First-principles investigation of the very large perpendicular magnetic anisotropy at Fe | MgO and Co | MgO interfaces

The perpendicular magnetic anisotropy (PMA) arising at the interface between ferromagnetic transition metals and metallic oxides was investigated via first-principles calculations. In this work very large values of PMA, up to 3 erg/cm${}^{2}$, at Fe$|$MgO interfaces are reported, in agreement with recent experiments. The origin of PMA is attributed to overlap between O-${p}_{z}$ and transition metal ${d}_{{z}^{2}}$ orbitals hybridized with ${d}_{xz(yz)}$ orbitals with stronger spin-orbit coupling-induced splitting around the Fermi level for perpendicular magnetization orientation. Furthermore, it is shown that the PMA value weakens in the case of over- or underoxidation due to the fact that oxygen ${p}_{z}$ and transition metal ${d}_{{z}^{2}}$ orbital overlap is strongly affected by disorder, in agreement with experimental observations in magnetic tunnel junctions.