Mechanical Rippling for Diverse Ferroelectric Topologies in Otherwise Nonferroelectric SrTiO_{3} Nanofilms

Polar topological structures such as skyrmions and merons have become an emerging research field due to their rich functionalities and promising applications in information storage. Up to now, the obtained polar topological structures are restricted to a few limited ferroelectrics with complex heterostructures, limiting their large-scale practical applications. Here, we circumvent this limitation by utilizing a nanoscale ripple-generated flexoelectric field as a universal means to create rich polar topological configurations in nonpolar nanofilms in a controllable fashion. Our extensive phase-field simulations show that a rippled SrTiO_{3} nanofilm with a single bulge activates polarizations that are stabilized in meron configurations, which further undergo topological transitions to Néel-type and Bloch-type skyrmions upon varying the geometries. The formation of these topologies originates from the curvature-dependent flexoelectric field, which extends beyond the common mechanism of geometric confinement that requires harsh energy conditions and strict temperature ranges. We further demonstrate that the rippled nanofilm with three-dimensional ripple patterns can accommodate other unreported modulated phases of ferroelectric topologies, which provide ferroelectric analogs to the complex spin topologies in magnets. The present study not only unveils the intriguing nanoscale electromechanical properties but also opens exciting opportunities to design various functional topological phenomena in flexible materials.