  We study the electronic and magnetic states of as-grown and annealed
$M\text{Fe}_2\text{O}_4$(111)/$\text{Al}_2\text{O}_3$(111) ($M=\text{Co, Ni}$)
thin films with various thicknesses grown on Si(111) substrates with the
$\gamma$-$\text{Al}_2\text{O}_3$(111) buffer layers by using x-ray absorption
spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD), to investigate
magnetically dead layers in these films. Although the magnetically dead layers
in the as-grown samples are formed near the interface with the
$\text{Al}_2\text{O}_3$ buffer layer, we reveal that ferrimagnetic order is
partially recovered by post-deposition annealing at 973 K for 48 hours in air.
By analyzing the line shapes of the XAS and XMCD spectra, we conclude that, in
the dead layers, there are a significant number of vacancies at the $T_d$ sites
of the spinel structure, which may be the microscopic origin of the degraded
ferrimagnetic order in the $M\text{Fe}_2\text{O}_4$(111) thin films.
