Electronic structure, exchange interactions, and Curie temperature in diluted III-V magnetic semiconductors: (GaCr)As, (GaMn)As, (GaFe)As

We complete our earlier [Phys. Rev. B 66, 134435 (2002)] study of the electronic structure, exchange interactions, and Curie temperature in (GaMn)As and extend the study to two other diluted magnetic semiconductors (GaCr)As and (GaFe)As. Four concentrations of the $3d$ impurities are studied: 25, 12.5, 6.25, 3.125 %. (GaCr)As and (GaMn)As are found to possess a number of similar features. Both are semimetallic and ferromagnetic, with similar properties of the interatomic exchange interactions and the same scale of the Curie temperature. In both systems the presence of the charge carriers is crucial for establishing the ferromagnetic order. An important difference between two systems is in the character of the dependence on the variation of the number of carriers. The ferromagnetism in (GaMn)As is found to be very sensitive to the presence of the donor defects, such as ${\mathrm{As}}_{\mathrm{Ga}}$ antisites. On the other hand, the Curie temperature of (GaCr)As depends rather weakly on the presence of this type of defects but decreases strongly with decreasing number of electrons. We find the exchange interactions between $3d$ atoms that make a major contribution into the ferromagnetism of (GaCr)As and (GaMn)As and propose an exchange path responsible for these interactions. The properties of (GaFe)As are found to differ crucially from the properties of (GaCr)As and (GaMn)As. (GaFe)As does not show a trend to ferromagnetism and is not half-metallic that makes this system unsuitable for the use in spintronic semiconductor devices.