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

## TL;DR

This paper develops a theoretical framework using Landau Ginzburg Devonshire theory to analyze how flexoelectric coupling induces soft acoustic modes and spatially modulated phases in ferroelectrics, supported by comparison with experimental data.

## Contribution

It provides analytical expressions for acoustic phonon mode behavior and predicts conditions for soft mode emergence and phase modulation in ferroelectrics due to flexoelectric effects.

## Key findings

- Prediction of soft acoustic mode at critical flexoelectric coefficient
- Agreement of dielectric susceptibility with experimental data in specific ferroelectrics
- Semi-quantitative match with neutron scattering data in organic 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.

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Source: https://tomesphere.com/paper/1705.02512