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First principles investigation of magnetocrystalline anisotropy at the L2$_1$ Full Heusler|MgO interfaces and tunnel junctions

Magnetocrystalline anisotropy at Heusler alloy$|$MgO interfaces have been studied using first principles calculations. It is found that Co terminated Co$_{2}$FeAl$|$MgO interfaces show perpendicular magnetic anisotropy up to 1.31 mJ/m$^2$, while those with FeAl termination exhibit in-plane magnetic anisotropy. Atomic layer resolved analysis indicates that the origin of perpendicular magnetic anisotropy in Co$_{2}$FeAl$|$MgO interfaces can be attributed to the out-of-plane orbital contributions of interfacial Co atoms. At the same time, Co$_{2}$MnGe and Co$_{2}$MnSi interfaced with MgO tend to favor in-plane magnetic anisotropy for all terminations.