Crystal stability and the theory of ferroelectricity part II. Piezoelectric crystals

In Part I the dielectric properties of cubic crystals with atoms in special positions were discussed, with particular reference to crystals which become unstable against a transverse optic mode of vibration of long wavelength. These considerations are now extended to crystals of general symmetry, and it is shown that the anomalous temperature dependence of certain dielectric, piezoelectric, and elastic constants in the paraelectric phase of ferroelectric crystals can be described and correlated in a very natural way in terms of crystal stability. A formula relating the dispersion frequency of the anomalous dielectric constant to the spontaneous polarization and the displacements of the atoms in a ferroelectric transition, previously derived for barium titanate, is generalized. The transitions in KH₂PO₄ and in NH₄H₂PO₄, and the ordering of the hydrogen atoms in these crystals, are discussed qualitatively in terms of the stability of normal modes of vibration.     

Intermediate coupling theory of electronic ferroelectricity

We calculate the quantum phase diagram of an extended Falicov-Kimball model for one- and two-dimensional systems in the intermediate coupling regime. Even though some features of the phase diagram are obtained analytically, the main results are calculated with a constrained path Monte Carlo technique. We find that this regime is dominated by a Bose-Einstein condensation of excitons with a built-in electric polarization. The inclusion of a finite hybridization between the bands removes the condensate but reinforces the ferroelectricity.     

Crystal field theory and the Shubnikov point groups

Two pieces of theory which have so far remained unconnected, crystal field theory and the theory of corepresentations of non-unitary groups, are brought together here for the study of the splitting of atomic energy levels in a crystalline field with the symmetry of one of the magnetic (Shubnikov) point groups. The cases of the various possible relative strengths of the crystalline field and of spin-orbit coupling are considered.

Tables are presented which enable the splitting of any atomic energy level to be obtained very easily in a crystalline field with the symmetry of any one of the 58 magnetic point groups. Examples of the use of these tables are given.

A discussion is given of the relevance of Kramers' theorem to the energy levels of electrons in surroundings with the symmetry of any one of the 58 magnetic point groups.     

Electronic ferroelectricity in the falicov-kimball model

I show that a spontaneous electric polarization exists in the solution of the Falicov-Kimball model by mapping the strong coupling limit of this Hamiltonian into an xxz spin 1/2 model with a magnetic field. In this way, I determine the phase diagram of the strongly interacting model and show the existence of a transition to a mixed-valence regime containing two phases: an orbitally ordered state and a Bose-Einstein condensation of excitons with a built-in electric polarization.     

Local suppression of ferroelectricity at PbTiO3 surface steps: a density functional theory study

Ab initio (first-principles) density functional theory (DFT) calculations are performed within the local density approximations (LDA) to investigate the ferroelectricity at PbTiO(3) surface steps consisting of (001) and (100) surfaces with a spontaneous polarization along [100]. For both the PbO- and TiO(2)-terminated surface steps, the [100] polarization is suppressed and the [001] polarization appears at their upper terraces, which results in a rotation of polarizations at the surface steps. The polarization rotation is induced by the local variation of the covalent Pb-O bond due to the charge redistribution at the surface steps. Furthermore, we investigate the interaction of the surface steps. Although surface steps with the same polarization configuration exhibit little interaction, steps of different types interact with each other strongly, suppressing the ferroelectricity, especially on the upper terrace.     

Piezoelectricity and ferroelectricity in polyvinylidene fluoride

The dielectric, elastic and electrostrictive constants of polyvinylidene fluoride (pvdf) are influenced by thermal molecular motion, particularly at the glass transition temperature. High temperature poling is caused by both dipolar orientation and space-charge redistribution. Low temperature poling and dielectric hysteresis under a strong electric field are caused by crystalline dipolar orientation. The ferroelectric nature of pvdf is confirmed by x-ray and infrared analyses. The piezoelectric constants for a single crystal are theoretically calculated in agreement with experimental values. The piezoelectricity in poled films originates from the intrinsic piezoelectricity of the crystal and the residual polarization in the crystal coupled with electrostriction and dimensional change in the non-crystalline phase.     

Competition between ferroelasticity and ferroelectricity

In the crystals of the KH₂PO₄ family, the properties of ferroelasticity and ferroelectricity strongly interact. It is for example possible to change by application of an electric field the orientation of the phase front between high temperature and low temperature phases, and to observe the rotation of reticular planes during an electric hysteresis cycle drawing. These phenomena, as the existence of a quasi constant domain width illustrate the particular competition between ferroelasticity and ferroelectricity in these compounds.     

