Giant interfacial perpendicular magnetic anisotropy in Fe/CuIn$_{1-x}$Ga$_x$Se$_2$ beyond Fe/MgO.

We study interfacial magnetocrystalline anisotropies in various Fe/semiconductor heterostructures by means of first-principles calculations. We find that many of those systems show perpendicular magnetic anisotropy (PMA) with a positive value of the interfacial anisotropy constant $K_{\rm i}$. In particular, the Fe/CuInSe$_2$ interface has a large $K_{\rm i}$ of $\sim 2.3\,{\rm mJ/m^2}$, which is about 1.6 times larger than that of Fe/MgO known as a typical system with relatively large PMA. We also find that the values of $K_{\rm i}$ in almost all the systems studied in this work follow the well-known Bruno's relation, which indicates that minority-spin states around the Fermi level provide dominant contributions to the interfacial magnetocrystalline anisotropies. Detailed analyses of the local density of states and wave-vector-resolved anisotropy energy clarify that the large $K_{\rm i}$ in Fe/CuInSe$_2$ is attributed to the preferable $3d$-orbital configurations around the Fermi level in the minority-spin states of the interfacial Fe atoms. Moreover, we have shown that the locations of interfacial Se atoms are the key for such orbital configurations of the interfacial Fe atoms.