Heavy fermion phonons

In a heavy fermion compound Yb MnSbn, the dephasing rate of the coherent optical phonons decreased with lowering temperature above Curie temperature Tc, but increased below Tc- The results were attributed to the coupling between an optical phonon mode and the Kondo effect [100]. 

Fig. 12. Total heat capacity of a single crystal of PrFe4Pi2 vs. temperature in various applied magnetic fields (a) low fields and (b) high fields. The dashed fines in (b) correspond to the best fit of the heavy fermion state to die resonant level model (Crlm)-Cph is the estimate of die phonon contribution to the heat capacity (Aoki et al., 2002).

In the last two reviews of this volume, a theorist (Thalmeier in chapter 96 and Grewe in chapter 97) and an experimentalist (Liithi in chapter 96 and Steglich in chapter 97) combine their talents to present interesting and stimulating assessments of their areas of expertise - electron-phonon coupling and heavy Fermion phenomena, respectively. 

Microscopic theory of electron-phonon coupling in heavy-fermion compounds... 

De Haas-van Alphen (dHvA)-type quantum oscillations as observed in the sound velocity and sound attenuation provide important information about the Fermi surface and the electron-phonon interaction (Roberts 1968, Fawcett et al. 1980). This technique has been successfully applied to intermetallic rare-earth compounds as discussed below. Recent progress in dHvA techniques for heavy-fermion materials (Taillefer et al. 1987, Reinders et al. 1986) should make similar MAQO experiments also possible. Compounds studied so far are LaAg, LaB5, LaAlj, RBj, CeSn3, CeB, CeCu and CePbj. 

In this chapter we want to focus on the electron-phonon effects in the mixed-valence and heavy-fermion compounds. In the mixed-valence compounds one usually observes an extremely low bulk modulus Cg (table 6). As an example the case of Sm Yi S is given in fig. 44, see Penney and Melcher (1976). In addition, the so-called Poisson ratio v is negative in these compounds (see table 6). Analogously, certain phonon branches exhibit anomalies. A detailed discussion and explanation of these facts and related experiments will be given in sect. 4.5. 

The phenomenological Griineisen parameter electron-phonon coupling for the heavy-fermion compounds is very successful in describing the thermal expansion and temperature dependence of elastic constants. The parameters deduced from the different experiments agree with each other and they agree also with the parameters used in the microscopic description, sect. 4.3. 

Elastic anomalies in actinide-based heavy-fermion systems are most pronounced for UPt3. The temperature dependences of two representative elastic modes are shown in flg. 36 (Yoshizawa et al. 1985). Unlike the case of UPdj, CF effects as a possible source do not seem very likely. The phonon dispersions of UBOjj, as measured by neutron scattering (Robinson et al. 1986), do not show strong anomalies. The elastic constant Cj2, however, is negative at low temperatures, similar to some IV compounds. Remarkably, UBejj possesses a low Debye... 

For heavy fermions at low temperatures, > 50 dominates Q and C /T 1 J/mol dominates Cy so this correction can be quite large. For example, for UPts at lOK, where Q = 40, V = 42.4 cm /mol and C =3.25 J/mol K the correction is of order 12kbar, which is a large fraction of the total anomaly in the bulk modulus. (For mixed-valent compounds with To > lOOK this is less of a problem because the thermodynamic Gruneisen parameter is dominated by the phonon term, which is small.) Note that for heavy fermions, when Q Qe and C Cg, we have, by eqs. (8) and (13),... 

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