Unusual heat transport of the Kitaev material Na${}_2$Co${}_2$TeO${}_6$: putative quantum spin liquid and low-energy spin excitations

We studied the field dependent thermal conductivity ($\kappa$) of Na${}_2$Co${}_2$TeO${}_6$, a compound considered as the manifestation of the Kitaev model based on the high-spin $d^7$ Co${}^{2+}$ ions. We found that in-plane magnetic fields beyond a critical value $B_c\approx$~10 T are able to drastically enhance $\kappa$ at low temperatures, resulting in a double-peak structure of $\kappa (T)$ that closely resembles the behavior of $\alpha$-RuCl${}_3$. This result suggests that heat transport in Na${}_2$Co${}_2$TeO${}_6$ is primarily phononic, and it is strongly affected by scattering from magnetic excitations that are highly tunable by external fields. Interestingly, for magnetic fields $B\mathrm{/}\mathrm{/}a$ (i.e., along the zigzag direction of the Co-Co bonds), there is an extended field range which separates the long-range magnetic order for $B\le B_c\approx 10$ T and the partially spin-polarized gapped high-field phase for $B\gtrsim 12$ T. The low-energy phonon scattering is particularly strong in this field range, consistent with the notion that the system becomes a quantum spin liquid with prominent spin fluctuations down to energies of no more than 2 meV.