We calculate the nature of magnetic interactions in transition-metal doped ZnO using the local spin density approximation and (LSDA) the $\mathrm{LSDA}+U$ (Coulomb interaction) method of density functional theory. We investigate the following four cases: (i) single-transition-metal-ion types (Cr, Mn, Fe, Co, Ni and Cu) substituted at Zn sites, (ii) substitutional magnetic transition-metal ions combined with additional Cu and Li dopants, (iii) substitutional magnetic transition-metal ions combined with oxygen vacancies, and (iv) pairs of magnetic ion types (Co and Fe, Co and Mn). Extensive convergence tests indicate that the calculated magnetic ground state is unusually sensitive to the $k$-point mesh and energy cutoff, the details of the geometry optimizations, and the choice of the exchange-correlation functional. We find that ferromagnetic coupling is sometimes favorable for single-type substitutional transition-metal ions within the LSDA. However, the nature of magnetic interactions changes when correlations on the transition-metal ion are treated within the more realistic $\mathrm{LSDA}+U$ method, often disfavoring the ferromagnetic state. The magnetic configuration is sensitive to the detailed arrangement of the ions and the amount of lattice relaxation, except in the case of oxygen vacancies when an antiferromagnetic state is always favored.

• Received 28 May 2006

DOI:https://doi.org/10.1103/PhysRevB.74.094418