Mechanism of the Appearance of an Energy Gap in Mixed-Valent Rare-Earth Compounds

Abstract

The origin of an energy gap at the Fermi level in mixed-valent SmB₆, gold-phase SmS, YbB₁₂, CeNiSn and Ce₃Pt₃Bi₄ has been a subject of controversy.^1–6 In case of SmB₆, for instance, valence of Sm ions is about +2.6, and then the number of conduction electrons per formula unit has been believed to be 0.6, because RB₆ compounds with R=Ca²⁺ and Eu²⁺ are semiconductors and La³⁺B₆ is a monovalent metal. How to construct an energy gap and how to obtain a semiconducting property in such a metallic state have been an attractive theme for theorist. Models of hybridization gap,⁷ Wigner-crystal formation⁸ and coherence pseudogap⁹ have been proposed so far. From an experimental point of view, it has been required to distinguish the gap due to the effect of f-electrons from the one in the non-f electronic states. Furthermore, to find a requisite condition for the gap opening, it is also necessary to find other exemplifications, especially, in isomorphous compounds in which rare-earth ions exist as a well-defined valence state in one compound and as different valence state in another one, both of which show semiconducting properties. Recently, based on our experimental finding of the appearance of semiconducting properties in both Ce₃Au₃Sb₄ with well-defined Ce³⁺ ions and the mixed-valent compound Ce₃Pt₃Sb₄, we have pointed out that the valence of Ce ions in Ce₃Pt₃X₄(X=Bi,Sb) is formally 4+ and the origin of the energy gap is not so much different from those of Ce₃Au₃Sb₄ and La₃Au₃Sb₄.¹⁰ Furthermore, we pointed out that there are common features in the band structures of their reference systems without f electrons.^10,11 For Sm- and Yb-based mixed-valent compounds, for instance, the band calculations of CaB₆ ^(ref.12) and YB₁₂ ^(ref.13) predicted that non-f R²⁺B₆ and non-f R²⁺B₁₂ can be semiconductors, i.e., band structures of compounds with rare-earth sites replaced by non-f 2+ ions have a gap at the Fermi level.