Microscopic picture of Co clustering in ZnO

Density functional theory was applied to study the chemical and magnetic interactions between Co atoms doped in ZnO. It was found that the Co impurities tend to form nanoclusters and the interactions between these atoms are antiferromagnetic within the local spin-density approximation $\left(\text{LSDA}\right)+\text{Hubbard}$ $U$ approach. The extracted interatomic exchange parameters agree reasonably well with recent experimental results. We have analyzed and compared the electronic structure obtained using the LSDA and $\text{LSDA}+U$ approaches and found that the $\text{LSDA}+U$ gives the most reasonable result, highlighting the importance of short-ranged antiferromagnetic interactions due to superexchange.

Figure 1

(Color online) Schematic illustrations of the Co clusters in the ZnO matrix for various cluster sizes and configurations. Co, Zn, and O atoms are shown as blue (dark), turquoise light), and red (small gray) colored balls, respectively. The bond lengths calculated by $\text{LSDA}+U$ method are shown. Magnetic configurations are evident from the arrows connected with the Co atoms.

Figure 2

(Color online) Dependence of the exchange interactions on the structure and cluster size. Filled symbols correspond to $\text{LSDA}+U$ results and open symbols to LSDA results.

Figure 3

(Color online) Formation energy as a function of the size of Co cluster for the corresponding ground-state magnetic configurations.

Figure 4

(Color online) Calculated DOS for the Co monomer in the LSDA (a) and $\text{LSDA}+U$ (b) and for the Co tetramer in the LSDA (c) and $\text{LSDA}+U$ (d). The solid black (dark) line represents the total DOS, the blue shaded line stands for the $\text{Co}3d$ states, while the red (light) line is for the mediating $\text{O}2p$ states.

Figure 5

(Color online) Magnetization density of a Co monomer in a ZnO matrix, evaluated within the $\text{LSDA}+U$ for an energy interval of 0.2 eV below the Fermi level. Positive (negative) values of the magnetization density are represented in red (blue).

Figure 6

(Color online) Same as in Fig. 5 but for a Co tetramer evaluated for an energy interval of 0.7 eV below the Fermi level.