Kondo anomalies specific heat

Fig. 26. High-temperature specific heat of three Kondo eompounds with an abnormal Schottky anomaly, after de Boer et al. (1985) and Felten (1987). The continuous curve is a Schottky contribution for a F-j-Fg thermal promotion.

Knowing the excitation spectrum one can compute the thermodynamic properties. In the local-moment regime they exhibit low-temperature T 7 ) Kondo anomalies that are due to the resonance states. For example, the static magnetic susceptibilty x(T), the specific heat, various transport coefficients and also dynamical quantities (photoemission spectra, dynamical structure function for neutron scattering) have been calculated (Bickers et al. 1985, Cox et al. 1986). An excellent model system for comparison with experimental data are the dilute (La, Ce)Bg alloys because of a fourfold degenerate Fg ground state of cerium (Zirngiebl et al. 1984). 

The interaction between impurity ions with partially filled d or f electron shells and the conduction electrons of a metallic host can lead to variations in certain physical properties with temperature and magnetic field which have come to be associated with the Kondo effect . In zero magnetic field, these temperature-dependent anomalies in the physical properties scale with a characteristic temperature Tk, the so-called Kondo temperature, above which the matrix-impurity system behaves magnetically and below which the matrix-impurity system behaves nonmagnetically. The physical properties which exhibit anomalies attributable to the Kondo effect include the electrical resistivity, magnetic susceptibility, thermoelectric power, specific heat and, in systems where appropriate, superconducting properties such as the critical temperature and the jump in specific heat which occurs at T. ... 

As mentioned in the Introduction (section 1), the electrical resistivity, specific heat, magnetic susceptibility and thermoelectric power anomalies of concentrated lanthanide Kondo systems are qualitatively similar to those found in the dilute lanthanide systems discussed previously. However the importance of the concentrated systems is that they provide a totally new view of Kondo-like phenomena. Lattice constant. X-ray photoemission (XPS) and Mossbauer isomer shift measurements indicate a strong correlation between systems that exhibit Kondo-like anomalies and systems in which the lanthanide ion has a mixed or intermediate valence. By mixed valence we mean that there are two 4f electron configurations accessible to each rare earth ion (e.g., Ce -Ce, Eu -Eu ", Yb -Yb ). Phenomenologically the traditional... 

This form, often believed to be valid for the Kondo problem, yields the relationship j3e = QeCe/FBr, given as eq. (1), where = /3o + and Cv = Cq + Ce are the thermal expansion and specific heat, Bj = Bq+ B is the isothermal bulk modulus, and the subscripts 0 and e refer to the background and electronic (e.g. Kondo) contributions, respectively. The magnitude of /3e can be anomalously large in the materials of interest and often Pe exhibits a maximum as a function of temperature. We will discuss the nature of the lattice coupling that causes these lattice anomalies in some detail in sect. 4. For now, it will suffice to say that the 4f-ionic size is sensitive to changes in valence and/or hybridization. The isothermal bulk modulus is then (Yoshizawa et al. 1986)... 

We next demonstrate these relations for the mixed-valent compound YbCuAl. As seen in fig. 8, this material has a susceptibility maximum near 25 K, with a linear coefficient of specific heat ) =0.26 J/molK (Mattens et al. 1980, Pott et al. 1981a). These numbers imply (Rajan 1983) a Kondo temperature in the range 60-100 K. The thermal-expansion anomaly is negative in Yb compounds because the trivalent state has a smaller volume than the divalent state that is increasingly favored at low temperature due to the hybridization. In the inset of fig. 25 we show the volume expansion... 

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