(M=Co, Fe, Mn, and Ni)*

Inspired by the observation of the extremely large anomalous Hall effect in the absence of applied magnetic fields or uniform magnetization in CoNb₃S₆^1,2, we performed first-principles study of this and related compounds of the MNb₃S₆-type with different transition metal M ions to determine their magnetic orders and the anomalous Hall conductivity (AHC)³. We find that non-coplanar antiferromagnetic ordering is favored relative to collinear or coplanar order in the case of M=Co, Fe and Ni, while ferromagnetic ordering is favored in MnNb₃S₆ at low temperatures.  The AHC in these materials with non-coplanar spin ordering can reach about e²/h per crystalline layer, while being negligible for coplanar and collinear cases. We also find that the AHC depends sensitively on doping and reaches a maximum for intermediate values of the local spin exchange potential between 0.3 and 0.8 eV. Our AHC results are consistent with the reported Hall measurements in CoNb₃S₆ and motivate the magnetic phase diagram study of a triangular lattice without inversion symmetry using an atomistic model calculation⁴.

 

[1] N. Ghimire et al, Nature Comm. 9, 3280 (2018).

[2] G. Tenasini et al., Phys. Rev. Research 2, 023051 (2020)

[3] H. Park, O. Heinonen, and I. Martin, arXiv:2110:03029

[4] O. Heinonen, R. A. Heinonen, and H. Park, arXiv:2109.13837