Large Scale Ferroelectric Domain Mapping by 4D STEM

The emergence of ferroelectricity originates from polar displacements of lattice atoms, connotating a one-to-one correlation between electronic and structural properties at the atomic level. An established approach that allows for determining associated structural variations is scanning electron diffraction (SED). In SED, a focused electron beam is scanned over the specimen, probing elastically and inelastically diffracted electrons at each position of the raster scan. The corresponding diffraction patterns represent unique fingerprints of the probed areas, containing a multitude of structural information.<br/>Here, we explore ferroelectric long-range order utilizing a direct electron detector (DED) in combination with SED, enabling simultaneous detection of both strong and weak signal intensities with nanoscale spatial resolution. We demonstrate the potential and opportunities of this innovative 4D-STEM approach using improper ferroelectric ErMnO₃ as an instructive example. ErMnO₃ is an ideal model system as its basic ferroelectric properties and atomic-scale structure are well understood. In the ferroelectric state, the Er ions exhibit characteristic up-up-down and down-down-up patterns, corresponding to ferroelectric 180° domains with positive (+<i>P</i>) and negative (-<i>P</i>) polarization, respectively. These shifts cause different Bragg scattering conditions for the electrons and, hence, specific diffraction patterns that we utilize for domain imaging. In addition, assisted by supervised and unsupervised machine learning algorithms, we analyze weakly scatted intensities to access more subtle changes within the crystal lattice. Our DED-based SED approach provides new opportunities for the study of domain walls and point defects ferroelectrics, and the investigation of electronically inhomogeneous materials in general.