Materials tuned to the neighbourhood of a zero temperature phase transition often show the emergence of novel quantum phenomena. Much of the effort to study these new effects, like the breakdown of the conventional Fermi-liquid theory of metals has been focused in narrow band electronic systems. Ferroelectric crystals provide a very different type of quantum criticality that arises purely from the crystalline lattice. In many cases the ferroelectric phase can be tuned to absolute zero using hydrostatic pressure or chemical or isotopic substitution. Close to such a zero temperature phase transition, the dielectric constant and other quantities change into radically unconventional forms due to the quantum fluctuations of the electrical polarization. The simplest ferroelectrics may form a text-book paradigm of quantum criticality in the solid-state as the difficulties found in metals due to a high density of gapless excitations on the Fermi surface are avoided. We present low temperature high precision data demonstrating these effects in pure single crystals of SrTiO 3 and KTaO 3 . We outline a model for describing the physics of ferroelectrics close to quantum criticality and highlight the expected 1/T 2 dependence of the dielectric constant measured over a wide temperature range at low temperatures. In the neighbourhood of the quantum critical point we report the emergence of a small frequency independent peak in the dielectric constant at approximately 2 K in SrTiO 3 and 3 K in KTaO 3 believed to arise from coupling to acoustic phonons. Looking ahead, we suggest that ferroelectrics could be used as systems in which to controllably build in extra complexity around the quantum critical point. For example, in ferroelectric or antiferroelectric materials supporting mobile charge carriers, quantum paraelectric fluctuations may mediate new effective electron-electron interactions giving rise to a number of possible states such as superconductivity.The study of quantum matter at low temperatures has given rise to a fascinating and often surprising catalogue of phenomena important to our understanding of nature 1 and to technological development 2 . In particular, the study of materials close to a continuous low temperature phase transition or so called quantum critical point forms an important branch of research within condensed matter physics. A chief reason for this is that close to such a transition, materials become highly degenerate and new states of matter are frequently found to emerge. In fact, it turns out that many materials end up being close to or within the quantum critical regime. This is because quantum critical phenomena can affect materials over a wide range of temperatures, pressures and other variables. In electrically conducting materials, the standard model of the metallic state, Landau's Fermi liquid theory is seen to breakdown close to the low temperature boundary between a magnetic and paramagnetic phase and is replaced with other forms of novel quantum liquid. For example, in some weakly magnet...

The emergence of complex and fascinating states of quantum matter in the neighborhood of zero temperature phase transitions suggests that such quantum phenomena should be studied in a variety of settings. Advanced technologies of the future may be fabricated from materials where the cooperative behavior of charge, spin and current can be manipulated at cryogenic temperatures. The progagating lattice dynamics of displacive ferroelectrics make them appealing for the study of quantum critical phenomena that is characterized by both space- and time-dependent quantities. In this key issues article we aim to provide a self-contained overview of ferroelectrics near quantum phase transitions. Unlike most magnetic cases, the ferroelectric quantum critical point can be tuned experimentally to reside at, above or below its upper critical dimension; this feature allows for detailed interplay between experiment and theory using both scaling and self-consistent field models. Empirically the sensitivity of the ferroelectric T 's to external and to chemical pressure gives practical access to a broad range of temperature behavior over several hundreds of Kelvin. Additional degrees of freedom like charge and spin can be added and characterized systematically. Satellite memories, electrocaloric cooling and low-loss phased-array radar are among possible applications of low-temperature ferroelectrics. We end with open questions for future research that include textured polarization states and unusual forms of superconductivity that remain to be understood theoretically.

