Based on a previously reported double-resonance mechanism, we present an analytical expression of the effective exchange interaction between impurity moments of transition-metal elements introduced in semiconductors. It is shown that the exchange interaction is enhanced by several orders of magnitude as compared with the ordinary RKKY interaction when the Fermi level and impurity states are close to the top of the valence band. Although the interaction is found to decay exponentially, the magnitude is large even when the distance between two impurities is several times as long as the lattice constant. The concentration dependence of the Curie temperature is calculated by using a percolation theory, and the calculated results are compared with the experimental findings.

• Received 26 July 2002

DOI:https://doi.org/10.1103/PhysRevB.67.125302