Imaging Local Polarization in Ferroelectric Thin Films by Coherent X-Ray Bragg Projection Ptychography

We used x-ray Bragg projection ptychography (BPP) to map spatial variations of ferroelectric polarization in thin film ${\mathrm{PbTiO}}_3$, which exhibited a striped nanoscale domain pattern on a high-miscut (001) ${\mathrm{SrTiO}}_3$ substrate. By converting the reconstructed BPP phase image to picometer-scale ionic displacements in the polar unit cell, a quantitative polarization map was made that was consistent with other characterization. The spatial resolution of 5.7 nm demonstrated here establishes BPP as an important tool for nanoscale ferroelectric domain imaging, especially in complex environments accessible with hard x rays.