Recently, transport phenomena involving quantum quasiparticles other than electrons have attracted significant interest in both fundamental and applied sciences. A prominent example is the magnon, a magnetic quasiparticle that propagates through magnetic insulators and carries heat and spin without electric charge. Due to their charge neutrality, magnons do not experience the Lorentz force and typically do not exhibit transverse transport under an external magnetic field, i.e., the thermal Hall effect in conventional insulators. However, when certain conditions are satisfied in the spin interactions or magnetic structure of a material, an emergent gauge field—a fictitious magnetic field—can arise and induce a magnon thermal Hall effect. This phenomenon has been interpreted in terms of emergent $\mathrm{U}(1)$ gauge fields, which can give rise to a nonzero thermal Hall conduction in materials with corner-sharing lattice geometries such as kagome and pyrochlore lattices. In contrast, for edge-sharing lattices such as square or triangular lattices, a so-called “no-go theorem” predicts the strict cancellation of the Hall conduction due to the commutative nature of the $\mathrm{U}(1)$ gauge field. As a result, magnon thermal Hall effects in edge-sharing lattices have long been considered unlikely, with rare exceptions such as our previous work [1] done in the ferromagnetic skyrmion lattice in GaV₄Se₈.

In this study [2], we have demonstrated that the spinel compound MnSc₂S₄, in which Mn atoms form a diamond lattice (Fig. 1(a)), exhibits a magnon-induced thermal Hall effect. This material undergoes antiferromagnetic ordering below approximately 2.3 K and, under magnetic fields of about 4–6 T, enters a novel magnetic phase known as an antiferromagnetic skyrmion lattice (AFM-SkL) composed of three interpenetrating sublattices (Fig. 1(b)). Each sublattice hosts a ferromagnetic skyrmion lattice, and collectively they form a 120^∘ antiferromagnetic configuration. Thermal transport measurements reveal a sharp increase in the thermal Hall conductivity by magnons within the AFM-SkL phase region, ollowed by a gradual decrease while retaining a positive value above 8 T (Fig. 2).

This experimental result goes beyond conventional understanding based on $\mathrm{U}(1)$ gauge fields, which cannot account for a finite Hall conductivity in edge-sharing lattices. Theoretical analysis based on the spin texture of the AFM-SkL reveals that an emergent $\mathrm{SU}(3)$ gauge field arises from the system. The three $\mathrm{U}(1)$ gauge fields associated with each sublattice couple via off-diagonal spin interactions and form a non-Abelian $\mathrm{SU}(3)$ gauge structure. The non-commutativity of $\mathrm{SU}(3)$ enables a net emergent magnetic flux that does not cancel out, allowing a finite magnon thermal Hall effect even in edge-sharing lattices. This work presents the first experimental signature of an emergent $\mathrm{SU}(3)$ gauge field in a solid-state system and highlights how the topological nature of magnetic order can fundamentally alter magnon transport, paving the way for new functional properties in quantum magnetic materials.

References

• [1] M. Akazawa et al., Phys. Rev. Research 4, 043085 (2022).
• [2] H. Takeda et al., Nature Commun. 15, 566 (2024).

Authors

• H. Takeda, M. Kawano^a, K. Tamura, M. Akazawa, J. Yan, T. Waki^b, H. Nakamura^b, K. Sato^c, Y. Narumi^c, M. Hagiwara^c, M. Yamashita, and C. Hotta^d
• ^aDepartment of Physics, Technical University of Munich
• ^bDepartment of Materials Science and Engineering, Kyoto University
• ^cCenter for Advanced High Magnetic Field Science, Graduate School of Science, Osaka University
• ^dDepartment of Basic Science, University of Tokyo