Contributions of magnetic structure and nitrogen to perpendicular magnetocrystalline anisotropy in antiperovskite $ϵ$-Mn${}_4$N

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