Condensed Matter Seminars

We examine magnetic moments (e.g. Mn impuritiesin GaAs) coupled via the indirect exchange RKKY interaction. We obtain via Monte Carlo the T=0 phase diagram as a function of the Mn density n_{i} and the carrier concentration n_{c}. As evidenced by a diverging correlation length and the magnetic susceptibility, the boundary between the ferromagnetic (FM) and the paramagnetic (PM) phases represents a line of zero temperature critical points with behavior very similar to a percolation transition. In particular, the ferromagnetic clusters increase in size and ultimately coalesce to span the system as the phase boundary is approached from the PM side. We have found this "ferromagnetic percolation" behavior in a variety of disordered magnetic systems with competing interactions, including the Edwards-Anderson model. In the RKKY system, we find that in the dilute limit, bulk ferromagnetism vanishes for n_{c}/n_{i} > 0.1. We also examine the impact of a strong local antiferromagnetic superexchange coupling between magnetic impurities, and we discuss the impact of a finite mean free path, which we include as a damping factor in the RKKY range function.