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

Magnetoelastic anisotropy in Heusler-type Mn$_{2-\delta}$CoGa$_{1+\delta}$ films