  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.
