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We report first-principle atomistic simulations on the effect of local straingradients on the nanoscale domain morphology of free-standing PbTiO$_3$ultrathin films. First, the ferroelectric properties of free films at theatomic level are reviewed. For the explored thicknesses (10 to 23 unit cells),we find flux-closure domain structures whose morphology is thickness dependent.A critical value of 20 unit cells is observed: thinner films show structureswith 90$^\circ$ domain loops, whereas thicker ones develop, in addition,180$^\circ$ domain walls, giving rise to structures of the Landau-Lifshitztype. When a local and compressive strain gradient at the top surface isimposed, the gradient is able to switch the polarization of the downwarddomains, but not to the opposite ones. The evolution of the domain pattern as afunction of the strain gradient strength consequently depends on the filmthickness. Our simulations indicate that in thinner films, first the 90$^\circ$domain loops migrate towards the strain-gradient region, and then thepolarization in that zone is gradually switched. In thicker films, instead, theswitching in the strain-gradient region is progressive, not involvingdomain-wall motion, which is attributed to less mobile 180$^\circ$ domainwalls. The ferroelectric switching is understood based on the knowledge of thelocal atomic properties, and the results confirm that mechanicalflexoelectricity provides a means to control the nanodomain pattern inferroelectric systems.

Strain-gradient-induced switching of nanoscale domains in free-standing ultrathin films