## CONCLUSION 

We have performed XMCD measurements on homo-epitaxial Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O thin films which were prepared with various relatively high oxygen pressures and showed both ferromagnetic and paramagnetic behaviors. The line shapes of the Co 2 p XAS and XMCD spectra are the same in all the samples, and indicate that the Co ions substitute for the Zn sites. The H and T dependences of Co 2 p XMCD suggest that paramagnetic behavior is dominant in the samples. Analyses using the Curie-Weiss law have revealed that the Curie constant of the samples are close to the value of Co 2+ and the Weiss temperature are negative, indicat- ing that the paramagnetic Co 2+ ions interact antiferromagnetically with each other. The saturation magnetizations estimated using the XMCD sum rules were almost the same as the magnetization measurements, suggesting that the ferromagnetic responses of the thin films are predominantly caused by magnetic moment of the doped Co ions and confirm- ing that we have probed the bulk magnetic properties. The paramagnetic susceptibility and saturation magnetization decreased by high-vacuum annealing. The suppression of the paramagnetism by annealing can be explained by thermal diffusion and aggregation of Co ions leading to spinodal decomposition and the antiferromagnetic interaction between the Co ions. Therefore, we propose that the formation of Co-rich nanoclusters coexists and/or competes with carrier-mediated ferromagnetic interaction in Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O depending on elec- tron carrier concentration. Further systematic XMCD measurements on Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O with controlled electron-carrier and/or oxygen-vacancy concentrations will provide us with un- derstandings of the carrier-induced ferromagnetism in Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O. 

## Acknowledgments 

This work was supported by a Grant-in-Aid for Scientific Research in Priority Area “Creation and Control of Spin Current” (19048012) from MEXT, Japan. MK acknowledges support from the Japan Society for the Promotion of Science for Young Scientists. 

∗ Present address: Department of Applied Chemistry, School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan 

