Fig. 1: Design schematics for low-pressure-driven polarization switching in PTO membranes.

a Schematic diagram of tip-induced flexoelectricity in freestanding membranes. b Experimental design of achieving low-pressure mechanical writing. The double-well potential of Landau free energy with homogeneous strain (blue solid and dotted lines) and with strain gradient (red solid and dotted lines) of cases I–III. The solid lines refer to straight 180° switching; the dotted lines refer to 180° switching consisted of two 90° rotations. PTO membranes epitaxially grown on STO substrates (case I) and freestanding PTO membranes transferred onto oxide substrates (case II) and softer underlying substrates (case III). c Energy barrier height for direct 180° polarization switching based on DFT calculations (blue and red lines); Switching barrier consisted of two 90° rotation has been obtained from an effective Hamiltonian model³¹ (purple line). d Finite-element method (FEM)-calculated vertical flexoelectric field distributions in PTO membranes subjected with the same tip force (2 μN).