Flexocoupling-induced phonons and ferrons in van der Waals ferroelectrics

Abstract: The contribution of flexoelectric coupling to the long-range order parameter fluctuations in ferroics can be critically important to the ferron dispersion and related polar, pyroelectric and electrocaloric properties. Here we calculate analytically the dispersion relations of soft optic and acoustic flexocoupling-induced phonons and ferrons by incorporating the flexoelectric coupling, damping, and higher elastic gradients in the Landau-Ginzburg-Devonshire free energy functional using the van der Waals uniaxial ferrielectric CuInP2S6 as an example. We analyze the changes in the flexocoupling-induced phonon and ferron spectra arising from the appearance of spatially modulated phases induced by the flexoelectric coupling. We show that the free energy landscape of CuInP2S6 determines the specific features of its phonon spectra and ferron dispersion. We also discuss the contributions of optic and acoustic flexocoupling-induced ferrons to the pyroelectric and electrocaloric responses of CuInP2S6 at low temperatures.