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 $$ -RuCl₃, the thermal Hall conductivity $$ has been attributed to Majorana fermions, chiral magnons, or phonons. Theoretically, the former two types of heat carriers can generate a "planar" $$ , whereby the magnetic field is parallel to the heat current, but it is unknown whether phonons also could. Here we show that a planar $$ is present in another Kitaev candidate material, Na₂Co₂TeO₆. Based on the striking similarity between $$ and the phonon-dominated thermal conductivity $$ , we attribute the effect to phonons. We observe a large difference in $$ between different configurations of heat current and magnetic field, which reveals that the direction of heat current matters in determining the planar $$ . Our observation calls for a re-evaluation of the planar $$ observed in $$ -RuCl₃.