Chiral Magnetism and Quantum Anomalous Hall Effect in a Low-energy Kondo Model on the Triangular Lattice

Abstract

We study an effective low-energy Kondo model on the triangular lattice in which itinerant electrons occupy a valence pocket at $\Gamma$ and three conduction pockets at the $M$ points of the Brillouin zone. This construction has a Fermi-surface nesting structure that favors triple-$Q$ magnetic order while only assuming the low-energy band-structure. Treating the local moments as classical spins on a four-sublattice magnetic unit cell, we find extended regions of non-coplanar order, including tetrahedral and related canted tetrahedral states, in addition to ferromagnetic and coplanar phases. The chiral phases remain stable over a broad range of inter-pocket Kondo couplings and persist in the presence of an external magnetic field. For certain chiral orders, the electronic bands can become gapped and host a quantum anomalous Hall state with $\sigma_{xy}=4\,e^2/h$. These results show that chiral magnetism and a quantized anomalous Hall effect on the triangular lattice do not rely on a specific tight-binding band structure, but can arise more generally from low-energy nested pockets at $\Gamma$ and $M$.