Instability-Driven Mechanically Locked States in Functional Oxide Membranes

While mechanical instabilities enable engineered nonlinear responses, their controlled application in functional crystalline oxides has remained largely unexplored. Recent advances in freestanding oxide membranes now allow their integration into nanoscale, bistable architectures. Here, we demonstrate that freestanding SrTiO3 and BaTiO3 membranes relax into well-defined metastable buckling states when they are transferred onto lithographically defined cavities. This deformation, driven by the interplay of residual strain, bending stiffness, and cavity geometry, produces reproducible bistable states with distinct strain distribution. Using atomic force microscopy, Kelvin probe measurements, and finite element modeling, we reveal that these mechanically locked states directly govern the electromechanical potential landscape of ferroelectric BaTiO3. We further demonstrate reversible snap-through transitions between degenerate states, establishing complex oxides as deterministic, geometry-tunable building blocks for nonlinear nanoelectromechanical architectures. These results provide a general strategy for exploiting mechanical instabilities to manipulate functional responses in ultrathin, crystalline membranes.