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.
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