Spin-order dependent anomalous Hall effect and magneto-optical effect in the noncollinear antiferromagnets Mn3X N with X=Ga, Zn, Ag, or Ni

The anomalous Hall effect (AHE) and the magneto-optical effect (MOE) are two prominent manifestations of time-reversal symmetry breaking in magnetic materials. 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 modeling, here we systematically study the spin-order dependent AHE and MOE in representative noncollinear AFMs Mn3XN(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 - σxy,σyz, and σzx - 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 σxy 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 Mn3AgN, which is comparable to other well-known noncollinear AFMs such as Mn3Ir and Mn3Ge. We evaluate also the magnetic anisotropy energy and find that the evolution of spin order is related to the number of valence electrons in the X ion. Interestingly, the left-handed spin chirality could exist in Mn3XN with some particular spin configurations. By extending our analysis to finite frequencies, we calculate the optical isotropy [σxx(ω)≈σyy(ω)≈σzz(ω)] and the magneto-optical anisotropy [σxy(ω)≠σyz(ω)≠σzx(ω)] of Mn3XN. Similar to the IAHC, the magneto-optical Kerr and Faraday spectra depend strongly on the spin order. The Kerr rotation angles in Mn3XN are in the range of 0.3 ∼0.4 , which is large and comparable to other noncollinear AFMs like Mn3Pt and Mn3Sn. Our finding of large AHE and MOE in Mn3XN suggests that these materials present an excellent antiferromagnetic platform for realizing novel spintronics and magneto-optical devices. We argue that the spin-order dependent AHE and MOE are indispensable in detecting complex spin structures in noncollinear AFMs.