the as-grown sample, there exist isolated Co ions and a small number of nanoclusters, which contribute to the Curie-Weiss paramagnetism and the weakly ferromagnetic antiferromag- netism, respectively. If the Co ions tend to aggregate in ZnO, thermal diffusion of Co ions by the annealing may lead the decrease of the number of isolated Co ions and the growth of the size of nanoclusters, suppressing the paramagnetic and ferromagnetic responses, respec- tively. Figure 7 shows schematic images of the Co-ion distribution in Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O. According to this picture, in the ferromagnetic hetero-epitaxial Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O thin film previously mea- sured by XMCD [17], there were possibly few paramagnetic isolated Co ions while there were smaller nanoclusters than the present homo-epitaxial films [see Fig. 7(c)]. Because the present homo-epitaxial films are expected to have higher crystal quality than the previous hetero-epitaxial ones, the nanocluster formation (or the aggregation of the Co ions) may be prevented compared to the hetero-epitaxial Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O film. Since the annealing suppresses the magnetization and the n is probably unchanged by the annealing, the suppression is attributed not to be originated from the mechanisms related to oxygen vacancy such as bound magnetic polaron [38] and donor impurity band exchange [39]. It should be noted that the model based on the spinodal decomposition cannot explain the carrier-related ferromagnetic properties of Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O such as the anomalous Hall effects [14, 15]. It is possible that there are two origins of ferromagnetism in Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O, that is, the formation of antiferromagnetic Co-rich wurtzite (Zn,Co)O nanoclusters and the electron carrier-mediated ferromagnetic interaction. In typical ferromagnetic DMS Ga$_{1}$$_{−}$$_{x}$Mn$_{x}$As, the origin of ferromagnetism is considered to be due to p - d exchange interaction for high carrier concentration and formation of bound magnetic polarons for low carrier concentra- tion. Considering that the value of M$_{s}$ of Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O ( < 2 µ$_{B}$ /Co) is smaller than the full moment of Co 2+ (3 µ$_{B}$ /Co), the antiferromagnetic interaction between neighboring Co ions and the carrier-mediated ferromagnetic interaction between distant Co ions may simultane- ously affect the magnetic properties of Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O. Based on the correlation between M$_{s}$ and n shown in Fig. 6, it is probable that in Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O, the spinodal decomposition is predominant in low n region ( n ≲ 10 19 cm − $^{3}$), while carrier-induced ferromagnetic interac- tion is predominant rather than the antiferromagnetic interaction in high n region ( n ≳ 10 19 cm − $^{3}$). It follows that electron carrier-induced ferromagnetism in Zn$_{1}$$_{−}$$_{x}$ Co$_{x}$O possibly needs a highly crystallized Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O thin film with high electron carrier concentration n ≳ 10 19 cm − $^{3}$. 10