  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.
