Abstract
An indirect spin-spin interaction via the intermediary of conduction electrons is investigated by the Green's functions method. The conduction electrons are considered as a gas of interacting electrons with an explicitly spin independent potential whose Fourier transform is a constant in momentum space. An asymptotic form of the spin-spin interaction for large distances is given for both a polarized and unpolarized electron gas. In the case of the polarized system the dependence on the distance has the same form as the Suhl-Nakamura spin-spin interaction via spin waves in ferromagnets. However, the behavior of the screening radius as a function of the magnetization is completely different and this interaction is more long range. In the unpolarized case our result in the limit of the non-interacting electron gas becomes the Ruderman-Kittel formula as it should be.
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