Enhancing $T_c$ in ferromagnetic semiconductors

We theoretically investigate disorder effects on the ferromagnetic transition (‘Curie’) temperature $T_c$ in dilute III${}_{1-x}$Mn${}_x$V magnetic semiconductors (e.g. Ga${}_{1-x}$Mn${}_x$As) where a small fraction ($x \approx 0.01-0.1$) of the cation atoms (e.g. Ga) are randomly replaced by the magnetic dopants (e.g. Mn), leading to long-range ferromagnetic ordering for $T<T_c$. We find that $T_c$ is a complicated function of at least eight different parameters including carrier density, magnetic dopant density, and carrier mean free path; nominally macroscopically similar samples could have substantially different Curie temperatures. We provide simple physically appealing prescriptions for enhancing $T_c$ in diluted magnetic semiconductors, and discuss the magnetic phase diagram in the system parameter space.