  The crossover between an impurity band (IB) and a valence band (VB) regime as
a function of the magnetic impurity concentration in models for diluted
magnetic semiconductors (DMS) is studied systematically by taking into
consideration the Coulomb attraction between the carriers and the magnetic
impurities. The density of states and the ferromagnetic transition temperature
of a Spin-Fermion model applied to DMS are evaluated using Dynamical Mean-Field
Theory (DMFT) and Monte Carlo (MC) calculations. It is shown that the addition
of a square-well-like attractive potential can generate an IB at small enough
Mn doping $x$ for values of the $p-d$ exchange $J$ that are not strong enough
to generate one by themselves. We observe that the IB merges with the VB when
$x >= x_c$ where $x_c$ is a function of $J$ and the Coulomb attraction strength
$V$. Using MC calculations, we demonstrate that the range of the Coulomb
attraction plays an important role. While the on-site attraction, that has been
used in previous numerical simulations, effectively renormalizes $J$ for all
values of $x$, an unphysical result, a nearest-neighbor range attraction
renormalizes $J$ only at very low dopings, i.e., until the bound holes wave
functions start to overlap. Thus, our results indicate that the Coulomb
attraction can be neglected to study Mn doped GaSb, GaAs, and GaP in the
relevant doping regimes, but it should be included in the case of Mn doped GaN
that is expected to be in the IB regime.
