Theory of perpendicular magnetocrystalline anisotropy in Fe/MgO (001)

The origin of large perpendicular magneto-crystalline anisotropy (PMCA) in Fe/MgO (001) is revealed by comparing Fe layers with and without the MgO. Although Fe-O $p$-$d$ hybridization is weakly present, it cannot be the main origin of the large PMCA as claimed in previous study. Instead, perfect epitaxy of Fe on the MgO is more important to achieve such large PMCA. As an evidence, we show that the surface layer in a clean free-standing Fe (001) dominantly contributes to $E_{MCA}$, while in the Fe/MgO, those by the surface and the interface Fe layers contribute almost equally. The presence of MgO does not change positive contribution from $\langle xz|\ell_Z|yz\rangle$, whereas it reduces negative contribution from $\langle z^2|\ell_X|yz\rangle$ and $\langle xy|\ell_X|xz,yz\rangle$.