  We calculate the magnetic interactions between two nearest neighbor
substitutional magnetic ions (Co or Mn) in ZnO by means of density functional
theory and compare it with the available experimental data. Using the local
spin density approximation we find a coexistence of ferro- and
antiferromagnetic couplings for ZnO:Co, in contrast to experiment. For ZnO:Mn
both couplings are antiferromagnetic but deviate quantitatively from
measurement. That points to the necessity to account better for the strong
electron correlation at the transition ion site which we have done by applying
the LSDA+U method. We show that we have to distinguish two different nearest
neighbor exchange integrals for the two systems in question which are all
antiferromagnetic with values between -1.0 and -2.0 meV in reasonable agreement
with experiment.
