Exchange Interaction in the Heavy Rare Earth Metals Calculated from Energy Bands

Abstract

The heavy rare earth metals were obtained in pure form and as single crystals about ten years ago. This made a detailed experimental investigation possible. Neutron scattering in particular has been an important tool. As a result we have, by now, obtained a very complete knowledge about the magnetic interactions. The experimental facts, which are reviewed in [₁], revealed that the magnetic properties are determined by an intricate interplay of forces of similar magnitude. The dominant is the indirect Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction, which we shall attempt to calculate from first principles, here. Of importance also is the crystal field anisotropy and magnetoelastic effects. The anisotropy of this origin is of a single ion type. Recent neutron scattering measurements [2] have shown also that two-ion anisotropy maybe of importance. There are numerous possibilities for anisotropy of the interaction between the moments at different sites. As we shall see, the RKKY interaction, which is mediated by the conduction electrons, is anisotropic in the magnetically ordered phase. The two-ion interaction, which is mediated by phonons, is strongly anisotropic. The magnitude of the interaction between the spin system and the lattice is determined by the coupling between the spin- and orbital-momentum of the electrons. If the spin-orbit coupling and the orbital momentum is large we must therefore expect large anisotropies both of single-ion and two-ion nature. Also the RKKY interaction becomes anisotropic, as discussed by Kaplan and Lyons [3].