We formulate a theory of doped magnetic semiconductors such as ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ which have attracted recent attention for their possible use in spintronic applications. We solve the theory in the dynamical mean field approximation to find the magnetic transition temperature $T_c$ as a function of magnetic coupling strength $J$, carrier density $n$, and Mn density $x$. We find that $T_c$ is determined by a subtle interplay between carrier density and magnetic coupling.

• Received 22 June 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.227202