Orbital and spin polarizations of conduction electrons in rare-earth intermetallic compounds. Theory

Recent experiments on rare-earth intermetallic compounds have given us data on the contribution from conduction electrons to the magnetization and hyperfine fields at rare-earth nuclei. Analyses based on isotropic bilinear exchange interactions between the $4f$ and conduction electrons have not been able to explain the systematic variation of these contributions across the rare-earth series. To explain these variations it is necessary to take into account the full $4f$ conduction-electron exchange interaction (higher-rank couplings) and the crystallographic symmetry at the rare-earth sites. In some cases, it is necessary to include the spin-orbit coupling of the conduction electrons. The conduction electrons in the rare-earth intermetallic compounds of interest are primarily of $5d$ and $6s$ character. In this paper we derive expressions for the orbital and spin polarizations of these conduction electrons and their contribution to the hyperfine field and magnetization. We take full account of the site symmetry, which is cubic for the compounds of interest, and the complete $4f-5d$ conduction-electron interaction.