The occurrence of superconductivity in doped SrTiO3 at low carrier densities points to the presence of an unusually strong pairing interaction that has eluded understanding for several decades. We report experimental results showing the pressure dependence of the superconducting transition temperature, Tc, near to optimal doping that sheds light on the nature of this interaction. We find that Tc increases dramatically when the energy gap of the ferroelectric critical modes is suppressed, i.e., as the ferroelectric quantum critical point is approached in a way reminiscent to behaviour observed in magnetic counterparts. However, in contrast to the latter, the coupling of the carriers to the critical modes in ferroelectrics is predicted to be small. We present a quantitative model involving the dynamical screening of the Coulomb interaction and show that an enhancement of Tc near to a ferroelectric quantum critical point can arise due to the virtual exchange of longitudinal hybrid-polar-modes, even in the absence of a strong coupling to the transverse critical modes.

BaFe12O19 is a popular M-type hexaferrite with a Néel temperature of 720 K and is of enormous commercial value ($3 billion/year). It is an incipient ferroelectric with an expected ferroelectric phase transition extrapolated to lie at 6 K but suppressed due to quantum fluctuations. The theory of quantum criticality for such uniaxial ferroelectrics predicts that the temperature dependence of the electric susceptibility χ diverges as 1/T3, in contrast to the 1/T2 dependence found in pseudo-cubic materials such as SrTiO3 or KTaO3. In this paper we present evidence of the susceptibility varying as 1/T3, i.e. with a critical exponent γ = 3. In general γ = (d + z – 2)/z, where the dynamical exponent for a ferroelectric z = 1 and the dimension is increased by 1 from deff = 3 + z to deff = 4 + z due to the effect of long-range dipole interactions in uniaxial as opposed to multiaxial ferroelectrics. The electric susceptibility of the incipient ferroelectric SrFe12O19, which is slightly further from the quantum phase transition is also found to vary as 1/T3.

A quantum critical point arises at a continuous transformation between distinct phases of matter at zero temperature. Studies in antiferromagnetic heavy-fermion materials have revealed that quantum criticality has several classes, with an unconventional type that involves a critical destruction of the Kondo entanglement. To understand such varieties, it is important to extend the materials basis beyond the usual setting of intermetallic compounds. Here we show that a nickel oxypnictide, CeNiAsO, exhibits a heavy-fermion antiferromagnetic quantum critical point as a function of either pressure or P/As substitution. At the quantum critical point, non-Fermi-liquid behaviour appears, which is accompanied by a divergent effective carrier mass. Across the quantum critical point, the low-temperature Hall coefficient undergoes a rapid sign change, suggesting a sudden jump of the Fermi surface and a destruction of the Kondo effect. Our results imply that the enormous materials basis for the oxypnictides, which has been so crucial in the search for high-temperature superconductivity, will also play a vital role in the effort to establish the universality classes of quantum criticality in strongly correlated electron systems.

Tris-sarcosine calcium chloride (TSCC) is a highly uniaxial ferroelectric with a Curie temperature of approximately 130K. By suppressing ferroelectricity with bromine substitution on the chlorine sites, pure single crystals were tuned through a ferroelectric quantum phase transition. The resulting quantum critical regime was investigated in detail -the first time for a uniaxial ferroelectric and for an organic ferroelectric -and was found to persist up to temperatures of at least 30K to 40K. The nature of long-range dipole interactions in uniaxial materials, which lead to non-analytical terms in the free-energy expansion in the polarization, predict a dielectric susceptibility varying as 1/T 3 close to the quantum critical point. Rather than this, we find that the dielectric susceptibility varies as 1/T 2 as expected and observed in better known multi-axial systems. We explain this result by identifying the ultra-weak nature of the dipoles in the TSCC family of crystals. Interestingly we observe a shallow minimum in the inverse dielectric function at low temperatures close to the quantum critical point in paraelectric samples that may be attributed to the coupling of quantum polarization and strain fields. Finally we present results of the heat capacity and electro-caloric effect and explain how the time dependence of the polarization in ferroelectrics and paraelectrics should be considered when making quantitative estimates of temperature changes induced by applied electric fields.There has been a great deal of interest recently in the field of ferroelectric quantum phase transitions [1,2]. A chief reason for this is that the properties of ferroelectrics may be readily tuned with gate voltages and strains, which make quantum ferroelectrics and paraelectrics particularly suited for applications in advanced cryogenic electronics. Highlighting SrTiO 3 as an example, one sees that a pristine optically transparent insulator with a band gap of more than 3eV, and a static dielectric constant greater than 10 4 , may be tuned through an insulator to metal to superconductor transition and back again with the application of just a few volts [3,4]. On the other hand modest strains [5], chemical doping [6] or isotope substitution [1,7], can induce ferroelectricity in an otherwise paraelectric ground state. Ferroelectric quantum critical fluctuations have been observed up to temperatures higher than those often seen in other systems, and over a wide range of tuning parameters. Proximity to a displacive ferroelectric quantum critical point where the transverse optical phonon frequency becomes very small, and the dielectric function can rise to very high values, is believed to be of importance in understanding superconductivity in materials such as chemically doped [8] or ionic-liquid-gated SrTiO 3 [7] and KTaO 3 [4], and in oxide interface materials [9] to name just a few.The nature of quantum criticality in ferroelectrics is strikingly different from that found in other systems, for example magnetic systems [1,10,11]. Quantu...

