This study reports the development of ferrimagnetic cubic Heusler compound ${\mathrm{Mn}}_{2}{\mathrm{Fe}}_{x}\mathrm{Ga}$ (MFG) thin films with large perpendicular magnetic anisotropy (PMA). By growing MFG on a Cr buffer layer, a cubic ${\mathrm{X}}_{\mathrm{a}}$ phase with a tetragonal distortion $c/a\ensuremath{\approx}1.04$ induced by the buffer layer was obtained in the range of $x=1.0--1.3$, leading to large PMA which exceeds $0.75\phantom{\rule{4pt}{0ex}}\mathrm{MJ}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}3}$ in stoichiometric ${\mathrm{Mn}}_{2}\mathrm{FeGa}$ $(x=1)$. Synchrotron M\"ossbauer spectroscopy revealed that these cubic MFG thin films show good chemical ordering close to the ${\mathrm{X}}_{\mathrm{a}}$-ordered state. First-principles calculations demonstrated that, in ${\mathrm{X}}_{\mathrm{a}}$-ordered cubic MFG, the characteristic electronic structure of Fe around the Fermi level causes a large uniaxial magnetocrystalline anisotropy under the tetragonal strain consistent with experiment. The half-metallic-like band structure of cubic MFG was also shown to be preserved under the strain. Cubic ${\mathrm{Mn}}_{2}\mathrm{FeGa}$ with its small saturation magnetization, large PMA, and possibility of being highly spin polarized make this material an ideal candidate for the development of magnetic random-access memory and other spintronic devices.
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