Displacive-type Ferroelectrics Research Articles

Microscopic theory of lattice instability in displacive type ferroelectrics

Abstract A new first principle approach to the problem of ferroelectric instability is advanced. This model-free approach permits to investigate the role of dipolar forces in the origin of ferroelectric instability in crystals of arbitrarily low ionicity possessing finite but anyhow small dielectric gap width in the electronic spectrum. In this approach, a contribution of dipolar forces to the frequencies of longwave transversal polar optic modes is deduced from the macroscopic quantities accessible from the experimental data. Some applications to IV-VI compounds and ferroelectric perovskites are presented.

Theory of the non-hydrogen-isotope effect on displacive-type ferroelectricity.

The non-hydrogen-isotope effects on ${\mathit{T}}_{\mathit{c}}$ in displacive-type ferroelectric phase transitions such as in ${\mathrm{BaTiO}}_{3}$ are discussed theoretically. Using a quantum-mechanical electron-phonon interaction model with a higher-order vertex term, we calculate the reduced force constant k${\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}_{\mathit{s}}$ of the transverse-optical phonon relating the ferroelectric phase transition. It is concluded that a light-isotope-enriched crystal shows a higher ${\mathit{T}}_{\mathit{c}}$ than a crystal with a heavier isotope, which is in agreement with the experimental Ba- and Ti-isotope effects in ${\mathrm{BaTiO}}_{3}$ recently discovered.

Common aspects of ferroelectricity and high-temperature superconductivity

Abstract The lattice dynamics of high-temperature superconducting oxides are investigated within an extended version of the polarizability model of displacive type ferroelectrics. The local non-linear electron-phonon coupling together with an electronic instability are suggested to play the driving mechanism for electron pairing in superconductors. The transformation of the classical Hamiltonian to an extended Peierls-Hubbard type model admits the investigation of parameter regimes where pairing of electrons (holes) occurs.

Rhodes-wohlfarth plot and two types of phase transition mechanism in ferroelectrics

Abstract Ratios of the paraelectric moment to the saturated moment deviate from unity in displacive type ferroelectrics. This fact is shown to be explained by a self-consistent phonon theory, which is applied to the discussion on the quantum paraelectricity.

Competition of anharmonic electron-phonon and electron-electron interaction in ferroelectric and superconducting oxides

An extended version of the polarizability model for displacive type ferroelectrics combines the local anharmonic electron-phonon interaction with an anharmonic electron-electron interaction. Two types of phase transitions are attributed to the respective double-well potentials which either yield a polar ferroelectric state (electron-phonon) or a frozen in shell-shell configuration (electron-electron) which - in a quantum mechanical analogue - can be identified as a paired electron (hole) state. The lattice dynamics of BaPb0.75Bi0.15O3 are calculated within this model and compared to experimental data. The isotope effect on both transition temperatures is investigated using the self-consistent phonon approximation. The transition temperature to the ferroelectric state increases with increasing mass while an insignificant decrease is observed for the paired electron state. The transformation of the classical Hamiltonian to an extended Peierls-Hubbard type Hamiltonian admits the determination of the parameter regimes where pairing of electrons (holes) occurs and thus possibly superconductivity may be observed.

A unified theory of ferroelectric phase transitions in analogy with the Moriya theory on itinerant electron ferromagnets

Abstract A unified theory of ferroelectric phase transitions is presented in the self-consistent phonon approximation using the analogy with the Moriya theory on itinerant electron ferromagnets. The “Rhodes-Wohlfarth ratios” are evaluated from available experimental data in ferroelectrics and the deviations of these ratios from unity in displacive type ferroelectrics are shown to be explained from this theory. The quantum effect on the dielectric susceptibility near T = 0 is studied as an application of the present theory.

Applications of the polarizability model to various displacive-type ferroelectric systems.

We apply the theory of ferroelectricity in the framework of the polarizability model, which has been presented in a previous paper, to various classes of displacive-type ferroelectrics. We show that the experimental data of temperature-dependent quantities like soft-mode frequencies and dielectric constants can be well reproduced using a very limited set of parameters. We present results for AB${\mathrm{O}}_{3}$ perovskites, IV-VI compounds, SbSI, ${\mathrm{K}}_{2}$${\mathrm{SeO}}_{4}$, hydrogen-bonded ferroelectrics, antiferroelectric compounds, and their mixed isostructural ferroelectrics.

