  We present a detailed study of the electronic and magnetic interactions of
Ba2CoO4, structurally very uncommon because of the isolated CoO4 distorted
tetrahedral coordination. We show the presence of Co(d)-O(p) hybridized states
characterized by spin polarized oxygen atoms, with their magnetic moments
parallel to that on Co. The calculated isotropic exchange interaction
parameters, which include the contributions from ligand spins, demonstrate the
presence of a 3D network of magnetic couplings, that are partially frustrated
in the identified magnetic ground state. Our results indicate that the dominant
indirect exchange mechanism responsible for this ground state is mediated by O
atoms along the Co-O...O-Co path.
