Size effect of soft phonon dispersion law in nanosized ferroics

Using Landau-Ginsburg-Devonshire theory, we derive and analyze analytical expressions for the frequency dispersion of soft phonon modes in nanosized ferroics and perform numerical calculations for a thin SrTiO3 film. We revealed the pronounced "true" size effect in the dependence of soft phonon spatial dispersion on the film thickness and predict that it can lead to the "apparent" or "false" size effect of dynamic flexoelectric coupling constants