Fig. 3.

Phase-field simulations. a Simulated out-of-plane (z-x plane) vector map of flexoelectric polarisation induced by the scanning probe microscope (SPM) tip under a static contact force of 4 µN. Arrows denote the direction of the polarisation vectors, and their lengths correspond to the magnitude of the induced polarisation. b Simulated in-plane (x-y plane) normalised vacancy concentration (NVC) map around the tip-STO contact region, which shows a depletion and enrichment of $V_{\mathrm{o}}^{\cdot \cdot }$ underneath the tip and around the contact edge, respectively. c, d The component-resolved in-plane distribution of depolarisation field around the tip-STO contact region. The z-component, $E_z^{\mathrm{dep}}$ c, and the x-component, $E_x^{\mathrm{dep}}$ d. The in-plane distribution of the y-component, $E_y^{\mathrm{dep}}$, should be viewed as the same as the one in d but rotated by 90° in the x-y plane