The anomalous Hall effect in non-collinear antiferromagnetic Mn$_{3}$NiN thin films

We have studied the anomalous Hall effect (AHE) in strained thin films of the frustrated antiferromagnet Mn$_{3}$NiN. The AHE does not follow the conventional relationships with magnetization or longitudinal conductivity and is enhanced relative to that expected from the magnetization in the antiferromagnetic state below $T_{\mathrm{N}} = 260$\,K. This enhancement is consistent with origins from the non-collinear antiferromagnetic structure, as the latter is closely related to that found in Mn$_{3}$Ir and Mn$_{3}$Pt where a large AHE is induced by the Berry curvature. As the Berry phase induced AHE should scale with spin-orbit coupling, yet larger AHE may be found in other members of the chemically flexible Mn$_{3}A$N structure.