Competition between electronic ground states near a quantum critical point (QCP)--the location of a zero-temperature phase transition driven solely by quantum-mechanical fluctuations--is expected to lead to unconventional behaviour in low-dimensional systems. New electronic phases of matter have been predicted to occur in the vicinity of a QCP by two-dimensional theories, and explanations based on these ideas have been proposed for significant unsolved problems in condensed-matter physics, such as non-Fermi-liquid behaviour and high-temperature superconductivity. But the real materials to which these ideas have been applied are usually rendered three-dimensional by a finite electronic coupling between their component layers; a two-dimensional QCP has not been experimentally observed in any bulk three-dimensional system, and mechanisms for dimensional reduction have remained the subject of theoretical conjecture. Here we show evidence that the Bose-Einstein condensate of spin triplets in the three-dimensional Mott insulator BaCuSi2O6 (refs 12-16) provides an experimentally verifiable example of dimensional reduction at a QCP. The interplay of correlations on a geometrically frustrated lattice causes the individual two-dimensional layers of spin-(1/2) Cu2+ pairs (spin dimers) to become decoupled at the QCP, giving rise to a two-dimensional QCP characterized by linear power law scaling distinctly different from that of its three-dimensional counterpart. Thus the very notion of dimensionality can be said to acquire an 'emergent' nature: although the individual particles move on a three-dimensional lattice, their collective behaviour occurs in lower-dimensional space.

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A potentially new kind of glass transition may exist among phase-separated regions in La 0.215 Pr 0.41 Ca 3/8 MnO 3 . We have observed a very large damping of ultrasonic waves in the dynamically phase-segregated state of this material. This damping is connected to the motion of structural interfaces at megahertz frequencies, which is a much faster time scale than that of magnetic relaxation effects. At lower temperatures, the dynamics of the phase-separated state freeze at the glass transition. Our observations link the onset of this freezing to a sudden decrease in mobility of interfaces between structurally dissimilar phasesegregated regions.

Temperature-and field-dependent measurements of the Hall effect of pure and 4% Rh-doped URu 2 Si 2 reveal low density (0:03 hole=U) high mobility carriers to be unique to the ''hidden order'' phase and consistent with an itinerant density-wave order parameter. The Fermi surface undergoes a series of abrupt changes as the magnetic field is increased. When combined with existing de Haas-van Alphen data, the Hall data expose a strong interplay between the stability of the ''hidden order,'' the degree of polarization of the Fermi liquid, and the Fermi surface topology. DOI: 10.1103/PhysRevLett.98.016401 PACS numbers: 71.20.Lp, 71.18.+y, 71.27.+a When observed, quantum oscillatory effects such as the de Haas-van Alphen (dHvA) effect provide a definitive measure of the Fermi surface topology in metals. There are some situations, however, in which quantum oscillatory effects lose their sensitivity-at very low magnetic fields, through a thermally driven phase transition, or, more recently, at a quantum phase transition. As the predictive power of Hall theory improves, the Hall effect is becoming increasingly recognized as a viable alternative for understanding Fermi surface changes in f-electron antiferromagnets and ferromagnets tuned close to quantum criticality [1,2]. Any knowledge of the extent to which the f electrons contribute to the Fermi surface topology is of crucial importance for understanding the nature of the ordering and the fate of the heavy quasiparticles.In URu 2 Si 2 , Fermi surface measurements have the potential to assist in the identification of the ''hidden order'' phase that forms below T 0 17:5 K [3,4]. Even if the order parameter cannot be seen directly, its effect on modifying the Fermi surface topology could provide valuable information on its symmetry breaking properties. Strong correlations make this all the more challenging by both restricting the observable temperature (T) range of quantum oscillations to T T 0 [5] and inhibiting the predictive ability of band structure calculations. Under strong magnetic fields (B 0 H), the HO phase is destabilized through a cascade of first order phase transitions between consecutive field-induced phases (see Fig. 1) [6]. A strengthening of the correlations in the vicinity of a putative field-tuned quantum critical point at B m 37 T [7] is identified as a likely factor, although the changes in the Fermi surface topology have not been addressed.In this Letter, we show that Hall effect measurements extended to high magnetic fields reveal the anomalous contribution to become weak at low T. The remaining orbital Hall effect uncovers an intricate level of interplay between the Fermi surface topology and the stability of the various phases of pure and 4% Rh-doped URu 2 Si 2 [7]. At low H and T, the enhancement of the Hall coefficient and Hall angle [8][9][10] shows that the otherwise large Fermi surface is reconstructed into small high mobility pockets below T 0 in URu 2 Si 2 : a finding that is ubiquitous among

The study of abrupt increases in magnetization with magnetic field known as metamagnetic transitions has opened a rich vein of new physics in itinerant electron systems, including the discovery of quantum critical end points with a marked propensity to develop new kinds of order. However, the electric analogue of the metamagnetic critical end point, a "metaelectric" critical end point, has been rarely studied. Multiferroic materials wherein magnetism and ferroelectricity are cross-coupled are ideal candidates for the exploration of this novel possibility using magnetic-field (H) as a tuning parameter. Herein, we report the discovery of a magnetic-fieldinduced metaelectric transition in multiferroic BiMn 2 O 5 , in which the electric polarization (P) switches polarity along with a concomitant Mn spin-flop transition at a critical magnetic field H c . The simultaneous metaelectric and spin-flop transitions become sharper upon cooling but remain a continuous cross-over even down to 0.5 K. Near the P = 0 line realized at μ 0 H c ≈18 T below 20 K, the dielectric constant (ε) increases significantly over wide field and temperature (T ) ranges. Furthermore, a characteristic powerlaw behavior is found in the P(H) and ε(H) curves at T = 0.66 K. These findings indicate that a magnetic-field-induced metaelectric critical end point is realized in BiMn 2 O 5 near zero temperature. T he term "critical end point" refers to a singular point in the phase diagram of matter at the end of a first order phase line, as for example, the liquid-gas critical point of water. The importance of this special point for broad classes of matter has rapidly increased in recent years (1, 2). Not only can it provide large thermal fluctuations as a necessary ingredient for displaying universal power-law of physical quantities, but in the special case where the phase transition is suppressed to zero temperature, it can give rise to intense quantum mechanical fluctuations with a marked propensity to develop instabilities into new kinds of ground state. The latter case has been recently realized in itinerant metamagnets such as Sr 3 Ru 2 O 7 (3) and URu 2 Si 2 (4). These developments motivate a parallel search for a metaelectric critical end point. By analogy with magnetism, one might expect sudden cross-overs in electric polarization in the vicinity of a metaelectric critical endpoint to be a rather general phenomenon in (anti)ferroelectric materials under application of an electric field (E). However, to date, such metaelectric transitions induced by electric fields have been limitedly observed in specific systems such as relaxor ferroelectrics (5) and DyVO 4 with the Jahn-Teller structural distortion (6). One possible reason for the scarcity of the phenomenon is the practical difficulty of applying the large voltages required ( 1 kV) without inducing electrical breakdown. Magnetic fields may in fact be better candidates for inducing metaelectric transitions, because they not only avoid the problem of electrical breakdown but also provide a reversi...