Magnetic ground states of a model for (TM)Nb${}_3$S${}_6$, TM=Co, Fe, Ni

The transition-metal intercalated dichalcogenide CoNb${}_3$S${}_6$ is a triangular antiferromagnet that has recently been shown to exhibit a large anomalous Hall effect (AHE) below the N'eel temperature, even though the response to an external field is very small. This suggests that there is an interesting magnetic structure that interacts with the electronic structure to yield the AHE, as collinear antiferromagnets cannot exhibit a nonzero AHE. We propose a model for magnetic transition-metal intercalated dichalcogenides and examine its ground state as function of interaction parameters. The model exhibits transitions between planar spin spirals, non-planar spin spirals, and a particular non-coplanar so-called $3q$ state. This latter state must exhibit a nonzero AHE, while the spin spirals do not.