Magnetoelastic anisotropy in Heusler-type Mn2−δCoGa1+δ films

Perpendicular magnetization is essential for high-density memory application using magnetic materials. High-spin polarization of conduction electrons is also required for realizing large electric signals from spin-dependent transport phenomena. The Heusler alloy is a well-known material class showing the half-metallic electronic structure. However, its cubic lattice nature favors in-plane magnetization and thus minimizes the perpendicular magnetic anisotropy (PMA), in general. This study focuses on an inverse-type Heusler alloy, ${\mathrm{Mn}}_{2\ensuremath{-}\ensuremath{\delta}}{\mathrm{CoGa}}_{1+\ensuremath{\delta}}$ (MCG), with a small off-stoichiometry ($\ensuremath{\delta}$), which is expected to be a half-metallic material. We observed a relatively large uniaxial magnetocrystalline anisotropy constant (${K}_{u}$) of the order of ${10}^{5}$ J/${\mathrm{m}}^{3}$ at room temperature in MCG films with a small tetragonal distortion of a few percent. A positive correlation was confirmed between the $c/a$ ratio of lattice constants and ${K}_{u}$. Imaging of magnetic domains using Kerr microscopy clearly demonstrated a change in the domain patterns along with ${K}_{u}$. X-ray magnetic circular dichroism (XMCD) was employed using a synchrotron radiation soft x-ray beam to get insight into the origin of PMA. Negligible angular variation of orbital magnetic moment ($\mathrm{\ensuremath{\Delta}}{m}_{\mathrm{orb}}$) evaluated using the XMCD spectra suggested a minor role of the so-called Bruno's term to ${K}_{u}$. Our first-principles calculation reasonably explained the small $\mathrm{\ensuremath{\Delta}}{m}_{\mathrm{orb}}$ and the positive correlation between the $c/a$ ratio and ${K}_{u}$. The origin of the magnetocrystalline anisotropy was discussed based on the second-order perturbation theory in terms of the spin-orbit coupling, claiming that the mixing of the occupied $\ensuremath{\uparrow}$- and the unoccupied $\ensuremath{\downarrow}$-spin states is responsible for the PMA of the MCG films.