Computational studies on magnetism and ferroelectricity

Magnetics, ferroelectrics, and multiferroics have attracted great attentions because they are not only extremely important for investigating fundamental physics, but also have important applications in information technology. Here, recent computational studies on magnetism and ferroelectricity are reviewed. We first give a brief introduction to magnets, ferroelectrics, and multiferroics. Then, theoretical models and corresponding computational methods for investigating these materials are presented. In particular, a new method for computing the linear magnetoelectric coupling tensor without applying an external field in the first principle calculations is proposed for the first time. The functionalities of our home-made Property Analysis and Simulation Package for materials (PASP) and its applications in the field of magnetism and ferroelectricity are discussed. Finally, we summarize this review and give a perspective on possible directions of future computational studies on magnetism and ferroelectricity.     

Group theory and kink stability equations

Starting from Schrödinger equations withSU(2) group-theoretic potentials, we consider a general family of kinks labeled by two (half-)integers (l, n) with ¦n¦l. A particular choice ofn=0,l=L (L positive integer) leads to a generalL-family, whereL=1 corresponds to sine-Gordon theory, whileL=2 represents the ( ⁴)₁₊₁ model. The ( ⁶)₁₊₁ model can also be recovered withl=3/2,n=–1/2, a particular case of theories labeled byl andn such thatl-n=2 which possess simple kink solutions. We also discuss one-loop order corrections to the kink masses in supersymmetric versions of theL-family. As a byproduct, we obtain the SUSY renormalization of the so-called parameter in sine-Gordon theory.     

Investigation of the frustration between ferroelectricity and antiferroelectricity in smectics

A molecular-statistical theory that describes the smectic phases with frustration between the ferroelectric and antiferroelectric ones has been developed. The molecular model is used to estimate the mean-field parameters responsible for the formation of complex smectic phases with long periods. A general phase diagram is constructed and the helix pitch is estimated in all phases. The results obtained are compared with the experimental ones.     

Topology and ferroelectricity in group-V monolayers

The group-V monolayers(MLs) have been studied intensively after the experimental fabrication of two-dimensional(2D) graphene and black phosphorus. The observation of novel quantum phenomena, such as quantum spin Hall effect and ferroelectricity in group-V elemental layers, has attracted tremendous attention because of the novel physics and promising applications for nanoelectronics in the 2D limit. In this review, we comprehensively review recent research progress in engineering of topology and ferroelectricity, and several effective methods to control the quantum phase transition are discussed. We then introduce the coupling between topological orders and ferroelectric orders. The research directions and outlooks are discussed at the end of the perspective. It is expected that the comprehensive overview of topology and ferroelectricity in 2D group-V materials can provide guidelines for researchers in the area and inspire further explorations of interplay between multiple quantum phenomena in low-dimensional systems.     

Ion specificity and the theory of stability of colloidal suspensions

A theory is presented which allows us to accurately calculate the critical coagulation concentration of hydrophobic colloidal suspensions. For positively charged particles, the critical coagulation concentrations follow the Hofmeister (lyotropic) series. For negatively charged particles, the series is reversed. We find that strongly polarizable chaotropic anions are driven towards the colloidal surface by electrostatic and hydrophobic forces. Within approximately one ionic radius from the surface, the chaotropic anions lose part of their hydration sheath and become strongly adsorbed. The kosmotropic anions, on the other hand, are repelled from the hydrophobic surface. The theory is quantitatively accurate without any adjustable parameters. We speculate that the same mechanism is responsible for the Hofmeister series that governs stability of protein solutions.     

A nonperturbative stability theory of quantum field theory models

A nonperturbative method of analysis of the stability problem of quantum field theory models is proposed. The method consists in the systematic analysis of the functional dependence on boson field B of the effective boson Lagrangian S^eff(B) consisting of the fermion term S_l^F(B), constraint term S_l^FP(B) and the boson self-interaction term S_l(B). A new heat kernel representation for S_l^F(B) is derived in which counterterms are calculated in the explicit functional form by means of the analytic renormalization method. Using these results the instabillity of Yukawa₄, four-Fermi₄, and the massive Gürsey models is demonstrated.