Abstract
Theory of an analog of anomalous Hall effect for heat transfer in paramagnetic dielectric, discovered experimentally in [1], is developed. The appearance of phonon heat flux normal both to temperature gradient and manetic field is connected with the interaction of magnetic ions with crystal field oscillations. In crystals with arbitrary phonon spectrum this interection creates the elliptical polarisation of phonons. The kinetics related to phonon scattering indused by spin-phonon interaction stipulates the origin of off-diagonal phonon desity matrix. The combination of both factors is decisive for phenomenon under consideration.