Anomalous Hall effect for the phonon heat conductivity in paramagnetic dielectric

TL;DR

This paper develops a theoretical framework explaining the anomalous Hall effect in phonon heat conductivity within paramagnetic dielectrics, linking magnetic ion interactions and phonon polarization to heat flux perpendicular to temperature gradient and magnetic field.

Contribution

It introduces a new theory connecting spin-phonon interactions and phonon polarization to the anomalous Hall effect in heat transfer for paramagnetic dielectrics.

Findings

Phonon heat flux is perpendicular to temperature gradient and magnetic field.

Elliptical polarization of phonons arises from spin-phonon interactions.

Off-diagonal phonon density matrix is key to the effect.

Abstract

The theory of anomalous Hall effect for the heat transfer in a paramagnetic dielectric, discovered experimentally in [1], 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 the both factors is decisive for the phenomenon under consideration.