g-Shift and Anomalous Hall Effect in Gadolinium Metals

It is shown that the coupling between spins of conduction and localized electrons due to a covalent mixing between them can be expressed by a usual exchange type interaction with negative (antiferromagnetic) sign. It is proposed that the mixing effect is large in gadolinium metal under the assumption that the energy level corresponding to a trivalent gadolinium ion is very near and below the Fermi surface. Then it is shown that the mixing effect gives rise to a large negative g-shift for the localized spin, which substantially cancels the positive g-shift which comes from the exchange interaction, thus leading to a good agreement with the observation. Furthermore, by introducing a spin-orbit coupling of localized electrons, we can obtain an anisotropic interaction between conduction and localized electrons, which is found to account for a large anomalous Hall effect observed in gadolinium metal.