Planar thermal Hall effect from phonons in a Kitaev candidate material

The thermal Hall effect has emerged as a potential probe of exotic excitations in spin liquids. In the Kitaev magnet α α -RuCl 3 , the thermal Hall conductivity κ _xy κ x y has been attributed to Majorana fermions, chiral magnons, or phonons. Theoretically, the former two types of heat carriers can generate a “planar” κ _xy κ x y , whereby the magnetic field is parallel to the heat current, but it is unknown whether phonons also could. Here we show that a planar κ _xy κ x y is present in another Kitaev candidate material, Na 2 Co 2 TeO 6 . Based on the striking similarity between κ _xy κ x y and the phonon-dominated thermal conductivity κ _xx κ x x , we attribute the effect to phonons. We observe a large difference in κ _xy κ x y between different configurations of heat current and magnetic field, which reveals that the direction of heat current matters in determining the planar κ _xy κ x y . Our observation calls for a re-evaluation of the planar κ _xy κ x y observed in \,α α -RuCl 3 .