  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.
