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Quantum Critical Matter and Phase Transitions Chapter 280 327 first-order nature. Then there is a dome called “Phase III” whose top is second order, but end points first order. An early proposal was an hidden QCP, a metamagnetic end point, extrapolated under the dome to T1⁄40—see Fig. 21. Most recently Bragg neutron scattering has been performed in fields up to 40 T, and thus a local magnetic order clarification of Phase III became avail- able. The result is that Phase III is a long-range AFM state, thereby removing the necessity for a quantum critical endpoint (Knafo, 2015). A way of reduc- ing the fields needed for Phase III is to dope Ru sites with a small amount (4%) of Rh (Kuwahara et al., 2013). This leads to a complete destruction of the HO, yet Phase III remains intact. Magnetic Bragg-peaks confirmed the AFM as now found for pure URu2Si2 (Kuwahara et al., 2013). Therefore, with Phase III fully established as long-range AFM, there seems to be no QPT in URu2Si2. 5 QUANTUM CRITICALITY BEYOND RARE EARTHS AND ACTINIDES The concept of quantum criticality extends beyond the rare earth and actinide materials discussed in the previous sections. We wish to provide, for the inter- ested reader, a brief list of other putative QCP’s. Much of the proposed quan- tum critical behavior is spin based, and occurs in magnetic transition metal compounds. l There has long been the claim of a QCP in the high temperature cuprate superconductors, beneath the superconducting dome. From the theoretical prospective, see Sachdev (2003) and the experimental works of Valla et al. (1999) and Broun (2008). A very recent review of putative QCP’s in the cop- per oxides is by Keimer et al. (2015). Also the more recently discovered pnic- tides (Fe-based compounds) have been reviewed by Shibauchi et al. (2014) with again evidence for a QCP lying beneath the superconducting dome. l Bose–Einstein condensation of magnons in quantum magnets offers another route toward QCP via magnetic field tuning. It has been suggested in mainly oxide compounds with 3d transition metals, and has been stud- ied intensively during the last twenty or so years with a complete review by Zapf et al. (2014). Here, there is clear evidence, both theoretically and experimentally, of QPTs with surprising behavior at the QCP. l Low-dimensional spin insulators, ie, Ising and Heisenberg chains and lad- ders, are tunable with a magnetic field toward a QPT. In this regime, there is a wide variety of quantum behavior, from Luttinger liquids to dimen- sional crossovers. Accordingly, there are the 1D topics of perturbations of the lattice, various magnetic couplings, Ising or Heisenberg class, spin gaps for integer (S1⁄41) and half-integer (S1⁄41/2) spins, and different pro- totypes of QCP’s. Complete reviews of 1D quantum magnetism are by Giamarchi (2004) and Mikeska and Kolezhuk (2004). A more recent brief overview of quasi-one-dimensional systems is by Giamarchi (2010).PDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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