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Abstract Complexity of quantum phases of matter is often understood theoretically by using gauge structures, as is recognized by the $${{\mathbb{Z}}}_{2}$$ Z 2 and U(1) gauge theory description of spin liquids in frustrated magnets. Anomalous Hall effect of conducting electrons can intrinsically arise from a U(1) gauge expressing the spatial modulation of ferromagnetic moments or from an SU(2) gauge representing the spin-orbit coupling effect. Similarly, in insulating ferro and antiferromagnets, the magnon contribution to anomalous transports is explained in terms of U(1) and SU(2) fluxes present in the ordered magnetic structure. Here, we report thermal Hall measurements of MnSc2S4 in an applied field up to 14 T, for which we consider an emergent higher rank SU(3) flux, controlling the magnon transport. The thermal Hall coefficient takes a substantial value when the material enters a three-sublattice antiferromagnetic skyrmion phase, which is in agreement with the linear spin-wave theory. In our description, magnons are dressed with SU(3) gauge field, which is a mixture of three species of U(1) gauge fields originating from the slowly varying magnetic moments on these sublattices.

We investigate both the longitudinal thermal conductivity (κ_{xx}) and the planar thermal Hall conductivity (κ_{xy}) in the Kitaev spin liquid candidate of the cobalt-based honeycomb antiferromagnet Na_{2}Co_{2}TeO_{6} in a magnetic field (B) applied along the a- and a^{*}-axes. A finite κ_{xy} is resolved for both field directions in the antiferromagnetic (AFM) phase below the Néel temperature of 27 K. The temperature dependence of κ_{xy}/T shows the emergence of topological bosonic excitations. In addition, the field dependence of κ_{xy} shows sign reversals at the critical fields in the AFM phase, suggesting the changes in the Chern number distribution of the topological magnons. Remarkably, a finite κ_{xy} is observed in B∥a^{*} between the first-order transition field in the AFM phase and the saturation field, which is prohibited in a disordered state by the two-fold rotation symmetry around the a^{*} axis of the honeycomb lattice, showing the presence of a magnetically ordered state that breaks the two-fold rotation symmetry. Our results demonstrate the presence of topological magnons in this compound in the whole field range below the saturation field.