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To study how nitrogen contributes to perpendicular magnetocrystallineanisotropy (PMA) in the ferrimagnetic antiperovskite Mn$_4$N, we examined boththe fabrication of epitaxial Mn$_4$N films with various nitrogen contents andfirst-principles density-functional calculations. Saturation magnetization($M_{\rm s}$) peaks of 110 mT and uniaxial PMA energy densities ($K_{\rm u}$)of 0.1 MJ/m$^3$ were obtained for a N$_2$ gas flow ratio ($Q$) of $\sim 10 \%$during sputtering deposition, suggesting nearly single-phase crystalline$\epsilon$-Mn$_4$N. Segregation of $\alpha$-Mn and nitrogen-deficient Mn$_4$Ngrains was observed for $Q \approx 6\%$, which was responsible for a decreasein the $M_{\rm s}$ and $K_{\rm u}$. The first-principles calculations revealedthat the magnetic structure of Mn$_4$N showing PMA was "type-B" having acollinear structure, whose magnetic moments couple parallel within the c-planeand alternating along the c-direction. In addition, the $K_{\rm u}$ calculatedusing Mn$_{32}$N$_x$ supercells showed a strong dependence on nitrogendeficiency, in qualitative agreement with the experimental results. Thesecond-order perturbation analysis of $K_{\rm u}$ with respect to thespin-orbit interaction revealed that not only spin-conserving but alsospin-flip processes contribute significantly to the PMA in Mn$_4$N. We alsofound that both contributions decreased with increasing nitrogen deficiency,resulting in the reduction of $K_{\rm u}$. It was noted that the decrease inthe spin-flip contribution occurred at the Mn atoms in face-centered sites.This is one of the specific PMA characteristics we found forantiperovskite-type Mn$_4$N.

Contributions of magnetic structure and nitrogen to perpendicular magnetocrystalline anisotropy in antiperovskite $\epsilon$-Mn$_4$N