Roto-flexoelectric coupling impact on the phase diagrams and   pyroelectricity of thin SrTiO3 films
  The influence of the flexoelectric and rotostriction coupling on the phase diagrams of ferroelastic-quantum paraelectric SrTiO3 films was studied using Landau-Ginzburg-Devonshire (LGD) theory. The phase diagrams in coordinates temperature - film thickness were calculated for different epitaxial misfit strains. Tensile misfit strains stimulate appearance of the spontaneous out-of-plane structural order parameter (displacement vector of an appropriate oxygen atom from its cubic position) in the structural phase. Compressive misfit strains stimulate appearance of the spontaneous in-plane structural order parameter. Gradients of the structural order parameter components, which inevitably exist in the vicinity of film surfaces due to the termination and symmetry breaking, induce improper polarization and pyroelectric response via the flexoelectric and rotostriction coupling mechanism. Flexoelectric and rotostriction coupling results in the roto-flexoelectric field that is antisymmetric inside the film, small in the central part of the film, where the gradients of the structural parameter are small, and maximal near the surfaces, where the gradients of the structural parameter are highest. The field induces improper polarization and pyroelectric response. Penetration depths of the improper phases (both polar and structural) can reach several nm from the film surfaces. An improper pyroelectric response of thin films is high enough to be registered with planar-type electrode configurations by conventional pyroelectric methods. 
A.N. Morozovska, E.A. Eliseev, S.L. Bravina, A.Y. Borisevich, and S.V.   Kalinin
cond-mat.mtrl-sci