Fig. 2: Origin of asymmetric friction and wear of ferroelectrics.

a–c Schematic of flexoelectrically induced mechanism, in which the asymmetric tribological properties depend on the direction of the out-of-plane polarization, leading to a larger contact area during the scanning in up domains. The probe sinks deeper in the ferroelectric up domain than the down domain because of stiffness asymmetry (a). During the dynamic scan, the absolute value of the lateral signal in the position-sensitive photodiode is higher in the up domain than the down domain because of the larger contact area and indentation depth (b). The resulting height after continuous scans is higher in the down domain due to continuous milling with higher friction in the up domain (c). d Schematic of unscreened surface charge-driven mechanism. e–g Computational mechanics approach of asymmetric friction in LiNbO₃. Indentation depth (e) and contact area (f) of up and down domains based on cubic flexoelectricity with equal longitudinal and transversal coefficients corresponding to a flexocoupling coefficient of 10 V. Insets are magnifications of the red dotted area. Friction ratio (up/down) obtained from the numerical simulation and experiments (g). Flexocoupling coefficients simulated in (g) are between 1 and 10 V. Ten measurement points were averaged for each data point with error bars given by standard deviations. h–j Investigation of tribological asymmetry with a non-conductive diamond probe. Friction during the milling scan with non-conductive probe (h), resulting AFM height (milled inside) with pristine background region (i) and PFM phase (j) using conductive diamond probe after one milling scan. k–n Results of high voltage application to tip during the milling. Friction during the 1st milling scan (k) and line profiles in the 150 V, 0 V and −150 V regions (l). Arrows indicate the polarization orientation. Resulting AFM topography (m) and PFM phase (n) after 10 milling scans (scan angle of 90° with the fast scan axis perpendicular to the domain walls). Red circles indicate higher topography in electrically switched regions. Scale bars in (h–n) are 5 μm.