Flexoelectricity induced increase of critical thickness in epitaxial   ferroelectric thin films
  Flexoelectricity describes the coupling between polarization and strain/stress gradients in insulating crystals. In this paper, using the Landau-Ginsburg-Devonshire phenomenological approach, we found that flexoelectricity could increase the theoretical critical thickness in epitaxial BaTiO3 thin films, below which the switchable spontaneous polarization vanishes. This increase is remarkable in tensile films while trivial in compressive films due to the electrostriction caused decrease of potential barrier, which can be easily destroyed by the flexoelectricity, between the ferroelectric state and the paraelectric state in tensile films. In addition, the films are still in a uni-polar state even below the critical thickness due to the flexoelectric effect. 
Hao Zhou, Jiawang Hong, Yihui Zhang, Faxin Li, Yongmao Pei and Daining   Fang
cond-mat.mtrl-sci