The Gd3Ga5-xAlxO12 (0 ≤ x ≤ 5) solid solution has been prepared using ceramic synthesis routes and the structural and magnetic properties were investigated using x-ray diffraction, magnetic susceptibility, χ, and isothermal magnetisation, M(H), measurements. Our results indicate a contraction of the unit cell and more significant antiferromagnetic interactions as x increases. Despite the decrease in the magnetic polarisation on the application of a field and the corresponding decrease in the change in the magnetic entropy, ΔS, we find that Gd3Al5O12 has a significantly higher observed (17%) and theoretical (14%) ΔS per unit mass than Gd3Ga5O12. The theoretical increase in ΔS per unit volume (7%) is offset by the increased antiferromagnetic interactions in Gd3Al5O12. The differences in ΔS are driven by a decrease in both the mass and the density as Al ions replace Ga ions. These results highlight the importance of changes to the crystal structure when considering materials for solid state magnetic cooling.

The applicability of mean field models of ferroelectric and ferromagnetic quantum critical points is examined for a selection of d-electron systems. Crucially, we find that the tendency of the effective interaction between critical fluctuation modes to become attractive and anomalous as the ordering temperatures tend to absolute zero results in particularly complex and striking phenomena. The multiplicity of quantum critical fields at the border of metallic ferromagnetism, in particular, is discussed here. 1 Introduction We consider the nature of quantum phase transitions driven by changes in composition of materials or changes in applied pressure, magnetic field or electric field in the low temperature limit. Quantum phase transitions exhibit surprisingly subtle and complex behaviour even in comparatively simple examples of cubic ferroelectric materials and ferromagnetic metals of high purity, which will be the main focus of this article.Early descriptions of quantum critical points (QCP), developed independently in ferroelectric materials [1] and ferromagnetic metals [2][3][4][5][6] in the 1970s, were based essentially on f 4 -quantum field models. They differ from the Ginzburg-Landau-Wilson models of classical critical phenomena by the inclusion of the dynamics of the order parameter field f(r,t), which represents a coarse-grained electric or magnetic polarization as a function of spatial coordinate r and temporal coordinate t (the imaginary time, which has a finite range at non-zero temperatures, 0 < t < h=k B T) [7]. The inclusion of the thermal coordinate increases the relevant dimension from the spatial dimension d to the effective dimension d eff ¼ d þ z, where z is the dynamical exponent defining the dispersion relation, i.e., the wavevector dependence of the frequency spectrum of fluctuations of the field f at small wavevectors (see x2).The self-consistent-field approximation, which applies in the case of classical critical phenomena for d > 4 in the classical f 4 model, might apply under a less restrictive condition d > 4 -z in the f 4 quantum treatment of critical