Enhancement of Interactions Between Magnetic Ions in Semiconductors Due to Declustering

It is often assumed that the exchange interaction between two magnetic ions in a semiconductor host depends only on the distance and orientation of the magnetic ions. Using first-principles electronic structure calculations of Mn impurities in GaAs, we show that the exchange interaction between two magnetic ions depends also on the concentration and spatial arrangement of the other, "spectator" magnetic ions. Thus, such systems cannot be described by a Heisenberg Hamiltonian with fixed exchange interactions. Specifically, we find that at fixed Mn concentration, association ("clustering") of Mn impurities leads to a decrease of the Curie temperature, while dissociation ("declustering") leads to higher Curie temperatures. We conclude that clustering is the major impediment to achieve high Curie temperatures in Mn-doped GaAs.