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Quantum Critical Matter and Phase Transitions Chapter 280 315 Experiments of the Gr€uneisen ratio G1⁄4(Vmol/kT)(acr/Ccr) and magnetic Gr€uneisen ratio Gmag 1⁄4 (dM/dT)/C, ie, the magnetocaloric effect (1/T)(dT/dH) at constant entropy, were performed by K€uchler et al. (2003) and Tokiwa et al. (2009), respectively. Inverse power-law divergences were generally found indicating a QPT as predicted by theory (Zhu et al., 2003), see Section 2.3. Finally, inelastic neutron scattering (INS) experiments were carried out in magnetic fields down to temperatures of T$0.1 K, which is still above TN, by Stock et al. (2012) to probe the NFL state of YbSi2Si2. These dynamical reso- nances detect the spin fluctuations in the meV energy range and their momen- tum dependence within the Brillouin zone. The zero-field spin fluctuations are incommensurate in the basal plane with ferromagnetic interplane correlations. There is a strong dependence of the fluctuation spectra with temperature due to the competition between ferromagnetic and incommensurate antiferromag- netic components. In large magnetic fields, eg, H$210 T, local moment behavior is field-induced that can be interpreted as localized droplets of Yb+3 spins extending on a length scale of$10A ̊. This response indicates a change in behavior for low-field itinerancy, ie, Fermi surface nesting, to Kondo screened local moments (Stock et al., 2012). A very recent nuclear magnetic resonance (NMR) study of the spin-lattice relaxation time, T1, of 29Si spanning the QCP (Kambe et al., 2014) has con- cluded that a coexistence of both HFL and NFL phases exist. These paired states represent an itinerant HFL component degenerate at the QCP with a localized NFL whose ratio R(T, H) 1⁄4 fNFL/fHFL varies with T and H. The description assumes a “two-fluid” scaling relation that nicely fits the data with reasonable scaling exponents. Thus we have a novel interpretation that adds a new element to the quantum critical behavior, yet it leaves the antifer- romagnetic state, the putative SDW, unresolved with both quantum critical ferromagnetic and antiferromagnetic fluctuations playing a role (Kambe et al., 2014). So what then is nature of the antiferromagnetic transition below 0.07 K and how is this state perturbed with tiny fields of$0.06T to create the QCP? Additional microscopic or local experiments, such as angle-resolved photoemission spectroscopy (ARPES), STM (scanning tunneling microsco- py)/STS (scanning tunneling spectroscopy), quantum oscillations, core spec- troscopy, etc., are needed to answer this question. Although an enormous amount of effort and manpower resulting in many premier publications have been devoted to YbRh2Si2 and its QCP, the exact causes and their description have remained incomplete. Note that there are other ytterbium-based heavy fermion materials that exhibit quantum criticality. A recent example is YbNi4(P1xAsx)2, which is an itinerant ferromagnet that can be tuned to criticality by either a magnetic field or arsenic doping. A divergence of the Gr€uneisen ratio was found, incon- sistent with the HM predictions (Steppke et al., 2013).PDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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