Mixed valent metals

We review the theory of mixed-valent metals and make comparison with experiments. A single-impurity description of the mixed-valent state is discussed alongside the description of the nearly-integer valent or Kondo limit. The degeneracy N of the f-shell plays an important role in the description of the low-temperature Fermi-liquid state. In particular, for large N, there is a rapid cross-over between the mixed-valent and the Kondo limit when the number of f electrons is changed. We discuss the limitations on the application of the single-impurity description to concentrated compounds such as those caused by the saturation of the Kondo effect and those due to the presence of magnetic interactions between the impurities. This discussion is followed by a description of a periodic lattice of mixed-valent ions, including the role of the degeneracy N. The article concludes with a comparison of theory and experiment. Topics covered include the single-impurity Anderson model, Luttinger's theorem, the Friedel sum rule, the Schrieffer-Wolff transformation, the single-impurity Kondo model, Kondo screening, the Wilson ratio, local Fermi-liquids, Fermi-liquid sum rules, the Noziéres exhaustion principle, Doniach's diagram, the Anderson lattice model, the Slave-Boson method, etc.