Intermediate-valence materials

Closely related to the heavy fermions and spin fluctuators are the valence fluctuation/intermediate valence materials. The origin of this phenomenon starts with cerium and its a 7 transformation (see sections 3.3.4 and 3.7.2). Today it involves many cerium materials and also compounds of samarium, europium, thulium and ytterbium. Because of the breadth of the subject matter and space limitations in this chapter we refer the reader to the following reviews Jayaraman (1979), Lawrence et d. (1981), de Chatel (1982), Coqblin (1982), Nowik (1983), Brandt and Moshchalkov (1984), Varma (1985) and Stassis (1986). 

Dispersive effects indicating collective correlations have been difficult to find in intermediate-valence materials. TmSe, which is one of the few systems to order magnetically, does exhibit some dispersion, and there has been speculation that the excitation represents interband transitions. A strong increase in the response as > 0 was also observed in EuNi2P2- In this respect we note the controversial situation with respect to CePds. Since this is a canonical IV system, we would like to encourage the resolution of the experimental differences between those working on poly- and singlecrystalline samples. 

The interpretation of the susceptibility is the most tricky problem of intermediate valence because now we have to consider the various electronic configurations together with the spin. In the past there have been some ad hoc theories of susceptibility (e.g.. Sales and Wohlleben 1975) but until today there is no theory of susceptibility of intermediate valence materials taking into account the experimental fact of a gap in the DOS. 

The chapter by Wachter (132), which is one of the most extensive and comprehensive ones in the entire Handbook series, reviews intermediate valence and heavy fermions in a wide variety of lanthanide and actinide compounds, ranging from metallic to insulating materials. The behaviors of these materials are discussed from the basic idea that a gap exists between two narrow f-like subbands, i.e. the hybridization gap model, which can account for the observed physical and electronic properties. As pointed out by Wachter, heavy fermions are intermediate valence materials by virtue of the fact that they have nonintegral f occupation values. The main difference between normal intermediate valence materials is that their Fermi energies are in the hybridization gap, while for the heavy fermion materials the Fermi energy is not in the gap. 

Wachter ( ) have presented a very clear example of this behaviour in their studies of the moment formation in TmSe Te under pressure where both mixed valency, or intermediate valence (IV), and semiconductor to metal transition are found. The particular interest of this case is not only that these materials have been extensively characterized, but also because they show, from comparison of valences determined by two different experimental methods, that a unique picture which considers only one type of... 

A more thorough evaluation of surface chemistry on binary, non-metallic rare earth compounds, excluding the oxides, is not possible at present because of the lack of available data. We note, however, that investigation of surface reactivities on some of these compounds, in particular those showing intermediate valence phenomena (Campagna et al., 1976), should provide an exciting new field of activity in the surface chemistry of rare earth materials. 

A recent addition is CeRhAs (Yoshii et al. 1996), 3iidiich is closely related to CeRhSb. All these materials contain 4f elements that ate known candidates for intermediate valence behavior and at high temperatures one finds evidence for such an electronic state in the majority of cases. Published [iSR data exist mainly for the first two cases and also, to a more limited extend, for (10). The latter is, together with (3) and (6), a prime example of a typical Kondo insulator (Kasuya 1996), while (1) and (2) have always been classified as Kondo semiconductors instead. As better samples have become available, it has been realized that they are now better described as Kondo semimetals (Takabatake et al. 1996, 1998a). More details are provided below. 

The theory of intermediate valence (IV) forms the starting point for the treatment of HF materials. IV represents the limiting situation of a very strong coupling parameter g in strongly correlated electron materials, as can be seen from fig. 105. Kondo insulators in particular possess IV behavior at high temperatures as an essential ingredient. They form a borderline case. We have discussed them earlier as a separate class of materials. 

