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Ferrimagnetic Mn$_4$N is a promising material for heat flux sensors based onthe anomalous Nernst effect (ANE) because of its sizable uniaxial magneticanisotropy ($K_{\rm u}$) and low saturation magnetization ($M_{\rm s}$). Weexperimentally and theoretically investigated the ANE and anomalous Hall effectin sputter-deposited Mn$_4$N films. It was revealed that the observed negativeanomalous Hall conductivity ($\sigma_{xy}$) could be explained by two differentcoexisting magnetic structures, that is, a dominant magnetic structure withhigh $K_{\rm u}$ contaminated by another structure with negligible $K_{\rm u}$owing to an imperfect degree of order of nitrogen. The observed transversethermoelectric power ($S_{\rm ANE}$) of $+0.5\, \mu{\rm V/K}$ at $300\, {\rmK}$ gave a transverse thermoelectric coefficient ($\alpha_{xy}$) of $+0.34\,{\rm A/(m \cdot K)}$, which was smaller than the value predicted fromfirst-principles calculation. The interpretation for $\alpha_{xy}$ based on thefirst-principles calculations led us to conclude that the realization of singlemagnetic structure with high $K_{\rm u}$ and optimal adjustment of the Fermilevel are promising approaches to enhance $S_{\rm ANE}$ in Mn$_4$N through thesign reversal of $\sigma_{xy}$ and the enlargement of $\alpha_{xy}$ up to atheoretical value of $1.77\, {\rm A/(m \cdot K)}$.

Anomalous Hall and Nernst effects in ferrimagnetic Mn$_4$N films: possible interpretation and prospect for enhancement