  We fabricated two types of cobalt-ferrite (001) thin films, insulative
Fe-rich cobalt-ferrite CoxFe3-xO4+{\delta} (I-CFO) and conductive Fe-rich
cobalt-ferrite CoyFe3-yO4 (C-CFO), with perpendicular magnetic anisotropy (PMA)
on MgO (001) substrates. Although the stoichiometric cobalt-ferrite is known as
an insulating material, it is found that the conductivity of Fe-rich
cobalt-ferrites can be controlled by changing the source materials and
deposition conditions in the pulsed laser deposition technique. The I-CFO and
C-CFO films exhibit PMA through the in-plane lattice distortion. We
investigated the Fe-ion-specific valence states in both I-CFO and C-CFO films
by M\"ossbauer spectroscopy and X-ray magnetic circular dichroism, and found
that the difference in conductivity corresponds to the abundance ratio of Fe2+
state at the octahedral B-site (Oh) in the inverse spinel structure.
Furthermore, first-principles calculations reproduce the changes in the density
of states at the Fermi level depending on the cation vacancies at the B-site,
which explains the difference in the conductivity between I-CFO and C-CFO.
