  We have investigated the orbital states of the orbital-glassy (short-range
orbital ordered) spinel vanadate Co$_{1.21}$V$_{1.79}$O$_{4}$ using x-ray
absorption spectroscopy (XAS), x-ray magnetic circular dichroism (XMCD), and
subsequent configuration-interaction cluster-model calculation. From the sign
of the XMCD spectra, it was found that the spin magnetic moment of the Co ion
is aligned parallel to the applied magnetic field and that of the V ion
anti-parallel to it, consistent with neutron scattering studies. It was
revealed that the excess Co ions at the octahedral site take the trivalent
low-spin state, and induce a random potential to the V sublattice. The orbital
magnetic moment of the V ion is small although finite, suggesting that the
ordered orbitals mainly consists of real-number orbitals.
