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 $langle xz|ell_Z|yzrangle$, whereas it reduces negative contribution from $langle z^2|ell_X|yzrangle$ and $langle xy|ell_X|xz,yzrangle$.
Magnetism of FeRh (001) films strongly depends on film thickness and surface terminations. While magnetic ground state of bulk FeRh is G-type antiferromagnetism, the Rh-terminated films exhibit ferromagnetism with strong perpendicular MCA whose energ
y +2.1 meV/$Box$ is two orders of magnitude greater than 3$d$ magnetic metals, where $Box$ is area of two-dimensional unit cell. While Goodenough-Kanamori-Anderson rule on the superexchange interaction is crucial in determining the magnetic ground phases of FeRh bulk and thin films, the magnetic phases are results of interplay and competition between three mechanisms - the superexchange interaction, the Zener direct-interaction, and magnetic energy gain.
Dynamic second-order nonlinear susceptibilities, $chi^{(2)}(2omega,omega,omega)equiv chi^{(2)}(omega)$, are calculated here within a fully first-principles scheme for monolayered molybdenum dichalcogenides, $2H$-MoX$_2$ (X=S,Se,Te). The absolute valu
es of $chi^{(2)}(omega)$ across the three chalcogens critically depend on the band gap energies upon uniform strain, yielding the highest $chi^{(2)}(0)sim$ 140 pm/V for MoTe$_2$ in the static limit. Under this uniform in-plane stress, $2H$-MoX$_2$ can undergo direct-to-indirect transition of band gaps, which in turn substantially affects $chi^{(2)}(omega)$. The tunability of $chi^{(2)}(omega)$ by either compressive or tensile strain is demonstrated especially for two important experimental wavelengths, 1064 nm and 800 nm, where resonantly enhanced non-linear effects can be exploited: $chi^{(2)}$ of MoSe$_2$ and MoTe$_2$ approach $sim$800 pm/V with -2% strain at 1064 nm.
