The Crossover from Impurity to Valence Band in Diluted Magnetic Semiconductors: The Role of the Coulomb Attraction by Acceptor

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.