Thin films of ${\mathrm{Mn}}_4\mathrm{N}$ and related ternary metallic perovskites with perpendicular anisotropy are interesting for spintronics, but their magnetic structures differ from the triangular ferrimagnetism of the bulk. A temperature-independent anomalous Hall conductivity of $-90{\mathrm{\Omega }}^{–1}\mathrm{c}{\mathrm{m}}^{–1}$ was found in ${\mathrm{Mn}}_4\mathrm{N}$ films, in addition to the normal temperature-dependent contribution. Based on known spin structures of bulk ${\mathrm{Mn}}_{3}Z\mathrm{N}$ compounds and the distance dependence of the Mn-Mn exchange for first- and second-neighbor Mn-Mn pairs, we propose a topological noncollinear spin structure for the ${\mathrm{Mn}}_4\mathrm{N}$ films with perpendicular anisotropy. The Letter shows how a small change in symmetry of the spin structure can influence the magnetotransport properties of frustrated ferrimagnetic films.

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• Anomalous Hall effect
• Hall effect
• Magnetic interactions
• Magnetism
• Magnetotransport