Kondo impurity

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. 

Under an applied magnetic field is shifted to higher temperatures, while the value of Cm at 7 is found to decrease in CePd3Beo.45 and CePdjBeo.ss (Sereni et al. 1986) or to remain constant as in CeCue.jAlg 5 (Rauchschwalbe et al 1985). The resonance-level model for Kondo impurities predicts the narrowing and the increase of Cm (at T ) with field, as verified by Bredl et al. (1978) for (La, Ce)Al2 such a behaviour is also followed by CePd3B. 

Fig. 1. Temperature dependence of 4f-derived specific heat per mole of cerium as CJ T plotted against T for Ce,La,.,Cuj with x = l (O), 0.8 ( ) and 0.5 (x) (Onuki and Komatsubara 1987). Inset shows low-T data (Steglich et al. 1985). Dashed curve indicates result for an 5 = J Kondo impurity with r = 4.2K (Andrei et al. 1983).

Fig. 43. Specific heat as CIT against T for CeAlj (Biedl et al. 1978b). Solid line through data points is guide to the eye. Thin horizontal line indicates low-temperature value, yo = 0.135 JK mol" . Dashed line is Bethe-ansatz result for S = j Kondo impurity with = 0.68 T = 3.5 K (Andrei et al. 1983).

Fig. 39. Schematic shape of the electron band structure (a, b, c) and p(T) (a, b, c ) for metals with Kondo impurities (a, a ), concentrated Kondo systems (including systems with heavy fermions) at T < (b, b ) and for compounds...

Kondo-impurity region, L/Lq exceeds one. At, T < 1 K it is assumed that < /c, as has been noted above. 

Fig. 48. The temperature dependence of L/Lq in CeCu2Si2 (Franz et al. 1978). I is the coherent state region, II the intermediate region, and III the Kondo-impurity region.

It has been pointed out early that the ESR of local moments could be used to observe the Kondo effect directly by studying the resonance absorption of the Kondo impurity itself Spencer and Doniach (1967) calculated the g-shift and Walker (1968) the relaxation rate due to the Kondo effect. Both contributions are rather small and experimentally hard to measure. This is partly due to the large residual linewidths typically found in Kondo alloys. 

A number of multi-impurity experiments on Kondo systems were reported in the literature. Most of the early work is cited in the review by S.E. Barnes (1981a). A tutorial discussion on the Kondo effect has been given by Taylor (1975). Of these multi-impurity experiments, here we discuss Gd-ESR experiments obtained in LaA doped with Kondo impurities. Gd-ESR has been utilized to study the effects of a Kondo impurity in the pseudobinary alloy Lai jcCexAl2 Gd (Davidov et al. 1972). Similar experiments were performed by Weissenberger (1981) in the intermetallic compound (La,Y,Ce)Al2 Gd. In this alloy Ce behaves like a Kondo impurity and the Kondo temperature can be varied from 0.4 to 100 K. The most important result of this investigation was the dependence of the residual linewidth A/7o on the state of the Ce impurity, e.g. on the single-ion Kondo temperature. 

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