In recent experiments, high Curie temperatures Tc above room temperature were reported in ferromagnetic semiconductors Fe-doped GaSb and InSb, while low Tc between 20 K to 90 K were observed in some other semiconductors with the same crystal structure, including Fe-doped InAs and Mn-doped GaSb, InSb, and InAs. Here we study systematically the origin of high temperature ferromagnetism in Fe, Mn, Cr-doped GaSb, InSb, and InAs magnetic semiconductors by combining the methods of density functional theory and quantum Monte Carlo. In the diluted impurity limit, the calculations show that the impurities Fe, Mn, and Cr have similar magnetic correlations in the same semiconductors. Our results suggest that high (low) Tc obtained in these experiments mainly comes from high (low) impurity concentrations. In addition, our calculations predict the ferromagnetic semiconductors of Cr-doped InSb, InAs, and GaSb that may have possibly high Tc. Our results show that the origin of high Tc in (Ga,Fe)Sb and (In,Fe)Sb is not due to the carrier induced mechanism because Fe3+ does not introduce carriers.
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