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

TL;DR

This study investigates how nitrogen content and magnetic structure influence the perpendicular magnetocrystalline anisotropy in Mn4N antiperovskite films, combining experimental fabrication and first-principles calculations to reveal the underlying mechanisms.

Contribution

It provides new insights into the role of nitrogen deficiency and magnetic structure in determining PMA in Mn4N, supported by both experimental data and theoretical analysis.

Findings

Optimal nitrogen flow yields high $K_u$ and $M_s$ values.

Nitrogen deficiency reduces PMA and spin-flip contributions.

Magnetic structure is collinear 'type-B' with specific spin coupling.

Abstract

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 $\epsilon$-Mn$_4$N. Segregation of $\alpha$-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.