Possibility of a common origin to ferroelectricity and superconductivity in oxides.

We describe an extension of a lattice dynamical model for displacive-type ferroelectrics which might be applied to high-temperature superconductors. The model is based on the instability of the oxygen ion O/sup 2-/, dynamically described by an on-site nonlinear electron-ion coupling, and on the valence instability of the cation (e.g., Cu(I), Cu(III)), represented by a nonlinear electron-electron interaction which provides a pairwise coupling of the electrons. The equivalent quantum-mechanical Hamiltonian describes an extended Peierls-Hubbard system. The most important outcome of the model is that a ferroelectric instability is a necessary condition for paired electron states which indicate the possibility of superconductivity. Depending on the strength of the coupling constants, either a ferroelectric or a superconducting state results.

Two Different Mechanisms of the Curie-Weiss Dielectric Susceptibility in Ferroelectrics

The Curie-Weiss law of the dielectric susceptibility χ in ferroelectrics is shown to be derived from two different mechanisms in the self-consistent phonon approximation: One is the increase in the correlation between dipoles which is related to the magnitude of the electrostatic interaction D . The other is the decrease in the mean square amplitude of the soft mode, which leads to the Curie-Weiss law through the rate of increase 1/ t 0 of an individual susceptibility with the decreasing effective “dipole moment”. The dependence of χ on temperature has been numerically computed to investigate the dependence of the Curie constant on t 0 and D . The ratios of the paraelectric moment to the saturation moment have been evaluated from available experimental data in ferroelectrics. Deviations of these ratios from unity in displacive type ferroelectrics are explained in terms of t 0 .

Polarizability mechanisms and high temperature superconductivity

We describe a lattice dynamical model for high temperature superconductors which represents an extension of a polarizability model for displacive type ferroelectrics. The model is based on the instability of the oxygen ion O 2-, dynamically described by an on-site nonlinear electron-ion coupling, and on the valence instability of the copper ion, involving Cu(I), Cu(III), represented by a nonlinear electron-electron interaction which provides a pairwise coupling of the electrons. The transformation of the classical Hamiltonian to its quantum mechanical equivalent yields a combination of different Peierls-Hubbard-like Hamiltonians.

The soft mode concept and the history of ferroelectricity

I. THE SOFT MODE CONCEPT: In the late fifties ferroelectric research underwent a serious transition. Until that time the theory of ferroelectricity has been either phenomenological or consisted of attempts to develop microscopic theories for specific atomic structures. In 1959 Cochran1 pointed out that at second order ferroelectric transitions where the dielectric constant diverges there must be a transverse optical lattice vibration mode whose frequency goes to zero as the transition is approached. This suggestion turned out to be a tremendous stimulus to ferroelectric theory and research. Many first order transitions which are close to being second order ones also exhibit mode softening as the transition is approached. Whereas the soft mode idea was at first applied only to displacive type ferroelectrics, de Gennes2 extended it to order-disorder type crystals. In these systems one finds instead of soft phonons soft (usually overdamped) pseudo-spin wave type excitations3 or anomalously long relaxation times as the transition is approached.

Two Different Mechanisms of the Curie-Weiss Dielectric Susceptibility in Displacive-Type Ferroelectrics

By the use of the analogy between the self-consistent phonon theory and the self-consistent renormalized spin fluctuation theory on itinerant electron ferromagnets, the Curie-Weiss susceptibility in displacive-type ferroelectrics is shown to consist of two different mechanisms, (a) the decrease in the mean square amplitude of the soft mode and (b) the increase in the correlation between dipoles. The ratio of the paraelectric moment to the saturated moment is calculated from experimental data in typical ferroelectrics. The great deviation of this ratio from unity in displacive-type ferroelectrics is shown to be attributed to the mechanism (a), and the appearance of the relaxation mode in dynamical spectra to (b).

Influence of permanent magnetic field on the phase transitions in some displacive type ferroelectrics and antiferroelectrics

Influence of permenant magnetic fields H = 4, 6, 8 and 10 kOe on the Curie temperature Tc of ferroelectrics BaTiO3, Pb(Sc1/2Ta1/2)O3, (Pb1/2Ba1/2)Bi2Nb2O9, K2Sr4Nb10O30, Pb5Ge3O11, and antiferroelectrics PbHfO3, Pb(Mg1/2W1/2)O3 has been investigated. Displacement of the Tc in H was discovdered, the ΔTHc (H) dependencies were found to be non-linear. Results obtained confirm the predictions of the vibronic theory of ferroelectricity.

