Contributions of magnetic structure and nitrogen to perpendicular magnetocrystalline anisotropy in antiperovskite <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ɛ</mml:mi><mml:mtext>−</mml:mtext><mml:mi mathvariant="normal">M</mml:mi><mml:msub><mml:mi mathvariant="normal">n</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mi mathvariant="normal">N</mml:mi></mml:mrow></mml:math>
Shinji Isogami, Keisuke Masuda, Yoshio Miura
Abstract
To study how nitrogen contributes to perpendicular magnetocrystalline anisotropy (PMA) in the ferrimagnetic antiperovskite $\mathrm{M}{\mathrm{n}}_{4}\mathrm{N}$, we examined both the fabrication of epitaxial $\mathrm{M}{\mathrm{n}}_{4}\mathrm{N}$ 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 $0.1\phantom{\rule{0.16em}{0ex}}\mathrm{MJ}/{\mathrm{m}}^{3}$ were obtained for a ${\mathrm{N}}_{2}$ gas flow ratio ($Q$) of \ensuremath{\sim}10% during sputtering deposition, suggesting nearly single-phase crystalline $\ensuremath{\varepsilon}\text{\ensuremath{-}}\mathrm{M}{\mathrm{n}}_{4}\mathrm{N}$. Segregation of \ensuremath{\alpha}-Mn and nitrogen-deficient $\mathrm{M}{\mathrm{n}}_{4}\mathrm{N}$ grains were observed for $Q\ensuremath{\approx}6%$, and were responsible for a decrease in the ${M}_{\mathrm{s}}$ and ${K}_{\mathrm{u}}$. The first-principles calculations revealed that the magnetic structure of $\mathrm{M}{\mathrm{n}}_{4}\mathrm{N}$ 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 $\mathrm{M}{\mathrm{n}}_{32}{\mathrm{N}}_{x}$ 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 $\mathrm{M}{\mathrm{n}}_{4}\mathrm{N}$. 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 $\mathrm{M}{\mathrm{n}}_{4}\mathrm{N}$.