Impurity-vacancy complexes and ferromagnetism in doped sesquioxides

Based on hybrid density-functional calculations, we propose that ferromagnetism in the prototypical bixbyite sesquioxide In$_2$O$_3$ doped with Cr is due to Cr-oxygen vacancy complexes, while isolated Cr cannot support carrier-mediated magnetic coupling. Our proposal is consistent with experimental facts such as the onset of ferromagnetism in O-lean conditions only, the low or vanishing net moment in unintentionally doped material, and its increase upon intentional doping.