Complexity of quantum phases of matter is often understood theoretically by using gauge structures, as is recognized by the \({{\mathbb{Z}}}_{2}\) 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.

物质量子相的复杂性通常通过使用规范结构从理论上理解，正如 \（{{\mathbb{Z}}}_{2}\） 和 U（1） 规范理论对受挫磁体中自旋液体的描述所认识到的那样。导电电子的反常霍尔效应本质上可以来自表示铁磁矩空间调制的 U（1） 规范，也可以来自表示自旋轨道耦合效应的 SU（2） 规范。同样，在绝缘铁磁体和反铁磁体中，磁振子对异常输运的贡献可以用有序磁结构中存在的 U（1） 和 Su（2） 磁通量来解释。在这里，我们报告了 MnSc₂S₄ 在高达 14 T 的外加场中的热霍尔测量值，为此我们考虑了一个新兴的更高等级的 SU（3） 磁通量，控制磁振子传输。当材料进入三子晶格反铁磁斯格明子相时，热霍尔系数具有相当大的值，这与线性自旋波理论一致。在我们的描述中，磁振子带有 SU（3） 规范场，它是三种 U（1） 规范场的混合物，这些场起源于这些子晶格上缓慢变化的磁矩。