Ferroelectric quantum criticality

Paramagnets on the border of ferromagnetism at low temperatures are more subtle and complex than anticipated by the conventional theory of quantum critical phenomena. Could quantum criticality theory be more relevant in the corresponding case of quantum paraelectrics on the border of ferroelectricity? To address this question we have investigated the temperature dependence of the dielectric function of the displacive quantum paraelectrics SrTiO 3 , oxygen-18 substituted SrTiO 3 and KTaO 3 . In all of these materials on the border of ferroelectricity we observe non-classical T 2 temperature dependencies of the inverse dielectric function below 50 K, followed by anomalous upturns below a few kelvin extending into the millikelvin range. This non-classical behaviour can be understood quantitatively without adjustable parameters in terms of quantum criticality theory when extended to include the effects of long-range dipolar interactions and the coupling of the electric polarization field with acoustic phonons. The quantum critical regime in displacive ferroelectrics is thus strikingly different from that in the better-known ferromagnetic counterparts and offers unexpected prospects in the field of quantum phase transitions. Quantum criticality is often found in metallic compounds that are close to being magnetic. What about insulators in which the electric moments are fluctuating? These too can be described by the same framework—over a wider temperature range than in quantum critical metals.