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Y-kapellasite [Y3Cu9(OH)19Cl8] is a frustrated antiferromagnetic insulator which remains paramagnetic down to a remarkably low N\'eel temperature of about 2 K. Having studied this material in the paramagnetic regime, in which phonons are the only possible heat carriers, we report the observation of a planar parallel thermal Hall effect coming unambiguously from phonons. This is an advantage over the Kitaev quantum spin liquid candidates {\alpha}-RuCl3 and Na2Co2TeO6 where in principle other heat carriers can be involved [1-4]. As it happens, Y-kapellasite undergoes a structural transition attributed to the positional freezing of a hydrogen atom below about 33 K. Above this transition, the global crystal symmetry forbids the existence of a planar parallel signal - the same situation as in Na2Co2TeO6 and cuprates [3-5]. This points to the notion of a local symmetry breaking at the root of the phonon Hall effect. In this context, the advantage of Y-kapellasite over Na2Co2TeO6 (with high levels of Na disorder and stacking faults) and cuprates (with high levels of disorder coming from dopants and oxygen vacancies) is its clean structure, where the only degree of freedom available for local symmetry breaking is this hydrogen atom randomly distributed over six equivalent positions above 33 K. This provides a specific and concrete case for the general idea of local symmetry breaking leading to the phonon Hall effect in a wide range of insulators., Comment: 16 pages, 4 figures, 3 tables

Kitaev materials are a promising platform for the realization of quantum spin liquid states. The thermal Hall effect has emerged as a potential probe of exotic excitations within such states. In the Kitaev candidate material $\alpha$-RuCl$_{3}$, however, the thermal Hall conductivity $\kappa_{xy}$ has been attributed not only to exotic Majorana fermions or chiral magnons, but also to phonons. It has been shown theoretically that the former two types of heat carriers can generate a "planar" thermal Hall effect, whereby the magnetic field is parallel to the heat current, as observed experimentally, but it is unknown whether phonons also could. Here we show that a planar thermal Hall effect is present in another Kitaev candidate material, Na$_{2}$Co$_{2}$TeO$_{6}$. On the basis of a striking similarity between the temperature and field dependence of $\kappa_{xy}$ and that of the phonon-dominated thermal conductivity $\kappa_{xx}$, we argue that the planar thermal Hall effect in Na$_{2}$Co$_{2}$TeO$_{6}$ is generated by phonons. The phonon contributed planar $\kappa_{xy}$ also shows a strong sample dependence, which indicates an extrinsic origin of the mechanism. By conducting a complete study with different in-plane configurations of heat current $J$ and magnetic field $H$, $i.e.$ $H$ $\|$ $J$ and $H$ $\bot$ $J$, we observe a large difference in $\kappa_{xy}$ between these two configurations, which reveals that the direction of the heat current $J$ may play an important role in determining the planar thermal Hall effect. Our observation calls for a re-evaluation of the planar thermal Hall effect observed in $\alpha$-RuCl$_{3}$.

In a growing number of materials, phonons have been found to generate a thermal Hall effect, but the underlying mechanism remains unclear. Inspired by previous studies that revealed the importance of Tb$^{3+}$ ions in generating the thermal Hall effect in a family of pyrochlores, we investigated the role of Tm$^{3+}$ ions in TmVO$_{4}$, a paramagnetic insulator with a different crystal structure. We observe a negative thermal Hall conductivity in TmVO$_{4}$ with a magnitude such that the Hall angle, $|\kappa_{xy}$/$\kappa_{xx}|$, is approximately 1 x 10$^{-3}$ at $H$ = 15 T and $T$ = 20 K, typical for a phonon-generated thermal Hall effect. In contrast to the negligible $\kappa_{xy}$ found in the nonmagnetic pyrochlore analog (where the Tb$^{3+}$ ions are replaced with Y$^{3+}$), we observe a negative $\kappa_{xy}$ in YVO$_{4}$ with a Hall angle of magnitude comparable to that of TmVO$_{4}$. This shows that the Tm$^{3+}$ ions are not essential for the thermal Hall effect in this family of materials. Interestingly, at an intermediate Y concentration of $x$ = 0.3 in Tm$_{1-x}$Y$_{x}$VO$_{4}$, $\kappa_{xy}$ was found to have a positive sign, pointing to the importance of impurities in the thermal Hall effect of phonons., Comment: Figures modified and added, authors added, appendix added