Imaging 3D polarization dynamics via deep learning 4D-STEM

Recent advances in ferroelectrics highlight the role of three-dimensional (3D) polar entities in forming topological polar textures and generating giant electromechanical responses, during polarization rotation. However, current electron microscopy methods lack the depth resolution to resolve the polarization component along the electron beam direction, which restricts full characterization. Here, we present a deep learning framework combined with four-dimensional scanning transmission electron microscopy to reconstruct 3D polarization maps in Ba0.5Sr0.5TiO3 thin-film capacitors with picometer-level accuracy under applied electric fields. Our approach enables observation of polar nanodomains consistent with the polar slush model and shows that switching occurs through coordinated vector rotation toward <111> energy minima, rather than magnitude changes. Furthermore, regions with higher topological density exhibit smaller polarization variation when the electric field changes, indicating topological protection. Our work reveals the value of 3D polarization mapping in elucidating complex nanoscale polar phenomena, with broad implications for emergent ferroelectrics.