Mechanical Writing of Topological Torons in Freestanding Paraelectric SrTiO ₃ Membranes via Flexoelectric Symmetry Breaking

The realization of stable three-dimensional (3D) topological excitations in condensed matter represents a key pathway for next-generation high-density storage and low-power logic architectures. However, stabilizing such complex textures in ferroelectrics is often constrained due to thermodynamic instability and rigid substrate clamping. This work demonstrates the deterministic mechanical writing of topological torons─localized 3D skyrmion-tube–like polar textures terminated by Bloch points─in freestanding paraelectric SrTiO 3 nanomembranes utilizing phase-field simulations. By exploiting the spatially modulated strain gradients induced by a localized mechanical probe, the simulation reveals the generation of a sign-reversing flexoelectric field with magnitudes reaching approximately 3.5 MV/cm. This field acts as a local symmetry-breaking template, inducing a stable polar state from the room-temperature paraelectric background and forming a toroidal configuration. Systematic mapping of the topological evolution under increasing mechanical stimuli reveals a depth-dependent decoupling transition from a coherent Néel-type texture to a twisted Bloch-type configuration. Furthermore, a comprehensive phase diagram elucidates the role of flexoelectric anisotropy in governing the topological ground state. These results establish flexoelectric strain-gradient engineering as a precise, purely mechanical mechanism for creating and manipulating 3D polar topologies, providing quantitative theoretical guidelines for experimental implementation and the development of reconfigurable mechano-topological devices.