Exchange coupling and conduction-electron polarization in metals. II

The effect on the isotropic spin density of the (k,k) dependence of the exchange coupling J(k,k) between a localized magnetic moment and conduction electrons predicted by Ruderman-Kittel-Kasuya-Yosida (RKKY) theory is determined quantitatively. Spherical local moments are employed, viz., Gd(4f7) and Fe(3d5) (which are taken as representative of rare-earth and transition metal moments, respectively). The conduction bands are described by simple orthogonalized plane waves appropriate to a "free-electron" metal with k the wave vector of the incident electron and k that of the scattered electron. We find that a Q-dependent coupling (where Q|k-k) has some justification when dealing with a Gd local moment but has considerably less justification for Fe. Both the (k,k) and the Q-coupling schemes yield a "main" spindensity peak which is more diffuse than that yielded by coupling approximations traditionally applied to RKKY theory. Spin-density results were obtained which are appropriate to the outer reaches of a lattice site and to the nuclear site of either the local moment or neighboring atoms (these involve inclusion of core s terms in the spin density). These results suggest that spin distributions obtained by neutron diffraction and those inferred from hyperfine field measurements may differ significantly.