Phase diagram and critical behavior of the random ferromagnet Ga_{1-x}Mn_xN

Molecular beam epitaxy has been employed to obtain Ga1-xMnxN films with x up to 10% and Curie temperatures T_C up to 13 K. The magnitudes of T_C and their dependence on x, T_C(x) ~ x^m, where m = 2.2 +/- 0.2 are quantitatively described by a tight binding model of superexchange interactions and Monte Carlo simulations of T_C. 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 non-monotonic crossover in the values of the susceptibility critical exponent gamma_eff 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 Delta x = (0.2 +/- 0.1)%.