Ferromagnetic and ferroelectric quantum phase transitions

Abstract

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

Ferromagnetic quantum criticality: New aspects from the phase diagram of LaCrGe3

“…[17]). The wing-structure is shown as first-order transition planes which terminate at quantum wing critical points.…”

“…The myriad of fascinating phenomena associated with the phase diagram of ferromagnetic systems is illustrated in Fig.1, modified from Ref. [17].…”

Quantum criticality in a uniaxial organic ferroelectric

“…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]. Quantum criticality arises purely from the atomic vibrations of the lattice and not from electronic or spin degrees of freedom.…”

“…The nature of quantum criticality in ferroelectrics is strikingly different from that found in other systems, for example magnetic systems [1,10,11]. Quantum criticality arises purely from the atomic vibrations of the lattice and not from electronic or spin degrees of freedom.…”

Spotlighting quantum critical points via quantum correlations at finite temperatures

“…Since at T = 0 there are no thermal fluctuations, these tiny changes are caused only by quantum fluctuations, whose origin can be traced back to the Heisenberg uncertainty principle. Some well-known examples of QPTs are the paramagnetic-ferromagnetic transition in some metals [2], the superconductor-insulator transition [3], and superfluid-Mott insulator transition [4].…”