Spin-order dependent anomalous Hall effect and magneto-optical effect in noncollinear antiferromagnets Mn${}_{3}X$N ($X$ = Ga, Zn, Ag, and Ni)

Abstract

Noncollinear antiferromagnets (AFMs) have recently attracted a lot of attention owing to the potential emergence of exotic spin orders on geometrically frustrated lattices, which can be characterized by corresponding spin chiralities. By performing first-principles density functional calculations together with group-theory analysis and tight-binding modelling, here we systematically study the spin-order dependent anomalous Hall effect (AHE) and magneto-optical effect (MOE) in representative noncollinear AFMs Mn${}_{3}X$N ($X$ = Ga, Zn, Ag, and Ni). The symmetry-related tensor shape of the intrinsic anomalous Hall conductivity (IAHC) for different spin orders is determined by analyzing the relevant magnetic point groups. We show that while only the $xy$ component of the IAHC tensor is nonzero for right-handed spin chirality, all other elements, ${\sigma }_{xy}$, ${\sigma }_{yz}$, and ${\sigma }_{zx}$, are nonvanishing for a state with left-handed spin chirality owing to lowering of the symmetry. Our tight-binding arguments reveal that the magnitude of IAHC relies on the details of the band structure and that ${\sigma }_{xy}$ is periodically modulated as the spin rotates in-plane. The IAHC obtained from first principles is found to be rather large, e.g., it amounts to 359 S/cm in Mn${}_3$AgN. By extending our analysis to finite frequencies, we calculate the optical isotropy [${\sigma }_{xx}(\omega )\approx {\sigma }_{yy}(\omega )\approx {\sigma }_{zz}(\omega )$] and the magneto-optical anisotropy [${\sigma }_{xy}(\omega )\ne {\sigma }_{yz}(\omega )\ne {\sigma }_{zx}(\omega )$] of Mn${}_{3}X$N. We argue that the spin-order dependent AHE and MOE are indispensable in detecting complex spin structures in noncollinear AFMs.

arXiv comment13 pages, 7 figures

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