Theory of central peak and acoustic anomaly in cubic BaTiO 3 close to ferroelectric transition

We present a Ginzburg-Landau theory on statics and dynamics of BaTiO 3 -type ferroelectrics in the paraelectric phase with the cubic structure, where the order parameter is the polarization p. Unique effects are caused by the electrostrictive (ES) coupling between p and the elastic displacement u. We show that the ES coupling gives rise to a central peak in the Fourier-Laplace transform of the displacement time-correlation function at small wave numbers. It emerges and grows with a narrow width as the transition is approached. Such central peaks have long been observed in a number of scattering experiments in various ferroelectrics, but their origin has not been well understood. From the acoustic part of the displacement dynamic correlation we obtain the frequency-dependent elastic moduli C * 11 (ω), C * 12 (ω), and C * 44 (ω), whose singular parts arise from the ES coupling, We then calculate the singular sound velocity and attenuation. In the central peak and the elastic moduli, the frequency ω appears in the scaled form ωτ D , where τ D is the Debye relaxation time in the frequency-dependent dielectric constant.