in reducing atmosphere such as in high vacuum, which may produce oxygen vacancies, have been reported to enhance the ferromagnetism, while annealing in oxidizing atmosphere such as air decreases the magnetic moments of Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O [23–26]. In addition, we note that ferromagnetism has been reported in some oxide thin films without magnetic ions [27–29], probably due to defects such as oxygen vacancies. It is therefore important to investigate annealing effects and/or the role of oxygen vacancies for the understanding of the ferromagnetism in Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O. 

In the present work, we report on the results of H - and T -dependent XMCD measure- ments on homo-epitaxial Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O thin films which show coexisting paramagnetic and ferromagnetic properties. Analysis using the Curie-Weiss law suggests that antiferromag- netic correlation between the Co ions suppress the paramagnetic behavior. We have also found that the XMCD intensity decreases by high-vacuum annealing. Based on the exper- imental findings, a possible origin of the ferromagnetism in the Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O thin films shall be discussed. 

## EXPERIMENTAL 

Zn$_{1}$$_{−}$$_{x}$Co$_{x}$O thin films were homo-epitaxially grown on Zn-terminated ZnO(0001) sub- strates by the pulsed laser deposition technique with varying oxygen pressure ( P$_{O2}$ ) from 1 × 10 − 4 to 10 − 2 Pa. Four thin films were prepared: a x =0.07 film deposited at P$_{O2}$ =10 − 4 Pa, and x =0.10 films deposited at P$_{O2}$ =10 − $^{2}$, 10 − $^{3}$, and 10 − 4 Pa. During the deposition, the substrate temperature was kept at 400 $^{◦}$C. The thickness of each film was 50 − 150 nm. X-ray diffraction confirmed that the thin films had the wurtzite structure and no secondary phase was observed. The magnetization of those thin films was measured using a supercon- ducting quantum interference device (SQUID) magnetometer (Quantum Design, Co. Ltd). The present homo-epitaxial films are expected to have higher crystal quality [16] than the hetero-epitaxial one studied in the previous XMCD measurements [17]. However, the homo- epitaxial thin films have lower M$_{s}$ than the hetero-epitaxial ones because of the high P$_{O2}$ values [16]. 

X-ray absorption spectroscopy (XAS) and XMCD measurements were performed at the helical undulator beam line BL23SU of SPring-8 [30, 31]. The monochromator resolution was E/ Δ E> 10 , 000. Absorption spectra of right-handed ( µ $^{+}$) and left-handed ( µ $^{−}$) circularly 

