Anionic nickel and nitrogen effects in the chiral antiferromagnetic antiperovskite Mn$_3$NiN

Magnetic antiperovskites, holding chiral noncollinear antiferromagnetic ordering, have shown remarkable properties that cover from negative thermal expansion to anomalous Hall effect. Nevertheless, details on the electronic structure related to the oxidation states and the octahedral center's site effect are still scarce. Here, we show a theoretical study, based on first-principles calculations in the framework of the density-functional theory, DFT, on the electronic details associated with the nitrogen site effect into the structural, electronic, magnetic, and topological degrees of freedom. Thus, we show that the nitrogen-vacancy increases the values of the anomalous Hall conductivity and retains the chiral $\Gamma_{4g}$ antiferromagnetic ordering. Moreover, we reveal, based on the Bader charges and the electronic structure analysis, the negative and positive oxidation states in the Ni and Mn sites, respectively. The latter is in agreement with the expected $A_3^{\alpha+}B^{\beta-}X^{\delta-}$ oxidation states to satisfy the charge neutrality in the antiperovskites, but rare for transition metals. Finally, we extrapolate our findings on the oxidation states to several Mn$_3B$N compounds showing that the antiperovskite structure is an ideal platform to encounter negative oxidation states in metals sitting at the corner $B$-site.