Electrons in the heavy rare earth metals

A detailed description of the linear combination of muffin tin orbitals method of band structure calculation is presented. This method has been used to calculate relativistic bands for the hexagonally close packed rare earth metals Gadolinium, Terbium, Dysprosium, Holmium, Erbium, Thulium and Lutetium. In particular self-consistent relativistic band structures have been obtained for thulium. A ferromagnetic band structure has been calculated for gadolinium. For thulium the density of states and fermi surface have been found. Expectations for the fermi surfaces of the other elements have been discussed. The limited experimental evidence directly pertaining to the band structure of these elements is in good agreement with these results, particularly specific heat, transport properties and photoemission data. A de Haas-Van Alphen orbit is predicted for thulium and the relationship of these results to the valence of thulium and to the RKKY interaction is discussed qualitatively. The magnetic properties of gadolinium are investigated. The validity of treating the localised 4f electrons within the band theory is discussed. (author)