Figure 1

(a) Surface topography and (b) PFM amplitude image of the ${\mathrm{BiFeO}}_3$ surface before the SS-PFM experiment. (c) SS-PFM work of switching image. (d) Hysteresis loop shape in selected locations in (a). Hysteresis loop fine structure of (e) loop I, (f) loop II and (g) loop III. Shown are corresponding Gaussian fits. The positions and areas for each peak are given in parenthesis. The red circle illustrates the fine-structure feature on the forward branch studied in this work. Vertical scale in (a) is 20 nm.Reuse & Permissions

Figure 2

Domain growth in the presence of the defect. (a) For large separations, the defect affects domain growth only on late stages and hence does not contribute to the measured signal, corresponding to (b) nearly ideal PFS loops. (c),(d) For intermediate separations, nucleation can be initiated at the defect (rather than tip) site, resulting in a small change in PFM signal for low biases. The domain rapidly shifts towards the tip at higher voltages, resulting in fine structure in PFS. (e) For the tip positioned at the center of the defect, the nucleation starts at low voltages. The growth stops when the domain occupies the defect region, and resumes only when the bias becomes large enough to induce domain growth on the ideal surface. The size of the fine feature (f) is a direct measure of the defect size.Reuse & Permissions

Figure 3

(a) Schematics of domain nucleation in the vicinity of surface field defect. (b) Schematic dependence of normalized PR-response on the applied voltage $U$ in the vicinity of defect. The role of single Gaussian defect parameters $\{E_S,h_d,r_d,x_0\}$ on piezoresponse loop fine-structure maximal height $\Delta PR$: (c) $E_S=0.9\times {10}^9\mathrm{V}/\mathrm{m}$, $h_d=0.4$, 1, 2, 3 nm (curves 1, 2, 3, 4); (d) $r_d=10\mathrm{nm}$, $h_d=0.4$, 1, 2, 3 nm (curves 1, 2, 3, 4); (e) $E_S=0.9\times {10}^9\mathrm{V}/\mathrm{m}$, $r_d=10\mathrm{nm}$, $h_d=0.4$, 0.6, 1.2, 3 nm (curves 1, 2, 3, 4). Material parameters correspond to ${\mathrm{BiFeO}}_3$ (Ref. 22), $d=30\mathrm{nm}$.Reuse & Permissions

Figure 4

(a) Schematics of the hysteresis loop with a single fine-structure feature. 2D maps of (b) negative nucleation bias and integral fine structure for (c) forward and (d) reverse branch. Note the depression in (d) and associated ring structure in (c). Radial averages for (e) nucleation biases and (f) integral fine structure taken with respect to center of defect.Reuse & Permissions