  We study the prospect of using magnetic nanoparticles for the diluted
magnetic seminconductors. The Ruderman-Kittel-Kasuya-Yosida formula is modified
by explicitly taking into account the role of charge carriers inside the
nanoparticles in addition to those in the medium. Calculations are done
analytically. The final form of the coupling between nanoparticles is similar
to the original formula except for additional phase terms which render a novel
oscillatory feature with respect to the particle size - an interesting analogy
to the same behavior when we vary their distance. This is to be contrasted to
the previous approach which did not include the inner carriers and only favored
a ferromagnetic coupling. The effect of inevitable deviations from a perfect
sphere is estimated by the Born approximation. Our derivations can be readily
generalized to finite temperatures.
