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Reentrant phase in nanoferroics induced by the flexoelectric and Vegard effects

We explore the impact of the flexoelectric effect and Vegard effect (chemical pressure) on the phase diagrams, long-range polar order and related physical properties of the spherical ferroelectric nanoparticles using Landau-Ginzburg-Devonshire phenomenological approach. The synergy of these effects can lead to the remarkable changes of the nanoparticles' phase diagrams. In particular, a commonly expected transition from ferroelectric to paraelectric phase at some small critical size is absent; so that the critical size loses its sense. Contrary, the stabilization of the ferroelectric phase manifests itself by the enhancement of the transition temperature and polarization with the particle size decrease. Ferroelectric phase reentrant phenomenon was observed earlier in the tetragonal BaTiO3 nanospheres of radii 5-50 nm [Zhu et al., JAP 112, 064110 (2012)] and stayed unexplained up to now. Our calculations have shown the physical mechanism of the exciting phenomenon is the flexo-chemo-effect. Since the spontaneous flexoelectric coupling, as well as ion vacancies, should exist in any nanostructured ferroelectrics, obtained analytical results can be valid for many nanoferroelectrics, where reentrant phases appearance can be forecasted.