a, Topography, b, out-of-plane PFM phase images, c, in-plane PFM phase images, and d, in-plane PFM amplitude images of freestanding BFO films. Scale bars, 500 nm. All freestanding films exhibit a single out-of-plane domain. Only the freestanding films thicker than four unit cells show in-plane polarizations, which is consistent with the R-phase to T-phase transition observed in the atomically resolved HAADF images, as discussed in the main text. e, The corresponding local out-of-plane PFM hysteresis loops show the switchable out-of-plane polarizations in all ultrathin films. The asymmetry of the coercive field is probably due to asymmetric electrostatic boundary conditions and a self-poling effect, which arises at the interface between BFO and the conductive silicon substrate employed in the measurements.