Anisotropic in-plane heat transport of Kitaev magnet Na${}_2$Co${}_2$TeO${}_6$

We report a study on low-temperature heat transport of Kitaev magnet Na${}_2$Co${}_2$TeO${}_6$, with the heat current and magnetic fields along the honeycomb spin layer (the $ab$ plane). The zero-field thermal conductivity of ${\kappa }_{xx}^a$ and ${\kappa }_{xx}^{a\ast }$ display similar temperature dependence and small difference in their magnitudes; whereas, their magnetic field (parallel to the heat current) dependence are quite different and are related to the field-induced magnetic transitions. The ${\kappa }_{xx}^a(B)$ data for $B\parallel a$ at very low temperatures have an anomaly at 10.25–10.5 T, which reveals an unexplored magnetic transition. The planar thermal Hall conductivity ${\kappa }_{xy}^a$ and ${\kappa }_{xy}^{a\ast }$ show very weak signals at low fields and rather large values with sign change at high fields. This may point to a possible magnetic structure transition or the change of the magnon band topology that induces a radical change of magnon Berry curvature distribution before entering the spin polarized state. These results put clear constraints on the high-field phase and the theoretical models for Na${}_2$Co${}_2$TeO${}_6$.