Sommerfeld constant

The y values (Sommerfeld constants) for some metals are reported in Table 3.1. 

From the experimental data for the Sommerfeld constant yN in fig. 56, conclusions on the influence of substitutional disorder on the rare-earth site of YxLui Ni2B2C... 

Fig. 60. Concentration dependence of various properties of polycrystalline Y(Ni xPt )2B2C obtained by specific heat measurements transition temperature Tc exponent a and parameter Hc2 from eq. (6) upper critical field Hc2(0) at T =0, where the dotted line schematically describes the dirty limit corresponding to the isotropic single band case (in reality there is a finite intersection with the field-axis for the dotted asymptotic line, see Shulga and Drechsler 2002) exponent fi of eq. (8) for the curvature of the electronic specific heat in the mixed state and Sommerfeld constant xn (after Lipp et al. 2001).

The maximum deviation from this dashed line in Figure 62 is only about 1% and can not explain the observed 10% variation of the Sommerfeld constant. Therefore, taking into account Eq. (9), it was concluded that the local lattice distortions due to the different size of the Y and Lu ions in the YxLui xNi2B2C compounds mainly reduce the electron-phonon interaction (Rosner et al., 2000). The dependence of Xph on the Y concentration resulting from Eq. (9) and N( p) is... 

This study has been motivated by the recent discovery and investigations of a new family of superconductors metal-intercalated chloronitrides. For example, the compound Liu.48(THF)yHfNCl has arelatively high value of Tc 25K [l]-[5]. The mechanism of superconductivity for these materials had remained a puzzle. Indeed, according to theoretical calculations [6] the electron-phonon interaction is not sufficient to provide the observed value of Tc. Analysis of the data on heat capacity [2], based on the dependence 7 (1 + A), see [7], has led to a similar conclusion (7 is the Sommerfeld constant, A is the electron-phonon coupling constant). 

Specific heat. In the Fermi liquid theory, the expression for the electronic contribution to the specific heat is linear in temperature CXT) = yT, where the Sommerfeld constant is... 

Figure 10 Magnetic field dependence of the Sommerfeld constant of specific heat in (TMTSF)2C104 at low temperature, after [62].

Ideally, the specific heat of conduction electrons (or holes) in a metal is a linear function of temperature C = yT, where y, known as the Sommerfeld constant, is in the range 0.001 to 0.01 J/(molK ) for normal materials. In HF compounds, y reaches values up to 10 times larger (see tables 9, 10 and 11). In the basic theory of the specific heat of itinerant electrons (free Fermi gas), y is proportional to the effective mass m of the charge carriers, and so the name heavy fermions has come to be attached to these high-y materials (see Stewart 1984). The linear relation between C and T is strictly fulfilled only in the limit of a free degenerate electron gas. In real materials, weak non-linearities show up that can be encompassed by, for example, allowing y to be temperature dependent, y T). The Sommerfeld constant of interest is then the extrapolation of y for... 

Fig. 103. Sommerfeld constant vs. susceptibility for various established heavy-fermion compoimds. After P.A. Lee et al. (1986).

The distinction between Kondo metals, etc. and HF systems is fuzzy at best. As pointed out, the Kondo interaction is, among others, a basic ingredient of HF behavior. In a Kondo-lattice material one observes the effects of the Kondo interaction, for example on the magnetic properties, but very heavy quasiparticles are not formed and in consequence, the Sommerfeld constant is only slightly enhanced, That at least is the basis for a distinction we shall adopt. The hybridization between 4f and conduction electrons can lead to a hybridization gap in the density of states at the Fermi surface. The exact mechanism of gap formation is still under debate and also may vary from compound to compound. If a gap is present, one leaves the realm of Kondo metals and has, depending on the form of the gap (e.g., whether it is open in all crystallographic directions) and on its width, either a Kondo semimetal, semiconductor or insulator. The latter are certainly the most challenging class of Kondo compounds to understand. 

CeRuSi2- The Sommerfeld constant of CeRuSi2 is enhanced (y w 0.1 J/(mol K )) but still on the low side for a HF material. The crystal stmcture is monochnic (P2i/m) and differs from other members of the CeTX2 series. Curie-Weiss behavior is observed above 60 K but with an effective moment of only 1. 7/tb which is considerably lower than the Ce + free ion value (Nikiforov et al. 1993). A sharp upturn in xij) around 10 K, together with a A-like behavior in specific heat, indicates a magnetic transition (Velikhovskii and Nikiforov 1993). 

Ce Au-iSb. This compound belongs to the class of low-carrier-densit) HF systems, which have recently attracted much interest, mainly due to the work of Kasuya and his group (see, for example, Kasuya et al. 1993b). For these materials, the non-4f reference compounds are semimetals or narrow gap semiconductors and the related 4f containing compounds are characterized by a low carrier density on the order of 10" /(4f-atom). Despite the small mrniber of conduction electrons available to form a correlated state with the local 4f moments one observes typical HF behavior such as a substantially enhanced Sommerfeld constant. 

UCd. This cubic compound orders (antiferro-) magnetically around 5K. The spin structure is not known. Neutron scattering is difficult (because of the high absorption by Cd) and only an upper limit of 1.5/tb for the U ordered moment could be given (Thompson et al, 1988). Specific heat and susceptibility data (Fisk et al. 1984) established UCdn as a moderate HF material (the Sommerfeld constant, for example, is 0.25 J/(molK )) within the regime of magnetic order. 

---