Mechanical Control of Polar Patterns in Wrinkled Thin Films via Flexoelectricity

Intriguing topological polar structures in oxide nanofilms have drawn growing attention owing to their immense potential applications in nanoscale electronic devices. Here, we report a novel route to mechanically manipulate polar structures via flexoelectricity in wrinkled thin films. Our results present a flexoelectric polar transition from a nonpolar state to uniaxial polar stripes, biaxial meronlike or antimeronlike polar structures, and polar labyrinths by varying wrinkle morphologies. The evolution mechanisms and the outstanding mechanical tunability of these flexoelectric polar patterns were investigated theoretically and numerically. This strategy based on flexoelectricity for generating nontrivial polar structures will no longer rely on the superlattice structure and can be widely applicable to all centrosymmetric or noncentrosymmetric materials, providing a broader range of material and structure candidates for polar topologies.

Figure 1

Schematics of flexoelectric polarization in wrinkled thin films. (a) The prestretched film-substrate system. (b) The bilayer forms a complex wrinkling morphology after releasing the prestrains. The wrinkle-induced strain gradients break the symmetry of the nonpolar centrosymmetric crystals (c) and introduce positive (d) and negative (e) flexoelectric polarization at the crests [purple circle in (b)] and valleys [green circle in (b)] of the wrinkles.

Figure 2

The flexoelectric polar pattern in stripe wrinkle. (a),(b) Topography images (a) of the wrinkled film-substrate system and the deflection (b) of the neutral surface of the film. (c) Curves of the deflection (black solid), strain gradient (blue short dot), and polarization (red solid). (d) Periodic strain gradient map in the wrinkled STO film. (e) The nonuniform strain and corresponding dipole distribution. (f),(g) Spatial structure (f) and a section (g) of the wrinkle-induced flexoelectric polarization.

Figure 3

Flexoelectric meronlike polar structure in the checkboard wrinkle. (a),(b) Topography images (a) of the checkboard wrinkle and the deflection (b) of the neutral surface of the film. (c) Three-dimensional flexoelectric polar-vortex array structure in wrinkled STO film. (d) The flexoelectric polarization in the checkboard wrinkle is a helical rotation structure. (e) The out-of-plane strain gradients and the projection of corresponding polarization in the $x\text{−}y$ plane. The polarization is positive (red) at the peaks and negative (blue) at the valleys. (f) A magnified image of a single positive-negative polar vortex pair, revealing meronlike polar structures. (g),(h) The curl (g) of the in-plane flexoelectric polarization ${(\nabla \times \mathit{P})}_{[001]}$ and the corresponding in-plane polar vectors (h). The curl value (g) is mapped with a red-blue color scale, where anticlockwise (positive) is red and clockwise (negative) is blue, both extending along the $z$ direction. In (h), the red rotating arrows cover the wrinkle crests, the blue ones cover valleys and the green one represents the perimeter.

Figure 4

Polar pattern evolution for varying strain states. (a)–(d) Wrinkling morphologies for varying compression ratios. Compression ratios for (a), (b), (c), and (d), are 1.03, 1.04, 1.5, and 2, respectively. (e)–(h) Detailed strain gradients (e1)–(h1) and corresponding polar patterns (e2)–(h2) of the translucent blue panels in (a)–(d).

Figure 5

(a) Phase diagram of the polar pattern evolution. The data points for the checkboard (blue stars), stripes (red dots), herringbone patterns (green triangles), and labyrinth (white rings) are achieved from numerical simulations. Composite phases exist near the solid lines, so the solid lines do not represent strict phase boundaries. The inset shows the detailed phase diagram near the critical strain, as marked by the translucent green panel in (a). (b) Strain gradients and corresponding flexoelectric polarization for varying compressive strains. (c) Normalized wavelength versus modules ratio of the film-substrate system.