Magnon thermal Hall effect in insulating antiferromagnets

Abstract: In this paper we theoretically discuss thermal Hall effect of magnons in insulating N\'{e}el ordered antiferromagnets at zero external magnetic field. We show that non-zero thermal Hall effect requires absence of any symmetry between the two sublattices. The thermal Hall effect of magnons will be non-zero by a virtue of the spin-momentum splitting of the magnon spectrum due to the Dzyaloshinskii-Moriya interaction as well as anisotropic second-nearest exchange interaction different in the two sublattices, both corresponding to the broken symmetry. We construct a theoretical model in which an external electric field may change the symmetry of the antiferromagnetic system thus altering the thermal Hall effect of magnons.