Kondo temperature

We now ask how these moments can be observed. We have stated that at temperatures below the Kondo temperature there is no true moment but at high temperatures we expect a Curie susceptibility of the form... 

The approximation breaks down at the Kondo temperature when the term in square brackets vanishes, so that this approach gives for TK... 

The question of the existence of the Kondo effect in amorphous systems is of interest for the considerations of Chapter 5. There is no theoretical reason to suppose that the Kondo temperature will be greatly affected on the other hand, the short mean free path l should cut down the RKKY interaction, which, for distances r greater than / should fall off as e-r/ (de Gennes 1962). In alloys... 

Our Kondo temperature is set by parameters of the small dot. For small (large) dot of diameter 100mn(2pm) in a GaAs/AlGaAs heterostructure, it is possible to achieve um 3K > Tk IK Am 50mA. ... 

The main equation for the d-electron GF in PAM coincides with the equation for the Hubbard model if the hopping matrix elements t, ) in the Hubbard model are replaced by the effective ones Athat are V2 and depend on frequency. By iteration of this equation with respect to Aij(u>) one can construct a perturbation theory near the atomic limit. A singular term in the expansions, describing the interaction of d-electrons with spin fluctuations, was found. This term leads to a resonance peak near the Fermi-level with a width of the order of the Kondo temperature. The dynamical spin susceptibility in the paramagnetic phase in the hydrodynamic limit was also calculated. 

Relation (39) determines a low-energy scale for the spectral density of d-electrons, which is of the order of the Kondo temperature kl x for PAM. Because this scale results from the interaction with spin fluctuations of localized moments we also study the spin susceptibility of d-electrons. 

CeCu6 and CeRu2Si2 show neither superconductivity nor magnetic order down to 20 mK. Therefore, the behaviour of 1/7) in these compounds presents a fundamental property of heavy fermion material. As seen in Fig. 3,11,12 1/7) is temperature independent above the Kondo temperature, / , corresponding to a localized state of the 4/ electron. At higher temperatures 1/7) is expected to decrease due to the increase in the fluctuation rate of the localized 4f spin. Below 7k, 1/7) shows a 7) T= constant behaviour corresponding to the Fermi liquid state. 

An alternative approach to accounting for the maxima in the temperature dependence of p is based on the Kondo-lattice model (Lavagna et al. 1982). The periodic array of independent Kondo impurities, described by the single-ion Kondo temperature TK, provides a proper description at elevated temperatures, while a coherent state yielding a drop of the resistivity is attained when the system is cooled to below another characteristic temperature coh- Although this approach is suitable particularly for Ce compounds where the Kondo regime was identified inequiv-ocally, the coherence effects are probably significant also in narrow-band actinide materials, as indicated by an extreme sensitivity of the lower-temperature decrease of the resistivity to the presence of impurities. 

Chenevas-Paule et al. (1977) have recorded the resistivity versus temperature of the two phases in the range 1-300 K. From their results they estimate the Kondo temperature to lie between 20 and 50 K. They conclude that (M. SmS) is not a Kondo compound similar to CeAls and since the resistivity does not increase with temperature they believe in the presence of Sm. ... 

P(J ) distribution of Kondo temperatures A Gaussian width of field distribution... 

Tk (single ion) Kondo temperature Oc, spin of conduction electron... 

Whether the NCA model is a proper description of Kondo interaction in the present case could be questioned since Kondo temperature and CEF splittings are roughly equal. In addition, magnetic correlations have been completely n lected. It is true that the discussion is of a temperature range far above 7n, but on the other hand, it is known (see, for example sect. 5.3) that pSR senses such correlations far into the paramagnetic regime. 

In summary, the (xSR results together with the NMR data imply that a broad distribution of Kondo temperatures is present in UCus- Pd supporting a disorder-driven NFL state. This need not be coimected to marked crystalline disorder. A cooperative rather than a single-ion mechanism appears to be present. Only a small portion of moments is spin frozen in UCu4Pd, if at all. 

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