Ruderman-Kittel-Kasuya-Yosida interaction in disordered metals

The spin polarization in the vicinity of a magnetic impurity [the origin of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two spins] is calculated for small mean free paths of the conduction electrons in $d$ dimensions in terms of a quantum-interference effect. It is found that at zero temperature the polarization depends on the distance as $\frac{1}{r^d}$. It is strongly enhanced in thin films. At finite temperature its range is limited to the thermal diffusion length. A magnetic or electric field changes the local polarization and may reverse the sign of the RKKY interaction.