Exchange coupling and conduction-electron polarization in metals

The exchange-coupling integral, J(k, k′), between localized magnetic electrons and conduction electrons, treated as orthogonalized plane waves is investigated quantitatively for the case of a local moment which consists of the half-filled 4f7 shell of Gd3+ and for a range of k and k' values (the incident and scattered conduction-electron wave vectors). Ruderman-Kittel-Kasuya-Yosida (RKKY) theory is then employed, with and without an exchange-enhanced susceptibility, to obtain conduction-electron spin densities. For the special case of the rare-earth local moment, J(k, k′) is found to be well approximated by J(Q) [where Q‰|k-k′|] but with a Q dependence which differs markedly from those traditionally assumed in RKKY theory. This severely affects spin-density predictions for a region extending several lattice sites away from the local-moment site. Use of the computed exchange coupling reduces the qualitative disagreement between theory and experiment.