Dependence of Soft Phonon Spectra on Flexoelectric Cou-pling in Ferroelectrics

Abstract

Analytical expressions describing the frequency dispersion of the soft transverse acoustic (TA)and optic (TO) phonon modes in uniaxial ferroelectrics, as well as their dependence on theflexoelectric coupling constant f, have been analyzed in the framework of the Landau–Ginzburg–Devonshire theory. A critical behavior of the TA mode with respect to the f magnitude isrevealed.

Size effect of soft phonon dispersion in nanosized ferroics

“…The degeneration of the transverse optic and acoustic modes disappears in the ferroelectric phase in comparison with the paraelectric phase due to the synergy of flexoelectric coupling and ferroelectric nonlinearity. The soft acoustic modes and spatially modulated phases (SPM) can be induced by the flexoelectric coupling in ferroics [22,58,59] and the surface acoustic waves can propagate in nonpiezoelectric solids due to the static and dynamic flexoelectric effects [60].…”

“…Let us underline that the theoretical results [56][57][58][59][60], which can be important for the theoretical analyses of the neutron, Raman and Brillouin scattering experiments [22], have been obtained for unconfined [56][57][58][59] or semi-infinite [60] ferroics. However, to the best of our knowledge, the theoretical description of the phonon dispersion in nanoferroics (e.g.…”

“…The film is placed between two ideally conducting electrodes and clamped to a matched substrate that does not produce a misfit strain in the film. The only nonzero components of the long-range order parameters are ycomponents of electric polarization In contrast to the three-component case [56], the one-component approximation for polarization and strain allows considering only the lowest transverse optic and acoustic soft phonon modes in ferroics [57][58][59], because 0 = P div r and 0 = U div r in the case. As it was shown in Refs.…”