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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 ($M_{\rm s}$) 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 $ε$-Mn$_4$N. Segregation of $α$-Mn and nitrogen-deficient Mn$_4$N grains was observed for $Q \approx 6\%$, which was responsible for a decrease in the $M_{\rm s}$ and $K_{\rm u}$. 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 $K_{\rm u}$ 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 $K_{\rm u}$ 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 $K_{\rm u}$. 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.