Curvature-Controlled Polarization in Adaptive Ferroelectric Membranes

In this study, we explore the ferroelectric domain structure and mechanical properties of PbTiO$_3$-based membranes, which develops a well-ordered and crystallographic-oriented ripple pattern upon release from their growth substrate. The ferrolectric domain structure of the PbTiO$_3$ layer was examined at various length scales using optical second harmonic generation, piezoresponse force microscopy, and scanning transmission electron microscopy. These methods reveal the presence of purely in-plane domains organized into superdomains at the crest of the ripples, while an in-plane/out-of-plane domain structure was observed in the flat regions separating the ripples, in agreement with phase-field simulations. The mechanical properties of the membrane were assessed using contact resonance force microscopy, which identified distinct mechanical behaviors at the ripples compared to the flat regions. This study shows that the physical properties of the ferroelectric layer in membranes can be locally controlled within an ordered array of ripples, with well-defined geometric characteristics.