Fig. 3: Variations of polar textures with temperature.

Plan-view dark field STEM imaging of [(SrTiO₃)₁₆/(PbTiO₃)₁₆]₈ superlattice acquired with temperatures at (A) 223 K, (B) 298 K, and (C) 373 K. Insets, fast Fourier transform (FFT) of the images in A–C showing different types of ordering. Polarization maps reconstructed from the 4D-STEM dataset of superlattice at (D) 223 K, (E) 298 K, and (F) 373 K, showing the in-plane Bloch components of polar-skyrmions. D–F are acquired from nearby regions of A–C. The corresponding phase-field simulations with temperatures and in-plane lattice parameters (a,b) of (G) 223 K, a = 3.875 Å, b = 3.885 Å; H 298 K, a = b = 3.905 Å; and (I) 373 K, a = b = 3.899 Å. The color wheel hue (saturation) corresponds to the direction (magnitude) of the in-plane component of the ferroelectric polarization. We note that the phase field simulations capture the qualitative changes in morphology of particle-like objects as a function of temperature/strain conditions. However, while the general symmetry of the phase is predicted, the microscopic details of polar vectors at the boundaries require first-principles based calculations.