Impact of the Flexoelectric Coupling and Electrostriction on the Dispersion of Soft Phonon Modes and Neutron Scattering in Ferroelectrics

Abstract

Within the Landau–Ginzburg–Devonshire (LGD) theory framework, the impact of the flexocoupling and electrostriction on the soft phonon dispersion and neutron scattering spectra is analyzed, and analytical expressions are derived. The impact of the higher gradient term in the LGD functional is studied analytically. The existence of incommensurate modulations in a temperature interval higher than the Curie temperature TC, but lower than the temperature of incommensurate phase transition TIC, TC < T < TIC, and under the condition of the flexocoefficient magnitude ranging over the critical value, |f| > fcr(T), is established. The influence of the dynamic flexocoefficient M, suggested in [1], on phonon spectra is studied. We consider various parameters of the free energy functional; especially, we have discovered a significant contribution of the electrostriction to the appearance of a commensurate phase. In the recent years, the various methods based on the neutron scattering acquire more applications to study phonons in solid crystals. We have analyzed neutron scattering spectra and shown that theoretical predictions are in a very good agreement with observed data.