Quantum critical paraelectrics and the Casimir effect in time

Abstract

We study the quantum paraelectric-ferroelectric transition near a quantum critical point, emphasizing the role of temperature as a "finite size effect" in time. The influence of temperature near quantum criticality may thus be likened to a temporal Casimir effect. The resulting finitesize scaling approach yields 1 T 2 behavior of the paraelectric susceptibility (χ) and the scaling form, recovering results previously found by more technical methods. We use a Gaussian theory to illustrate how these temperature-dependences emerge from a microscopic approach; we characterize the classical-quantum crossover in χ, and the resulting phase diagram is presented. We also show that coupling to an acoustic phonon at low temperatures (T ) is relevant and influences the transition line, possibly resulting in a reentrant quantum ferroelectric phase.Observable consequences of our approach for measurements on specific paraelectric materials at low temperatures are discussed.

Theory of quantum paraelectrics and the metaelectric transition

“…At higher temperatures the T 2 contribution from the mean-field term dominates, which is also characteristic of quantum critical behavior and is in good agreement with recent experimental results [3]. We note that the T 2 behavior is recovered by other models, including a diagrammatic resummation [5,6], the quantum spherical model [22], renormalization group studies [23,24], a self-consistent phonon model [3], and an analogy to the temporal Casimir effect [9]. The behavior has also been observed experimentally [3,16,17].…”

“…One suggestion is that new phenomena are driven by the coupling of acoustic to optical phonons [3,6,9]. However, inspired by the ramifications of quantum fluctuations in ferromagnets [10], we show that the transverse coupling of fluctuating phonons can drive a first order metaelectric transition.…”

Dynamic Multiferroicity of a Ferroelectric Quantum Critical Point

“…We focus here on the ferroelectric (FE) QCP which is a key part of the discussion of FE behaviour, particularly in displacive quantum paraelectrics [6,7]. The behaviours that may occur near or as a result of such an FE QCP have been explored in various contexts [6][7][8][9][10][11][12][13], and the list of systems where the effects of quantum fluctuations can be observed is expanding, with temperatures up to ∼ 60K in some organic charge-transfer complexes [10,14].The concept of dynamical multiferroicity was introduced recently as the dynamical counterpart of the Dzyaloshinskii-Moriya mechanism, reflecting the symmetry between electric and magnetic properties [15]. In the Dzyaloshinskii-Moriya mechanism [16-18], ferroelectric polarisation is caused by a spatially varying magnetic structure, leading to strong coupling between ferroelectricity and magnetism [19][20][21].…”

“…We focus here on the ferroelectric (FE) QCP which is a key part of the discussion of FE behaviour, particularly in displacive quantum paraelectrics [6,7]. The behaviours that may occur near or as a result of such an FE QCP have been explored in various contexts [6][7][8][9][10][11][12][13], and the list of systems where the effects of quantum fluctuations can be observed is expanding, with temperatures up to ∼ 60K in some organic charge-transfer complexes [10,14].…”

Domain wall fluctuations in ferroelectrics coupled to strain

“…18 It has recently been suggested that unexpected behavior in the quantum phase transition of SrTiO 3 involves strain effects. 19,20 Understanding the role of the strain dynamics in ferroelectric domain walls may help explain some of these results.…”