Eliseev E. Size effects of polar and dielectric properties of ferroelectric nanomaterials

The phenomenological theory that studies the influence of size and correlation effects on polar properties and phase diagrams of ferroelectric nanomaterials is proposed. The Euler-Lagrange equations were solved by direct variational method. This approach leads to the free energy in the form of algebraic expression for different powers of polarization components with the coefficients dependent on film thickness or nanoparticles sizes. It was shown that the system geometry, depolarization field, surface effects and mechanical stresses significantly influence on the phase equilibrium and physical properties of thin ferroelectric and multifunctional ferroic films and nanoparticles. It was proved that the size decrease of conventional ferroelectrics (cylindrical, spherical nanoparticles or thin films) can lead to either enhancement or suppression of their ferroelectric properties as well as to the appearance of ferroelectricity in virtual ferroelectrics and antiferroelectrics. Analytical expressions for the thickness dependence of transition temperature was derived both for the conventional and incipient ferroelectrics. It was shown that although there is no ferroelectricity in the bulk incipient ferroelectrics it appears in thin film for the negative extrapolation length that is realized e.g. at positive surface stress coefficient and negative or zero misfit strain. In our consideration we came to the conclusion about thickness induced ferroelectricity in incipient ferroelectrics KTaO3 at room temperature for the thin enough films. Approximate analytical expressions for the paraelectric-antiferroelectric-ferroelectric transition temperatures dependences on film thickness, polarization gradient coefficient and extrapolation lengths were obtained. The thickness dependence of the electric field critical value that causes antiferroelectric-ferroelectric phase transition was calculated. Under the favorable conditions anti-ferroelectric phase at first transforms into the ferroelectric one and then into paraelectric phase with the film thickness decrease. Proposed theoretical consideration explains experimental results obtained in antiferroelectric PbZrO3 thin films. The approximate analytical expression for the paraelectric-ferroelectric transition temperature dependence on ferroelectric nanoparticle sizes, polarization gradient coefficient, extrapolation length, surface stress and electrostriction coefficient was derived. It was shown that the transition temperature could be higher than the one of the bulk material for nanorods and nanowires in contrast to nanodisks, where the decrease appears. In was shown that influence of flexoelectric effect in nanorods and thin pills leads to the phase transition temperature increase, as well as to the pronounced changes of nanoparticles shape.