Flexocoupling impact on the kinetics of polarization reversal
  The impact of flexoelectric coupling on polarization reversal kinetics and space charge dynamics in thin films of ferroelectric-semiconductors has been theoretically studied. The relaxation-type Landau-Khalatnikov equation together with the Poisson equation and the theory of elasticity equations have been used to calculate in a self-consistent way the spatial-temporal development of ferroelectric polarization, electric potential and space charge, elastic stresses, strains and their gradients. The analysis of the obtained results reveals a moderate increase of the flexocoupling influence on the polarization, elastic strain, electric potential and space charge distribution dynamics with the decrease of a ferroelectric film thickness. In contrast, the dependence of polarization switching time on the applied electric field is strongly affected by the flexocoupling strength. The polarization reversal process consists typically of two stages, the first stage has no characteristic time, while the second one exhibits a switching time strongly dependent on the applied electric field. 
Ivan S. Vorotiahin, Anna N. Morozovska, Eugene A. Eliseev, Yuri A.   Genenko
cond-mat.mtrl-sci