Magnon-Polaron Driven Thermal Hall Effect in a Heisenberg-Kitaev Antiferromagnet

The thermal Hall effect, defined as a heat current response transversal to an applied temperature gradient, is a central experimental probe of exotic electrically insulating phases of matter. A key question is how the interplay between magnetic and structural degrees of freedom gives rise to a nonzero thermal Hall conductivity (THC). Here, we present evidence for an intrinsic thermal Hall effect in the Heisenberg-Kitaev antiferromagnet and spin-liquid candidate Na$_2$Co$_2$TeO$_6$ brought about by the quantum-geometric Berry curvature of so-called magnon polarons, resulting from magnon-phonon hybridization. At low temperatures, our field- and temperature-dependent measurements show a negative THC for magnetic fields below 10 T and a sign change to positive THC above. Theoretically, the sign and the order of magnitude of the THC cannot be solely explained with magnetic excitations. We demonstrate that, by incorporating spin-lattice coupling into our theoretical calculations, the Berry curvature of magnon polarons counteracts the purely magnonic contribution, reverses the overall sign of the THC, and increases its magnitude, which significantly improves agreement with experimental data. Our work highlights the crucial role of spin-lattice coupling in the thermal Hall effect.