Effective Conduction-Electron-Local-Moment Exchange Interaction in Metals: Rare-Earth Interband Mixing

The effective diagonal-exchange parameter $J_{\mathrm{eff}}\mathrm{}\left(0\right)\mathrm{}$ which determines the exchange splitting of a metal's Fermi-surface conduction electrons, has been investigated with a model involving simple orthogonalized-plane-wave conduction-electron orbitals and rare-earth ion cores. The positive exchange integral and negative interband mixing contributions to $J_{\mathrm{eff}}\mathrm{}\left(0\right)\mathrm{}$ have been estimated for the rare earths as a function of nuclear charge $Z$. The results indicate that interband mixing may dominate, causing a net negative conduction-electron polarization, in agreement with a number of experiments. The interband mixing, and hence the sign of $J_{\mathrm{eff}}\mathrm{}\left(0\right)\mathrm{}$, is found to be very sensitive to conduction-electron character. The results also indicate that, for ions other than spherical Gd, the parameter $J_{\mathrm{eff}}\mathrm{}\left(0\right)\mathrm{}$ will vary strongly with conduction-electron k direction (with respect to the J of the rare-earth ion) and may even involve a variation in sign. Such anisotropies in $J_{\mathrm{eff}}\mathrm{}\left(0\right)\mathrm{}$ and the nondiagonal $J_{\mathrm{eff}}\mathrm{}\left(Q\right)\mathrm{}$ parameters should be a significant source of anisotropies in the Ruderman-Kittel-Kasuya-Yosida conduction-electron spin distribution.