Flexo-Strain Engineering of Phonons and Ferrons in Thin Films of Van der Waals Ferrielectrics

The influence of the flexoelectric coupling on the fluctuations of electric polarization and elastic strains can lead to the principal changes of the dispersion law of soft optical and acoustic phonons and ferrons in a bulk van der Waals ferrielectrics. Since the size, gradient and strain effects determine phase diagrams and polarization behavior in thin films, it is reasonable to assume that the flexocoupling and mismatch strains should have a strong influence on the dispersion of phonons and ferrons in thin films of van der Waals ferroelectrics. Using the Landau-Ginzburg-Devonshire approach, in this work we reveal that the dispersion of soft phonons and ferrons is strongly dependent on the sign and magnitude of elastic strains, which originate from the lattice constants mismatch in thin strained films of van der Waals ferrielectric CuInP2S6. In particular, the frequency of acoustic phonons and ferrons tends to zero at nonzero wavevectors k>k_cr, where the critical value of the wavevector k_cr is determined by the mismatch strain, flexoelectric coupling strength and temperature. Zeroing of the acoustic phonon frequency, that appears with increase of tensile strains, indicates a possible emergence of a spatially modulated incommensurate polar phase induced by the flexo-strain effects. Analytical results, derived in this work, open the way for flexo-strain engineering of soft phonon and ferron dispersion in thin films of van der Waals ferrielectrics.