Ferromagnetic transition temperature enhancement in (Ga,Mn)As semiconductors by carbon codoping

We present a theoretical study of (Ga,Mn)(As,C) diluted magnetic semiconductors with high C acceptor density that combines insights from phenomenological model and microscopic approaches. A tight-binding coherent-potential approximation is used to describe the electronic structure in the presence of ${\mathrm{Mn}}_{\mathrm{Ga}}$ and ${\mathrm{C}}_{\mathrm{As}}$ impurities. We find only a small effect of C on the distribution and coherence of electronic states close to the top of the valence band and on the coupling between Mn moments, even at doping levels of several per cent. These results justify applying the model of ferromagnetic Mn-Mn coupling mediated by itinerant holes in the valence band also to C doped samples. The increase of ferromagnetic transition temperature due to the presence of C acceptors is illustrated by calculations that use the $\mathbf{k}\cdot \mathbf{p}$ Kohn-Luttinger description of the GaAs valence band and assume systems where Mn local moment and itinerant hole densities can be varied independently.