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Quantum Critical Matter and Phase Transitions Chapter 280 307 susceptibility became broadened with no sign of the expected QCP divergence and unconventional frequency effects (Kopec ́, 1997). Wu et al. (1993) then suggested the disagreements with theory were the result of a first-order quan- tum SG transition. More recent measurements (Tabei et al., 2006) attribute this lack of QPT behavior to the induced random field Ising features thereby rendering the quantum criticality inaccessible. This conclusion was confirmed by Ancona-Torres et al. (2008) due to the competing effects of quantum entanglement and random fields. Schechter (2008) has demonstrated that a proper treatment of LiHoxY1xF4 in a transverse field is the random field- Ising model, not the canonical QPT description introduced in Section 2.2. Additional attempts at finding an Ising SG to confirm the predicted H? behav- ior remain unclear because of the above complications. At present, the closest realization of transverse field Ising criticality occurs in columbite CoNb2O6, a material outside the scope of this review (Coldea et al., 2010; Lee et al., 2010). As for rare earths and actinides, theory still greatly outweighs the “ideal” material experiments. 2.4.2 Ce(Cu,Au)6 The first heavy-fermion material CeCu6 was originally proposed (von L€ohneysen et al., 1994) to show a QCP with combinations of different tuning parameters: Au-dilution, pressure, and magnetic field. This well-studied inter- metallic compound was extensively reviewed by von L€ohneysen et al. (2007). Here, we briefly summarize the long history of CeCu6xAux and relate the QPT behavior to recently evolving work. Specific heat data are shown in Fig. 7, for various doping x and pressure P. Pure CeCu6 does not order magnetically down to at least 10 mK. In a good FL, the specific heat C/T should approach a constant as T!0, hence the slight upturn of C/T in Fig. 7 suggests the presence of spin fluctuations dis- turbing the FL. With increasing Au concentration the QCP is reached at xc 1⁄4 0.1, where the C/T behavior changes to C=T $ 1⁄2 lnðTo=TÞ. This temperature dependence indi- cates NFL behavior, an indication of possible quantum criticality. By further increasing the Au concentration x magnetic order is generated. This phase is an incommensurate SDW (Schr€oder et al., 1994) with small staggered magnetic moments, reaching m % 1.2mB/Ce at x1⁄41.0. The concentration dependence of TN is shown in the upper panel of Fig. 7. The Ne`el temperature TN begins to decrease above x1⁄41.0 due to the destructive effects of disorder affecting the band structure and Fermi surface of this strongly correlated material. As a func- tion of Au-concentration tuning, we thus have a V-shaped region of quantum criticality just above xc, as suggested by Fig. 2. Note that the putative FL state for concentrations xPDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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