Localization of electronic eigenstates and spin waves in diluted magnetic semiconductors at low carrier densities

Using mean-field and random-phase approximations, we perform numerical simulations on finite-size systems to investigate the effects of disorder on the nature (localized or extended) of both electronic states and collective magnetic (spin-wave) excitations for a prototypical disordered system with both electronic (fermionic) and magnetic degrees of freedom. We use a simple impurity model appropriate for dilute magnetic semiconductors at low charge carrier concentrations, below and near the metal-insulator transition. In our model, the positional disorder of the magnetic dopants is taken into account at the outset. We find that enhanced disorder implies significant inhomogeneity in magnetic properties, leading to appearance of localized electron states as well as localized collective magnetic excitations. As a result, positional disorder of the dopants can significantly influence transport and magnetic properties in such materials at low dopant and carrier densities.