Here we present a study of magnetism in \CTO\ anatase films grown by pulsedlaser deposition under a variety of oxygen partial pressures and depositionrates. Energy-dispersive spectrometry and transition electron microscopyanalyses indicate that a high deposition rate leads to a homogeneousmicrostructure, while very low rate or postannealing results in cobaltclustering. Depth resolved low-energy muon spin rotation experiments show thatfilms grown at a low oxygen partial pressure ($\approx 10^{-6}$ torr) with auniform structure are fully magnetic, indicating intrinsic ferromagnetism.First principles calculations identify the beneficial role of low oxygenpartial pressure in the realization of uniform carrier-mediated ferromagnetism.This work demonstrates that Co:TiO$_2$ is an intrinsic diluted magneticsemiconductor.
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