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

Abstract

In the framework of the kinetic approach based on the Boltzmann equation for the phonon distribution function, we analyze phonon heat transfer in a heterostructure containing a layer of a normal metal (N) and a layer of a ferromagnetic insulator (F). Two realistic methods for creating a temperature gradient in such a heterostructure are considered: by heating the N layer by an electric current and by placing the N/F bilayer between massive dielectrics with different temperatures. The electron temperature Te in the N layer and the magnon temperature Tm in the F layer are calculated. The difference in these temperatures determines the voltage VISHE on the N layer in the Seebeck spin effect regime. The dependence of VISHE on the bath temperature and on the thickness of the N and F layers is compared with the available experimental data.