Anomalous hall effect for the phonon heat conductivity in paramagnetic dielectrics

The theory of the anomalous Hall effect for the heat transfer in a parmagnetic dielectric, discovered by Strohm, Rikken, and Wyder [Phys. Rev. Lett. 95, 155901 (2005)], is developed. The appearance of the phonon heat flux normal to both the temperature gradient and the magnetic field is connected with the interaction of magnetic ions with the crystal field oscillations. In crystals with an arbitrary phonon spectrum this interaction creates the elliptical polarization of phonons. The kinetics related to phonon scattering induced by the spin-phonon interaction determines an origin of the off-diagonal phonon density matrix. The combination of both factors is decisive for the phenomenon under consideration.