We develop a theory for two-dimensional diluted magnetic semiconductor systems (e.g., ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ layers) where the itinerant carriers mediating the ferromagnetic interaction between the impurity local moments, as well as the local moments themselves, are confined in a two-dimensional layer. The theory includes exact spatial disorder effects associated with the random local moment positions within a disordered RKKY lattice field theory description. We predict the ferromagnetic transition temperature ($T_c$) as well as the nature of the spontaneous magnetization. The theory includes disorder and finite carrier mean-free path effects as well as the important correction arising from the finite temperature RKKY interaction, finding a strong density dependence of $T_c$ in contrast to the simple virtual crystal approximation.

• Received 7 January 2005

DOI:https://doi.org/10.1103/PhysRevLett.95.037201