  In recent years there has been an intense search for room temperature
ferromagnetism in doped dilute semiconductors, which have many potentially
applications in spintronics and optoelectronics. We report here the unexpected
observation of significant room temperature ferromagnetism in a semiconductor
doped with nonmagnetic impurities, Cu-doped TiO$_2$ thin films grown by Pulsed
Laser Deposition. The magnetic moment, calculated from the magnetization
curves, resulted surprisingly large, about 1.5 $\mu_B$ per Cu atom. A large
magnetic moment was also obtained from ab initio calculations using the
supercell method for TiO$_2$ with Cu impurities, but only if an oxygen vacancy
in the nearest-neighbour shell of Cu was present. This result suggests that the
role of oxygen vacancies is crucial for the appearance of ferromagnetism. The
calculations also predict that Cu doping favours the formation of oxygen
vacancies.
