= Conduction-electron-mediated exchange
A localized <magnetic moment> can polarize a metal's <conduction electrons>, whose response changes the energy of a second moment. This indirect <exchange interaction> can be long ranged and oscillate in sign with separation because of the <Fermi surface>. In the three-dimensional isotropic free-electron asymptotic limit its range dependence is proportional to $\cos(2k_Fr)/r^3$, with coupling-dependent prefactor and sign convention. The original calculation for nuclear moments used their contact <hyperfine interaction> with conduction electrons; it was motivated by nuclear magnetic resonance line widths in metallic silver.<Indirect Exchange Coupling of Nuclear Magnetic Moments by Conduction Electrons by M. A. Ruderman and Charles Kittel>[1954 abstract and introduction: second-order hyperfine coupling, indirect spin interaction and broad natural-silver resonance lines]{ref}
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