Emergent Dipolar Textures and Properties in All-Ferroelectric Superlattices

Emergent topological dipolar textures including vortices, dipolar waves, skyrmions, merons, hopfions, and more have generated considerable interest in the ferroelectrics and wider condensed-matter physics communities. The delicate balance of electric, elastic, and gradient energies of ferroelectrics can be tailored in low-dimensional forms and nanostructures to manipulate the order parameters. Exotic functional properties (<i>e.g.</i>, coexistence of phases, chirality, negative capacitance, and emergent ultrafast dynamical responses) make them interesting candidates for devices. Ferroelectric-dielectric superlattices such as (PbTiO₃)<i>_n</i>/(SrTiO₃)<i>_n</i> have been widely studied as a model system in part due to the high depolarizing field boundary condition provided by the SrTiO₃layer. Such layers, however, limit the incorporation of such heterostructures into devices that could use the electronic characteristics of these polar topologies.<br/><br/>Looking to expand upon this rich design space, we ask a simple question: can similar emergent dipolar textures be produced in all-ferroelectric (and other) heterostructures while providing additional tunability based on the susceptibilities of the constituent layers? Here, we demonstrate the formation of polar vortices in all-ferroelectric Pb_1-xSr_xTiO₃/PbTiO₃/Pb_1-xSr_xTiO₃trilayer and (Pb_1-xSr_xTiO₃)<i>_n</i>/(PbTiO₃)<i>_n</i> superlattice structures wherein 0.5 &lt; x &lt; 1 grown on DyScO₃ (110) substrates. Unlike their counterparts with SrTiO₃, the Pb_1-xSr_xTiO₃ layers exhibit robust, in-plane ferroelectric polarization and domain structures, but still provide the appropriate boundary condition for the formation of polar vortices in the PbTiO₃ layers. We describe the manifestation of complex polar order in these structures that combines traditional ferroelectric order with emergent dipolar textures. Reciprocal space mapping studies reveal that the strontium content in the Pb_1-xSr_xTiO₃provides a fine control knob over the vortex periodicity; as supported by molecular-dynamics simulations. Furthermore, while recent studies on in-plane ferroelectric switching of polar vortices showed classical bistable switching, here, the in-plane polarization component of the vortices in the PbTiO₃ layers and the ferroelectric domains in the Pb_1-xSr_xTiO₃layers exhibit strong elastic and dipolar coupling, leading to a coercivity enhancement of the trilayer stack upon decreasing the strontium content of the Pb_1-xSr_xTiO₃. Phase-field simulations further explain the polarization arrangement in the trilayer and the system’s subsequent collective switching pathway of the two order parameters. Formation of such in-plane domains in the Pb_1-xSr_xTiO₃leads to the formation of a labyrinthine vortex arrangement, unlike the highly unidirectional vortices observed in (PbTiO₃)<i>_n</i>/(SrTiO₃)<i>_n</i> superlattices. Further, we have explored the coupling between different emergent dipolar heterostructures of the from Pb_1-xSr_xTiO₃/PbTiO₃/Pb_1-xSr_xTiO₃/SrTiO₃/PbTiO₃/SrTiO₃. Therein, the thickness of the SrTiO₃layer separating the two vortex structures controls the strength of the elastic and electric fields that extend between layers, affecting the sequence in which each trilayer would switch and the number of switching events. The result is an ability to produce low-field multi-state, four-step switching with robust retention and fatigue performance. Finally, in (Pb_1-xSr_xTiO₃)<i>_n</i>/(PbTiO₃)<i>_n</i> superlattices we have explored the dielectric tunability and out-of-plane switching and find improved tunability as a function of the chemistry of the Pb_1-xSr_xTiO₃layer, antiferroelectric-like switching due to an unraveling of the vortex phase upon application of the electric-field, and strong back switching on releasing the same leading to improvements in the low-field energy storage as compared to (PbTiO₃)<i>_n</i>/(SrTiO₃)<i>_n</i>.