Quantized transports of fermions are topological phenomena determined by the sum of the Chern numbers of all the energy bands below the Fermi energy. For bosonic excitations, e.g. phonons and magnons in a crystal, topological transport is dominated b
y the Chern number of the lowest energy band because the energy distribution of the bosons is limited below the thermal energy. Here, we demonstrate the existence of topological transport by bosonic magnons in a lattice of magnetic skyrmions - topological defects formed by a vortex-like texture of spins. We find a distinct thermal Hall signal when the ferromagnetic spins in an insulating polar magnet GaV4Se8 form magnetic skyrmions. Its origin is identified as the topological thermal Hall effect of magnons in which the trajectories of these magnons are bent by an emergent magnetic field produced by the magnetic skyrmions. Our theoretical simulations confirm that the thermal Hall effect is indeed governed by the Chern number of the lowest energy band of the magnons in a triangular lattice of magnetic skyrmions. Our findings lay a foundation for studying topological phenomena of other bosonic excitations.
We have investigated the thermal-transport properties of the kagome antiferromagnet Cd-kapellasite (Cd-K). We find that a field suppression effect on the longitudinal thermal conductivity k_xx sets in below ~25 K, suggesting a large spin contribution
k_xx^sp in k_xx. We also find clear thermal Hall signals in the spin liquid phase in all Cd-K samples. The magnitude of the thermal Hall conductivity k_xy shows a significant dependence on the samples scattering time. On the other hand, the temperature dependence of k_xy is similar in all Cd-K samples; k_xy shows a peak at almost the same temperature of the peak of the phonon thermal conductivity k_xy^ph which is estimated by k_xx at 15 T. These results indicate the presence of a dominant phonon thermal Hall k_xy^ph at 15 T. In addition to k_xy^ph, we find that the field dependence of k_xy at low fields turns out to be non-linear at low temperatures, concomitantly with the appearance of the field suppression of k_xx, indicating the presence of a spin thermal Hall k_xy^sp at low fields. Remarkably, by assembling the k_xx dependene of k_xy^sp data of other kagome antiferromagnets, we find that, whereas k_xy^sp stays a constant in the low-k_xx region, k_xy^sp starts to increase as k_xx does in the high-k_xx region. This k_xx dependence of k_xy^sp indicates the presence of both intrinsic and extrinsic mechanisms in the spin thermal Hall effect in kagome antiferromagnets. Furthermore, both k_xy^ph and k_xy^sp disappear in the antiferromagnetic ordered phase at low fields, showing that phonons alone do not exhibit the thermal Hall effect. A high field above ~7 T induces k_xy^ph, concomitantly with a field-induced increase of k_xx and the specific heat, suggesting a coupling of the phonons to the field-induced spin excitations as the origin of k_xy^ph.
A clear thermal Hall signal ($kappa_{xy}$) was observed in the spin liquid phase of the $S=1/2$ kagome antiferromagnet Ca kapellasite (CaCu$_3$(OH)$_6$Cl$_2cdot 0.6$H$_2$O). We found that $kappa_{xy}$ is well reproduced, both qualitatively and quanti
tatively, using the Schwinger-boson mean-field theory with the Dzyaloshinskii--Moriya interaction of $D/J sim 0.1$. In particular, $kappa_{xy}$ values of Ca kapellasite and those of another kagome antiferromagnet, volborthite, converge to one single curve in simulations modeled using Schwinger bosons, indicating a common temperature dependence of $kappa_{xy}$ for the spins of a kagome antiferromagnet.
