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Based on hybrid density-functional calculations, we propose thatferromagnetism in the prototypical bixbyite sesquioxide In$_2$O$_3$ doped withCr is due to Cr-oxygen vacancy complexes, while isolated Cr cannot supportcarrier-mediated magnetic coupling. Our proposal is consistent withexperimental facts such as the onset of ferromagnetism in O-lean conditionsonly, the low or vanishing net moment in unintentionally doped material, andits increase upon intentional doping.

Impurity-vacancy complexes and ferromagnetism in doped sesquioxides