Topology analysis for anomalous Hall effect in the non-collinear antiferromagnetic states of Mn$_3\mathit{A}$N ($A$ = Ni, Cu, Zn, Ga, Ge, Pd, In, Sn, Ir, Pt)

Abstract: We investigate topological features of electronic structures which produce large anomalous Hall effect in the non-collinear antiferromagnetic metallic states of anti-perovskite manganese nitrides by first-principles calculations. We first predict the stable magnetic structures of these compounds to be non-collinear antiferromagnetic structures characterized by either $T_{1g}$ or $T_{2g}$ irreducible representation by evaluating the total energy for all of the magnetic structures classified according to the symmetry and multipole moments. The topology analysis is next performed for the Wannier tight-binding models obtained from the first-principles band structures. Our results reveal the small Berry curvature induced through the coupling between occupied and unoccupied states with the spin-orbit coupling, which is widely spread around the Fermi surface in the Brillouin zone, dominantly contributes after the $k$-space integration to the anomalous Hall conductivity, while the local divergent Berry curvature around Weyl points has a rather small contribution to the anomalous Hall conductivity.