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Flexoelectric effect impact on the generalized susceptibility and softphonons dispersion was not studied in the long-range ordered phases offerroics. The gap in the knowledge motivated us to establish the impact of theflexocoupling on the correlation function of the long-range order parameterfluctuations in ferroelectric phase of ferroics with local disordering sources.Within Landau-Ginzburg-Devonshire approach we obtained analytical expressionsfor the generalized susceptibility and phonon dispersion relations in theferroelectric phase. Unexpectedly, the joint action of static and dynamicflexoelectric effect induces non-diagonal components of generalizedsusceptibility, which amplitude is proportional to the convolution of thespontaneous polarization with flexocoupling constants. The flexocouplingessentially broaden the k-spectrum of generalized susceptibility and sodecreases the correlation radii, as well as leads to the additional "pushingaway" of the optical and acoustic soft mode phonon branches. The contributionof spontaneous polarization via ferroelectric nonlinearity and electrostrictionmechanisms can lead to both broadening and narrowing on the susceptibilityk-spectrum. Due to the joint action of flexoelectric coupling and spontaneouspolarization the degeneration of the transverse optic and acoustic modesdisappears in the soft phonon spectrum in a ferroelectric phase in comparisonwith the spectra in a paraelectric phase. These effects have been studiedquantitatively for ferroelectric lead zirconate titanate using realistic valuesof static and dynamic flexocouplings and cubic symmetry approximation for theelastic properties. Also we derived general expressions for correlationfunction for arbitrary symmetry, elastic and electrostrictive anisotropy.

Flexocoupling impact on the generalized susceptibility and soft phonon modes in the ordered phase of ferroics