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Complexity of quantum phases of matter is often understood by the underlyinggauge structures, as was recognized by the $\mathbb{Z}_2$ and U(1) gauge theorydescription of spin liquid in frustrated magnets. Anomalous Hall effect ofconducting electrons can intrisically arise from U(1) gauges expressing thespatial modulation of ferromagnetic moments or from SU(2) gauges representingthe spin-orbit coupling effect. Similarly, in insulating ferro andantiferromagnets, the magnon excitations can contribute to anomalous transportsby feeling the U(1) and SU(2) gauges arising from the features of orderedmoments or interactions. In this work, we report the emergent higher rank SU(3)gauge structure in the magnon transport based on the thermal conductivitymeasurements of MnSc$_2$S$_4$ in an applied field up to 14\,T. The thermal Hallcoefficient takes a substantial value when the material enters athree-sublattice antiferromagnetic skyrmion phase, which is confirmed by thelarge-scale spin wave theory. The excited magnons are dressed with SU(3) gaugefield, which is a mixture of three species of U(1) gauge fields originatingfrom the slowly varying magnetic moments on these sublattices.

Emergent SU(3) magnons and thermal Hall effect in the antiferromagnetic skyrmion lattice