Flexosensitive polarization vortices in thin ferroelectric films

We present a theoretical study on the influence of flexoelectric coupling spatial distribution and temperature behavior spontaneous polarization for several types stable domain structure in thin ferroelectric films, such as stripe domains vortices. Finite-element modeling (FEM) ${\mathrm{BaTiO}}_{3}$ films analytical calculations within Landau-Ginzburg-Devonshire approach reveals that an out-of-plane component can be very sensitive to periodic quasi-2D 3D vortex-antivortex structures. However, is rather different these The increases significantly amplitude small domains, ``up'' or ``down'' direction defined by sign coefficients. Concerning pairs, their antivortices with in-plane anti\cyrchar\cyrs{}irculation have smooth wide dipolar cores through entire film, whose shape other features are almost insensitive coupling. vortices vorticity spikelike quadrupolar moment induced located near film--dead-layer interfaces. FEM results corroborated prove change coefficient leads reorientation core axial polarization, making flexosensitive similar recently introduced ``flexons'' cylindrical nanoparticles. relatively range (from 200 400 K) vortices' existence gives us confidence they observed experimentally scanning-probe nonlinear optical microscopy methods.