Thermal conductivity of systems with an intermediate valence One could expect nonstandard behaviour of L(T /Lq in these systems too. Unfortunately, this case has not been discussed theoretically and it is not possible to draw any conclusions from the analysis of experimental data on thermal conductivity. In the classical compounds with an intermediate valence of the lanthanide atoms (SmBg, TmSe) kl > (especially in the low-temperature region). The contribution of to K,ot has not been taken into account during investigations of metals from this class of materials [e.g., CePdj (Schneider and Wohllcben 1981)]. 

CeRu2 is a mixed-valence system with a valency close to 4. The ESR experiments on this system are reviewed in sect. 12, which deals with local moment spin resonance in conventional superconductors. SmBs is an intermediate valence system, but belongs to a new class of small gap semiconductors. These materials exhibit Kondo-lattice behavior at elevated temperatures but evolve into semiconducting materials with small gaps of the order of a few kelvins or a few tens of kelvins as the temperature is lowered (Aeppli and... 

Electron-spin resonance (ESR) is an extremely useful tool for probing the localized magnetic moment in a variety of materials. The chapter (162) by Elschner and Loidl focuses on metallic lanthanide systems, reviewing both the classical ESR behaviors and the role of ESR in newly developed branches of solid-state physics. The former includes the determination of the site symmetry of the ESR probe and measurement of the crystal field (CF) and how it (CF) differs in metallic systems from that in insulators. The latter deals with Van Vleck systems, spin glasses, Kondo systems, heavy-fermion and intermediate-valence compounds, and high-temperature superconductors. 

After a brief review of the neutron formalism, we shall give examples of systems in which the crystal-field interaction dominates (sections 2,3), then turn to systems that order, but in which the f-d hybridization is significant (sect. 4), then cover materials with intermediate valence (sect. 5), which do not exhibit sharp excitations, and conclude with strongly interacting systems, such as heavy fermions (sect. 6). The conclusions are given in sect. 7. Except for the heavy fermions, the rationale for this order is that it corresponds to increasing hybridization between the 5f and other electron states. We have placed heavy fermions at the end because they are the most complex materials we will discuss, and, in addition, the chapter by Aeppli and Broholm (1994) covers them. 

These materials have been of interest for many years because of their unusual properties. In the last decade reasonably large crystals have become available by using the mineralization technique (Spirlet and Vogt 1984), so that many different neutron inelastic experiments have been performed. Although TmSe orders with a moment of about 2(Ub (Bjerrum-Moller et al. 1977), we shall discuss the Tm compounds with the NaCl-type structure in sect. 5 in coimcction with effects of intermediate valence (IV). 

Systems that exhibit intermediate valency behave in a completely different way to stable lanthanides (sect. 2). In materials that exhibit intermediate valency the Coulomb exchange interaction is more than an order of magnitude larger than the direct magnetic dipole interactions. One has to distinguish the following classes ... 

Anomalies in the phonon spectra of UTe have also been found (Buyers and Holden 1985) and attempts were made by the authors to use the same theories described above, which essentially relate to an intermediate-valence picture. Unfortunately, as Buyers and Holden describe (see their p. 304) this does not lead to a convincing conclusion. There is, of course, no direct electronic evidence (e.g., from photoemission) that materials such as UTe exhibit valence fluctuations. We must conclude that the electron-phonon interaction is different in detail between the 4f intermediate-valence matmals and tiie actinide compounds. In both cases, however, the result is a negative Poisson ratio (which is directly related to the elastic constant C12). 

In sect. 5 we discuss a large number of paramagnetic systems that exhibit no sharp crystal-field excitations. For the most part the materials are of intermediate valence (IV). Most of the experiments have been performed on polycrystalline materials. As discussed above, for the most part the interactions that lead to intermediate behavior are stochastic in nature so that little dispersion is anticipated - see also below. A good test for this is whether there is agreement between the neutron magnetic intensities (local susceptibility) and the bulk susceptibility. There is now considerable evidence that the magnetic response of these systems is inelastic at low temperatures. The energy of the peak position is... 

Materials exhibiting intermediate valence and having the Fermi energy in the hybridization... 

Materials exhibiting intermediate valence 5.3.1. The electrical resistivity 355... 

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