  Spinel-type CoFe$_2$O$_4$ is a ferrimagnetic insulator with the N\'eel
temperature exceeding 790 K, and shows a strong cubic magnetocrystalline
anisotropy (MCA) in bulk materials. However, when a CoFe$_2$O$_4$ film is grown
on other materials, its magnetic properties are degraded so that so-called
magnetically dead layers are expected to be formed in the interfacial region.
We investigate how the magnetic anisotropy of CoFe$_2$O$_4$ is modified at the
interface of CoFe$_2$O$_4$/Al$_2$O$_3$ bilayers grown on Si(111) using x-ray
magnetic circular dichroism (XMCD). We find that the thinner CoFe$_2$O$_4$
films have significantly smaller MCA values than bulk materials. The reduction
of MCA is explained by the reduced number of Co$^{2+}$ ions at the $O_h$ site
reported by a previous study [Y. K. Wakabayashi $\textit{et al.}$, Phys. Rev. B
$\textbf{96}$, 104410 (2017)].
