Field-angle dependence of phonon thermal Hall effect in Na₂ X ₂TeO₆ (X = Co, Zn)

The mechanism behind thermal Hall effects by phonons, which are observed in various materials, is not clarified despite the dominant contribution as heat carriers. Theoretically, mechanisms based on the intrinsic Berry phase and those on extrinsic impurity-induced scatterings have been proposed, which can be distinguished by comparing the field-angle dependence of the thermal Hall effect and that of the magnetic anisotropy. Here, we investigate the field-angle dependence of the thermal Hall effects in the antiferromagnet Na₂Co₂TeO₆ and its non-magnetic isostructural analogue Na₂Zn₂TeO₆ in the [Formula: see text] plane. We find that the field-angle dependence of the thermal Hall conductivity in both materials well follows that of the out-of-plane magnetization, showing a common mechanism by extrinsic impurity-induced scatterings in both the phonon thermal Hall effect and that enhanced by a coupling with the magnetism.