Relation between transition temperature, atomic displacement and spontaneous strain with special reference to structural symmetry

An analysis on the structrually classified displacive type ferroelectrics when further divided on the basis of space groups and the order of transition (n), gave fairly good agreement between the observed and calculated values of transition temperature (Tc) from the knowledge of Δz, the atomic displacement. The relation between transition temperature and spontaneous strain is least affected by structural symmetry.

On coupling constant in vibronic model of the displacive type ferroelectrics

By utilizing the molecular orbitals given by Wolfram et al. for TiO6 cluster to be the foundational structure in the perovskite type ferroelectrics such as BaTiO3, the coupling constant between the electron and the ionic vibration (pseudo Jahn-Teller effect) is estimated. Further, it is found that TiO6 cluster near the surface of the crystal tends to show clearer pseudo Jahn-Teller effect than the bulk cluster.

Canonical Correlation Formalism of an Anharmonic Brownian Oscillator Based on Projection Operator Technique

Two types of quantal Langevin equations are derived on the basis of the generalized Brownian motion theory, which is proposed by Mori, in canonical correlation formalism with the aid of the quantum noise source approach. But, in order to treat strongly anharmonic crystals, simple projections which project onto a linear set of variables are unsatisfactory. Thus, we derive kinetic equations for an anharmonic lattice vibrations by using a proper projection operator. From the kinetic equation and the neutron scattering cross section calculated, an origin of the central mode, which have been observed near the Curie point of displacive-type ferroelectrics, and the roles of anharmonicities are deduced in connection with the renormalized Hamiltonian which is transformed by the displacement operator.

Oscillatory to Non-Oscillatory State Transition Due to an External Noise in Self-Sustained Oscillator

The oscillatory mode in a self-sustained oscillator is found to be suppressed by an external noise. The oscillatory to non-oscillatory state transition is analogous to the phase transition in displacive type ferroelectrics which is caused by raising temperature.

Dynamical Behaviour of Displacive-Type Ferroelectrics near the Transition Point

Dynamical behaviour of both optical and acoustic modes near the transition point of displacive-type ferroelectrics such as BaTiO 3 and SrTiO 3 is investigated theoretically with the use of the correlation function method. Particular attention is paid to the behaviour concerning the memory effect due to the critical fluctuation of polarizations and the possibility of existence of a new-type oscillation peculiar to the critical regime is shown adopting the Silverman Hamiltonian. The dynamic scaling law in the original form is shown not to be applicable to these substances and its physical origin is clarified. An extended form of this law is given.

Theory of Neutron Scattering from Lattice Vibrations

The theory of neutron scattering from lattice vibrations is redeveloped from the first principles. The expression for the scattering cross section contains factors depending on the anharmonicity explicitly, in addition to the conventional results and recent results based on the phonon Green function. Near the Curie temperature T c of displacive-type ferroelectrics a certain term in the factors depends anomalously on temperature because of softening of frequencies and becomes comparable to or even greater than the conventional term. A similar deviation near the magnetic critical point in discussed briefly. A general theory of phonons at arbitrary temperature is also developed using the correlation function method which includes the ordinary phonon theory as the limiting case of the absolute zero, and the dispersion of the Cochran mode is determined. A self-consistent method of determining the frequency of a photon is proposed.

Anomalous Behavior of Sound near the Curie Points in Displacive-Type Ferroelectrics

The dynamical behavior of the acoustic mode in displacive-type ferroelectrics such as BaTiO 3 and SrTiO 3 is studied theoretically. The phenomenological theory of sound attenuation near the phase transition point due to Landau and Khalatnikov is extended to the system in which kinetic energy plays an essential role, so as to be applicable to displacive-type ferroelectrics. The nature implied in the phenomenological theory is examined. The dependence of the attenuation constant and the velocity change of sound upon temperature and wave number is explicitly calculated on the quantum-statistical basis by employing the Silverman Hamiltonian. Thereby the occurrence of anomalies in both the attenuation constant and sound velocity near the Curie points is predicted.