Local-moment-conduction-electron exchange coupling and RKKY spin densities in metals

The local-moment-conduction-electron exchange coupling J(k′k), important for all problems involving so-called s-d(s-f) exchange, has been assumed always to be either a constant or at best, a function only of Q(= |k′-k|). In this paper we extend our earlier work assuming J(Q) behavior¹ and examine, in some detail, the actual k′, k dependence of the exchange; these results are then applied to the spin densities obtained within lowest order Ruderman-Kittel-Kasuya-Yosida (RKKY) theory. The J (k′, k) were obtained using realistic local moment wave functions (Hartree-Fock 3d and 4f orbitals for Fe and Gd) and conduction electrons. Results, for Fe and Gd local moments, are reported and spin densities are compared for a range of assumed Fermi momentum (k_F) values (0.3<k_F<1.0). The spin density at a nuclear site in a metal differs from the bulk density behavior due to the penetration of the s shells in an ion core by the Bloch electrons and our calculations indicate this difference to be severe (a purely Q dependent correction² for this core penetration is found to be inadequate). Our results suggest that spin densities sampled at nuclear sites by NMR and Mössbauer measurements need not be correlated with the bulk behavior, determined by neutron diffraction.