We study an effective low-energy Kondo model on the triangular lattice in which itinerant electrons occupy a valence pocket at $\mathrm{\Gamma }$ 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 noncoplanar 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 interpocket 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 ${\sigma }_{xy}=4e^2/h$. 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 $\mathrm{\Gamma }$ and $M$.

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• Anomalous Hall effect
• Quantum anomalous Hall effect
• Chiral magnets
• Classical spin models
• Kondo lattice model