First-principles study of magnetic states and the anomalous Hall conductivity of $M$Nb${}_3$S${}_6$ ($M$=Co, Fe, Mn, and Ni)

Abstract

Inspired by the observation of the extremely large anomalous Hall effect in the absence of applied magnetic fields or uniform magnetization in CoNb${}_3$S${}_6$ [Nature Comm. 9, 3280 (2018); Phys. Rev. Research 2, 023051 (2020)], we perform a first-principles study of this and related compounds of the $M$Nb${}_3$S${}_6$ type with different transition metal $M$ ions to determine their magnetic orders and the anomalous Hall conductivity (AHC). 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 MnNb${}_3$S${}_6$ at low temperatures. The AHC in these materials with non-coplanar spin ordering can reach about $e^2/h$ 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 CoNb${}_3$S${}_6$ and suggest a possibility of similarly large anomalous Hall effects in related compounds.

arXiv comment9 pages, 6 figures

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