Fig. 3: Universal tribological asymmetry across a broad materials space.

The tribological asymmetry works universally regardless of the size and type of ferroelectric. a–e Nanopillar fabrication on LiNbO₃ single crystal by continuous mechanical milling after electrical switching, both with the same conductive diamond probe. Schematic of nanopillar fabrication (a). AFM height (b) and PFM phase (c) after ten milling scans at a loading force of 5 μN and a scan rate of 1.95 Hz. Scale bars in (b) and (c) are 1 μm. Average pillar height evolution with continuous milling scans (d). Pillar height was averaged from the line profiles across four pillars with 20 data points. The error bars indicate the standard deviations. Growth of nanopillars during continuous milling scans based on the line profiles from four pillars (e). Height data were acquired after the milling scan from 2 to 60 scans, as indicated by the color key. f–h Ferroelectric nanostructure fabrication on thin LiNbO₃ film. AFM height (f), PFM phase (g) and 3D surface images with color overlapped with their PFM phase (h). Scale bars in (f) and (g) are 6 μm. The full-length scale along each respective axis is shown with an arrow for (h). i Height and PFM phase line profiles along the blue marker in (f). j–m Nanofabrication of PbTiO₃ thin film. PFM phase after the artificial decoration of ferroelectric domains (j), Friction image during milling scans at 800 nN (k) and AFM height after multiple milling scans (l). Scale bars are 600 nm for (j) and (k) and 1 μm for (l). m Height and PFM phase line profile along the blue marker in (l).