  We present a spectroscopic study of (Zn,Co)O layers grown by molecular beam
epitaxy on sapphire substrates. (Zn,Co)O is commonly considered as a promising
candidate for being a Diluted Magnetic Semiconductor ferromagnetic at room
temperature. We performed magneto-optical spectroscopy in the Faraday
configuration, by applying a magnetic field up to 11 T, at temperatures down to
1.5 K. For very dilute samples (less than 0.5% Co), the giant Zeeman splitting
of the A and B excitons is observed at low temperature. It is proportional to
the magnetization of isolated Co ions, as calculated using the anisotropy and
g-factor deduced from the spectroscopy of the d-d transitions. This
demonstrates the existence of spin-carrier coupling. Electron-hole exchange
within the exciton has a strong effect on the giant Zeeman splitting observed
on the excitons. From the effective spin-exciton coupling,
<N0(Alpha-Beta)>_X=0.4 eV, we estimate the difference of the exchange integrals
for free carriers, N0|Alpha-Beta|=0.8 eV. The magnetic circular dichroism
observed near the energy gap was found to be proportional to the paramagnetic
magnetization of anisotropic Co ions even for higher Co contents.
