Karlo Penc
Topologically nontrivial band structures formed by magnetic excitations have gained considerable attention in the context of anisotropic magnets, where finite Dzyaloshinskii–Moriya interactions [1–3] or symmetric exchange anisotropies [4] endow magnons with complex hopping amplitudes generating finite Berry curvature. Noncoplanar magnetic textures can similarly provide emergent U(1) or SU(2) gauge fluxes, leading to anomalous magnon transport [5]. More recently, an even higher-rank SU(3) gauge structure was invoked to explain a magnon-based thermal Hall effect in an antiferromagnetic skyrmion lattice phase [6].
Motivated by these developments, we investigate the origin of finite Berry curvature and the magnon Hall effect in the triangular lattice, where the usual U(1) gauge mechanism arising from Dzyaloshinskii–Moriya interactions proves insufficient. We focus on an isotropic spin model with first- and second-neighbor Heisenberg couplings and ring exchange. Using variational approaches and exact diagonalization, we map out the phase diagram of this model, identify the noncoplanar phases, and discuss the magnon band topology and anomalous transport properties.
[1] H. Katsura et al., Physical Review Letters 104, 066403 (2010)[2] R. Shindou et al., Physical Review B 87, 174427 (2013)
[3] A. Mook et al., Physical Review B 89, 134409 (2014)
[4] P. A. McClarty et al., Physical Review B 98, 060404(R) (2018)
[5] M. Kawano and C. Hotta, Physical Review B 99, 054422 (2019)
[6] H. Takeda et al., Nature Communications volume 15, 566 (2024)