Fig. 2

Imaging the ferroelectric switching of BiFeO₃. a The poling cycle applied in the presented XDM dataset, where E is the electric field between the Pt and SRO electrodes and is oriented along [001]. At each point an electric pulse lasting 0.5 s is applied, followed by acquisition of an XDM image (acquisition time 0.2 s) with \(\varvec{q}_{0,0,2 - \delta }\), where δ ≈ 10⁻¹. b Representative XDM images taken at different values of the electric field cycle in a. The dashed line in the right panel indicates the edge of the Pt electrodes. After poling the BFO film underneath the Pt electrode, the domain-wall between two regions of the film with opposite out-of-plane polarization vectors produces amplitude contrast (negative) in diffraction imaging. The entire collection of XDM images acquired during the electric field cycle (~200 images) are unmixed using independent component analysis (ICA), assuming three independent components or sources. In c the XDM collection is projected onto these three different basis vectors and reshaped into images, while d shows the corresponding evolution of these independent components (IC) as a function of electric field. The landmark hysteresis polarization loop of BFO is obtained directly from IC1 and its spatial map in c shows the domain wall between the two opposite polarization states. The arrows in d indicate the direction of the poling cycle. The other two ICA components IC2, three are mostly closely associated with extrinsic instrumental factors that enter the data such as X-ray beam intensity fluctuations or drift, given that their evolution during the poling cycle is not physically relatable to ferroelectric behavior. I _MC represents the mean-centered intensity, whereby the mean intensity in each image in the original data is subtracted from the XDM collection before applying ICA