Spin Seebeck effect and phonon energy transfer in heterostructures containing layers of a normal metal and a ferromagnetic insulator