  Magnetic properties of Re substituting for the divalent Zn ions and impurity
pairs in wurtzite and zinc blende ZnO are analyzed by employing the Generalized
Gradient Approximation with the +U corrections. The +U term applied to d(Zn),
p(O), and d(Re) orbitals stabilizes spin polarization of Re. Re impurity
introduces a defect level located in the band gap, and Re2+ generates the local
spin 5/2 in both wurtzite and zinc blende structures. Magnetic coupling of
Re-Re pairs as a function of distance between the defects, their relative
orientation, and the charge state was calculated. All magnetic coupling between
impurities is antiferromagnetic and due to an intermediate O atom via strong
d(Re)-p(O) hybridization between Re and O states. The defect states and
magnetic moments come from d(Re) with a contribution of p(O) orbitals of the O
nearest neighbors of Re. The results show that the Re-doped wurtzite ZnO may be
a new type of magneto-optical materials with a great promise.
