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Extensive calculations based on density functional theory have been carried out to understand the origin of magnetism in undoped ZnO thin films as found in recent experiments. The observed magnetism is confirmed to be due to Zn, instead of O, vacancy. The main source of the magnetic moment, however, arises from the unpaired electrons at O sites surrounding the Zn vacancy with each nearest-neighbor O atom carrying a magnetic moment ranging from . Moreover, the study of vacancy-vacancy interactions indicates that in the ground state, the magnetic moments induced by Zn vacancies prefer to ferromagnetically couple with the antiferromagnetic state lying higher in energy. Since this is larger than the thermal energy at room temperature, the ferromagnetic state can be stable against thermal fluctuations. Calculations and discussions are also extended to ZnO nanowires that have …