Molecular beam epitaxy has been employed to obtain Ga1−xMnxN films with x up to 10% and Curie temperatures TC up to 13 K. The magnitudes of TC and their dependence on x, TC(x)∝xm, where m=2.2±0.2, are quantitatively described by a tight-binding model of superexchange interactions and Monte Carlo simulations of TC. The critical behavior of this dilute magnetic insulator shows strong deviations from the magnetically clean case (x=1), in particular, (i) an apparent breakdown of the Harris criterion, (ii) a nonmonotonic crossover in the values of the susceptibility critical exponent γeff between the high temperature and critical regimes, and (iii) a smearing of the critical region, which can be explained either by the Griffiths effects or by macroscopic inhomogeneities in the spin distribution with a variance Δx=(0.2±0.1)%.

We introduce a theoretical model to scrutinize the conductivity of small polarons in 1D disordered systems, focusing on two crucial – as will be demonstrated – factors: the density of states and the spatial extent of the electronic wave function. The investigation is performed for any temperature up to 300 K and under electric field of arbitrary strength up to the polaron dissociation limit. To accomplish this task, we combine analytical work with numerical calculations.