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302 Handbook on the Physics and Chemistry of Rare Earths The typical smoking gun for NFL behavior is an unconventional tempera- ture dependence of the resistivity, rðTÞ 1⁄4 r0 + aTn (16) where n1⁄42 would be for a standard FL. Many materials have n deviating from two—for example, the linear resistivity measured in YbRh2Si2 (Custers et al., 2003). Within the theoretical framework of HM theory, indeed anomalous exponents were found (Moriya and Takimoto, 1995), for example, Dr$T3/2 at a d1⁄43 antiferromagnetic QCP. However, this picture fails when the electron scattering is peaked at “hot spots” on the Fermi surface, that are ! connected by the antiferromagnetic wavevector Q. There critical fluctuations lead to a linear T scattering rate, but electrons on the remaining “cold spots” still follow the standard FL lure and the overall resistivity is expected to be Dr $ T2 again (Hlubina and Rice, 1995). Disorder can change this picture again (Rosch, 1999, 2000), which makes resistivity a difficult subject matter. Not all NFL behavior arises due to quantum criticality. To distinguish between NFL behavior due to disorder (Westerkamp et al., 2009) and actual criticality, the Gr€uneisen ratio G was introduced. For any QCP controlled by pressure, the ratio between the thermal expansion a 1⁄4 1 @S and the specific V @p heat at the critical pressure should diverge (Zhu et al., 2003), GðT, p 1⁄4 pcÞ 1⁄4 ca $ T1=nz: (17) V The standard theory of HM for a three-dimensional antiferromagnetic QPT gives z1⁄42 and the mean field correlation length exponent n1⁄41/2, hence the Gr€uneisen ratio should diverge as 1/T. A group of cerium-based compounds does seem to exhibit the critical behavior as predicted by HM theory. Most notable is CeNi2Ge2: at ambient pressure and zero field this material has a critical specific heat cV$T3/2 and a Gr€uneisen ratio G$T1, consistent with the HM predictions, see Fig. 3 (K€uchler et al., 2003). The resistivity is found to be Dr(T ) $ T3/2 (Gegenwart et al., 1999). The only suspicious aspect of this material is that it does not have exhibit antiferromagnetism (AFM), only pressure induced superconductivity (SC). However, the isostructural compound CePd2Si2 does become antiferromagnetic, yet it shows similar high pressure dependent SC. Thus Grosche et al. (2000) have suggested that the critical behavior of CeNi2Ge2 is related to the high-pressure QCP in CePd2Si2. Consequently, antiferromagnetic order in CeNi2Ge2 should exist at “negative” pressures—a challenging concept indeed. Two other related compounds, CeCu2Si2 and CeCu2Ge2, seem to have similar HM quantum critical behavior (Stockert et al., 2004), but it appears difficult to consistently synthesize these materials because tiny deviations in their stoichiometry leads to inhomogeneous and competing phases of magnetism and SC (von L€ohneysen et al., 2007).PDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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