Damped Ruderman-Kittel-Kasuya-Yosida interaction among local magnetic moments in the impurity-band regime of doped semiconductors

We consider a highly doped semiconductor with a metallic impurity band at T=0 K. A small number of localized spins is assumed to exist as well, with a site concentration much smaller than that of the dopant impurities. The carriers in the impurity band are described in an independent-particle tight-binding approximation. The effective interaction among the localized spins is expressed in terms of the spin susceptibility of the impurity band, which is obtained in turn by Green-function perturbative techniques within an approximation due to Matsubara and Toyozawa, asymptotically valid at high concentration. The range function of the effective interaction shows a damped oscillatory Ruderman-Kittel-Kasuya-Yosida form, with a wavelength of the order of the average separation of dopant impurities. Exponential decay is a consequence of the disorder of the one-electron impurity potential. The results are relevant in connection with the low-temperature magnetic properties of heavily doped semiconductors and also for magnetic multilayers with such systems as separators.