Chisa Hotta
The thermal Hall effect has previously been observed in noncentrosymmetric ferromagnets with Dzyaloshinskii-Moriya (DM) interactions or noncoplanar magnetic orderings. In these systems, bosonic excitations acquire a Peierls phase when hopping to neighboring sites, which fits the picture of a fictitious "magnetic field" or U(1) gauge field. In contrast, antiferromagnets were generally thought not to exhibit such effects, as these contributions typically cancel out.
In this work, we demonstrate that simple antiferromagnets can indeed host a thermal Hall effect, not by U(1) gauge field mechanism but by the higher-rank gauge fields. Indeed, in a two-sublattice bipartite antiferromagnet, the two species of magnons act as pseudo-spin degrees of freedom and their DM interaction resembles the spin-orbit coupling that mixes up and down electron spins in Rashba-Dresselhaus systems, described by SU(2) gauge fields [1]. In three-sublattice antiferromagnets, MnSc2S4 exhibiting skyrmions, thermal Hall effects can be understood in terms of SU(3) gauge fields [2].
We further show how the magnetic exchange interactions that cause such gauged boson excitations originate from the strongly correlated electrons with Rashba-spin orbit coupling described by the Hubbard model, where we find metallic skyrmions with topological bands and finite Chern numbers[3].
[2] H. Takeda, M. Kawano, et.al. Nature Comm. 15, 566(2024).
[3] R. Makuta and C. Hotta, Phys. Rev. Res. 6, 023133 (2024).