Quantum Fluctuation Of The Dielectric Properties Of Several Threatened Ferroelectrics

Incipient ferroelectrics or quantum paraelectrics constitutes a very unique subject of current interest due to its high value of dielectric constant, low dielectric losses and high degree of tenability by the external electric field and temperature. At high temperatures, the dielectric response of incipient ferroelectrics exhibits a Curie-Weiss law. However, instead of decreasing further at low temperature, its dielectric constant saturates at a high value. The saturation of the dielectric susceptibility has been attributed to large ground state quantum fluctuations due to the zero-point vibrations, which suppress the polar long-range ordering. This unusual feature was mainly investigated on perovskites like strontium titanate (SrTiO₃). Small perturbations (electric fields, elastic strains and impurities) can counteract the fluctuations and induce ferroelectricity at low temperature. Thus a great variety of observed phenomena makes the subject still very attractive both for theoretical and experimental investigations.Effective field approach has been approved a successful method to describe the phase transition property in ferroelectrics. It is simple in mathematics but rich in physics method. In its origin version, this method has already been applied to the second order phase transition properties in homogeneous ferroelectric systems. With including higher order terms of polarizations, properties in first order phase transitions can be also well described. With inclusion of zero-point energy, this approach can be extended to describe the dielectric behavior of quantum paraelectrics.Barrett formula is used to describe the saturation of the dielectric susceptibility of quantum ferroelectrics and their solid solutions at low temperature, which has successfully been fitted to the dielectric susceptibility of many quantum paraelectrics. However by fitting Barrett formula with the dielectric constant of SrTiO₃, it fails to fit the experimental data in the wholetemperature range, and by fitting the Barrett formula with the experimental data of CaTiC>3, a large negative Curie temperature has been obtained, which is unreasonable in physics.This work investigated the affections of quantum fluctuation on the dielectric behavior of two quantum paraelectrics SrTiO3, CaTiC>3 and their dilute solid solutions Sri.xCaxTiO3 from theoretical side using effective field approach including zero-point energy. It has been found that, when the zero point energy which responses for the saturation of dielectric constant of SrTiC>3 at low temperature changes from a small value at low temperature to a large value at high temperature, this can lead to a very good quantitative fitting of Barrett formula with experimental data. For CaTiC>3, the effect of quantum fluctuation on its dielectric behavior can be described by the Barrettt formula fairly well when the zero-point energy in CaTiCb changes with temperature as in SrTiCb does, and a positive Curie temperature be obtained.There are four parameters in the obtained temperature-dependent formula of zero-point energy. It was investigated that the effects of these parameters on both the quantum fluctuation and dielectric behavior, and observed that the main factors which influence the ferroelectricity are the zero-point energies at low temperatures and higher temperatures. When the zero-point energy at low temperatures is larger than the zero-point energy at higher temperatures, the ferroelectric phase transition will occurs.The dielectric behavior of doped incipient ferroelectrics is complex. Sri.xCaxTiO3 mixed crystals show three distinct regimes with increasing concentration of Ca2+: the quantum paraelectric state, XY quantum ferroelectricity and a diffusive or random-field domain state. Amusing zero-point energy is temperature dependent as the above conclusion, Barrett formula can fit with experimental data very well for the three states in the whole temperature range. The concentration of Ca2+ has clear effect on zero-point energy. These indicate that quantum fluctuation has impact on quantum ferroelectrics and diffusive ferroelectrics too.