Theoretical study of the magnetism of Mn-doped ZnO with and without defects

We calculate the exchange interaction parameters of a classical Heisenberg Hamiltonian for Mn-doped ZnO (Mn concentration between 5% and 20%) by an ab initio Korringa-Kohn-Rostoker coherent-potential-approximation method in the framework of density functional theory. A weak antiferromagnetic exchange interaction is observed in pure Mn-doped ZnO in the dilute limit with an increase in the strength of interactions with increasing concentration of Mn. In the presence of donor defects, such as oxygen vacancies and interstitial Zn, the interactions remain antiferromagnetic, whereas in case of acceptor defects like Zn vacancies and N substitution of O, ferromagnetic interactions are observed. Due to the short-ranged character of interactions and disorder effects, the Curie temperatures calculated from Monte Carlo simulations yield low values (similar to 45 K). However, in a few combinations of Mn and defect concentrations, the calculated Curie temperature can be as high as 135 K. If clustering of Mn atoms on a zinc-blende lattice is taken into account, the Mn-Mn spin correlations within a cluster are found to persist up to 600 K. Finally, we have shown that a modified mean-field theory, which we refer to as the "average mean field" estimate, yields values of the ordering temperature that are in good agreement with Monte Carlo simulations.