Transverse thermal conductivity of paramagnetic dielectrics in the isotropic model

A mechanism in which the transverse thermal conductivity of paramagnetic dielectrics is governed by spin-phonon (SP) scattering, which should be involved in the right-hand side of the kinetic equation in the above-Born approximation. In this model, transverse sound modes are degenerate and comprise two circularly polarized waves. The main part of phonon scattering is not associated with magnetic moments. It follows that the above-Born terms of the collision integral, which are linear by the ion moments, can lead to the heat flux of interest in direction. When deriving the expression playing the role of the collision integral cubic by scattering amplitudes, it is assumed that the spin states of ions during phonon scattering are invariable and independent of each other for various ions. If the magnetic field is directed along Z and the temperature gradient is directed along X, the PHE is specified by the component of the thermal conductivity tensor.