  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.
