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316 Handbook on the Physics and Chemistry of Rare Earths 3 3.1 PRESENT THEORIES Critique of HM and the Kondo Effect As discussed in the previous section, both CeCu6xAux and YbRh2Si2 display features that are incompatible with standard HM theory. This forces us to look at reasons why this itinerant SDW picture should not apply. The most fundamental critique originates in the microscopic nature of the materials. In addition to the usual set of conduction electrons, the materials discussed in this chapter contain electrons localized in f-orbitals. The interac- tion between conduction electrons and localized d or f-states was first studied by Kondo (1964), who introduced the model of a single magnetic impurity in a metal, H1⁄4XEkc{kscks +J!S !s (19) ks ! TK $ expð1=JN0Þ, where N0 is the density of states of the conduction elec- trons at the Fermi level, Kondo showed that the localized spin forms a singlet state with the conduction electrons. This process of Kondo screening effec- tively delocalizes the initially localized f-electron (Anderson, 1970; Hewson, 1993; Kondo, 1964). It was expected that Kondo hybridization will also occur in materials that have localized f-electrons in every unit cell. The corresponding Kondo lattice model (Doniach, 1977) X{X!! H1⁄4 Ekckscks +J Si si (20) ks i is suggested to be a standard FL below the Kondo coherence temperature Tcoh. Below this temperature, the f-electrons are hybridized with the conduction electrons, and the effective mass of the new electrons is drastically enhanced: a HFL. The delocalization of the f-electrons implies that the Fermi surface becomes larger than it would be when only the c-electrons would be mobile (Oshikawa, 2000). Even though the Kondo lattice model has been studied extensively with various methods (such as slave-boson theory Burdin et al., 2000, for further reading see Sec. II.F.2. of von L€ohneysen et al., 2007), there is currently no solid understanding of how the hybridization of f- and c-electrons works. This lack of understanding then carries over to the realm of HM theory that requires simple Landau fermi-liquid quasiparticles to start with. Nevertheless, the notion of a QCP in a Kondo lattice system can be intro- duced. AFM in the Kondo lattice model can arise from interactions between where S is the spin of a localized impurity, k is the electron momentum with dispersion E , and !s 1⁄4 P c{ !s c is the total spin of the conduction elec- k kk‘ ka ab k‘b trons at the impurity site. At temperatures below the Kondo temperature,PDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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