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Ferroelectric and dielectric properties of polydomain (twinned) single-crystalline $\mathrm{Pb}({\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x}){\mathrm{O}}_{3}$ thin films are described with the aid of a nonlinear thermodynamic theory, which has been developed recently for epitaxial ferroelectric films with dense laminar domain structures. For $\mathrm{Pb}({\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x}){\mathrm{O}}_{3}$ (PZT) films with compositions $x=0.9$, 0.8, 0.7, 0.6, 0.5, and 0.4, the ``misfit strain-temperature'' phase diagrams are calculated and compared with each other. It is found that the equilibrium diagrams of PZT films with $x\ensuremath{\geqslant}0.7$ are similar to the diagram of ${\mathrm{PbTiO}}_{3}$ films. They consist of only four different stability ranges, which correspond to the paraelectric phase, single-domain tetragonal ferroelectric phase, and two pseudotetragonal domain patterns. In contrast, at $x=0.4$, 0.5, and 0.6, the equilibrium diagram displays a rich variety of stable polarization states, involving at least one monoclinic polydomain state. Using the developed phase diagrams, the mean out-of-plane polarization of a poled PZT film is calculated as a function of the misfit strain and composition. Theoretical results are compared with the measured remanent polarizations of PZT films grown on ${\mathrm{SrTiO}}_{3}$. Dependence of the out-of-plane dielectric response of PZT films on the misfit strain in the heterostructure is also reported.

physical review. b, condensed matter and materials physics

Polarization states of polydomain epitaxial<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Pb</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>Zr</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>Ti</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>thin films and their dielectric properties

Polarization states of polydomain epitaxialPb(Zr1−xTix)O3thin films and their dielectric properties