Magnetic anisotropy of strained MnGa alloys

MnGa is a promising candidate for Rare Earth free permanent magnet applications because it has a large magnetocrystalline anisotropy. We examine the variation of the magnetocrystalline anisotropy of these alloys as function of bi-axial in-plane strain using ab-initio electronic structure calculations. We employed force theorem to calculate the MAE$=$E(\textbar \textbar )-E($\bot )$ as difference of energies of the system with magnetization along and perpendicular to the easy axis. Using projector augmented wave method implemented in VASP we have calculated MAE in MnGa, Mn$_{3}$Ga and Mn$_{\mathrm{1+x}}$Ga$_{\mathrm{1-x}}$ alloys. We find that the MAE is 2.5MJ/m$^{3}$ (0.42meV/u.c.) and 0.12MJ/m$^{3}$ (0.07meV/u.c.) in unstrained MnGa and Mn$_{3}$Ga, respectively. MAE decreases if bi-axial strain is applied in MnGa. Thus, the anisotropy of this system can be affected by the strain. We also discuss the effect of Mn disorder on MAE in Mn$_{\mathrm{1+x}}$Ga$_{\mathrm{1-x}}$ alloys.