Flexocoupling induced soft acoustic mode and the spatially modulated phases in ferroelectrics

Abstract

Using the Landau Ginzburg Devonshire theory and scalar approximation, we derived analytical expressions for the singular points (zeros, complex ranges) of the acoustic phonon mode (A mode) frequency in dependence on the wave vector k and examined the conditions of the soft A modes appearance in a ferroelectric depending on the magnitude of the flexoelectric coefficient f and temperature T. We predict that if the magnitude of the flexocoefficient f is equal to the temperature-dependent critical value fcr(T) at the temperature T=T_IC, the A mode frequency tends to zero at k=kr_0 and the spontaneous polarization becomes spatially modulated in a temperature range T<T_IC.The comparison of calculated physical properties with measured ones are performed for some ferroelectrics with SMP phases.In particular, temperature dependence of the calculated direct and inverse static dielectric susceptibility is in an agreement with experimental data in Sn2P2(SexS1-x)6 that gives us additional background to predict flexo-coupling induced soft acoustic amplitudon-type mode in the SMP phase.The available experimental data on neutron scattering in organic incommensurate ferroelectric (CH3)3NCH2COO*CaCl2*2H2O are in a semi-quantitative agreement with our theoretical results. To quantify the theory, it is necessary to measure the frequency dependence of the A mode in a uniaxial ferroelectric with a spatially modulated phase in the temperature interval near its occurrence.

26 pages, 5 figures, 1 supplement

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Cited by in corpus (6)

• Phase diagram of ferroelectrics with tricritical and Lifshitz points at coupling between polar and antipolar fluctuations
• Hidden Symmetry of Flexoelectric Coupling
• Size effect of soft phonon dispersion law in nanosized ferroics
• Flexocoupling-induced phonons and ferrons in van der Waals ferroelectrics
• Probing phonon softening in ferroelectrics by the scanning probe microwave spectroscopy
• The Influence of Electric Field on the Anisotropic Dispersion of the Flexocoupling Induced Phonons and Ferrons in Van der Waals Ferrielectrics