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328 Handbook on the Physics and Chemistry of Rare Earths l Quantum spin liquids are usually created with frustration and can occur without a QPT but they can also be tuned toward a QCP. The spin liquids represent a most unconventional state of matter that are being sought in real systems. For a highly frustrated metallic spin liquid, eg, Pr2Ir2O7, a QCP has been proposed from quantum critical scaling of the Gr€uuneisen ratio Tokiwa et al. (2014). Strong spin–orbit interactions in competition with the magnetic exchange energy form a new tuning parameter. A recent review of the spin liquids is by Balents (2010). l Metallic Sr3Ru2O7 possesses a field-tuned dome-like phase around H % 8 T. By scanning the field a QCP can be created in two distinct ways: via a metamagnetic transition into the dome extrapolated to T 1⁄4 0; or at the edges of the dome along the T1⁄40 abscissa where there are two putative QCP’s denoting the left and right sides of the dome. Very recently a field-tunable antiferromagnetic SDW has been observed in the dome phase (Lester et al., 2015). This would exclude the extrapolated “metamagnetic” QCP and emphasize the dome end points as QCP’s. l Itinerant nearly ferromagnets compounds, eg, ZrZn2 and MnSi can be driven with pressure to a disordered state. However, the putative QCP is of first order. Thus, such transitions do not represent the continuous QPT we studied in this chapter. Only a year ago a new itinerant compound YFe2Al10 (Wu et al., 2014) was proposed to show a continuous QPT without any tuning. This material does not magnetically order down to 0.1 K and an array of bulk measurement and scaling relations at low temperatures offer evidence that YFe2Al10 is special example of a 2D compound where, due to quantum critical fluctuations, its ferromagnetic order is reduced to nearly 0 K. Additional experiments at yet lower temperatures and tuning, for example, (negative) pressure and doping are required to generate the putative ferromagnetic transition at finite temperatures. We have thus far listed only magnetic or spin-based QPTs. There are also numerous nonmagnetic QPTs, which include the following. l Quantum ferroelectrics, such as SrTiO3 and KTaO3, exhibit a lattice transition with a ferro-aligned spontaneous electric polarization, P. The quantum tuning parameter is the ratio of the a/c lattice constants divided by the Debye wavevector, L2. A recent review of this ferroelectric behav- ior and more analysis is given by Rowley et al. (2014). l Conductor–insulator QPTs have been treated for a variety of materials including metal-insulator transitions (MIT) in different dimensions, Anderson localization, superconducting-insulator transitions, etc., by Dobrosavljevic et al. (2012). This is a rather old field of study that has recently been considered from the modern QPT/QCP viewpoint. l Quantum dots are nanocrystals made of semiconductor materials that are small enough to exhibit quantum mechanical behavior. When formed inPDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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