Ferroelectric materials have become a prototypical example of functional oxides, attracting considerable interest both in fundamental research and device engineering. They have been utilized in a broad range of electronic, optical, and electromechanical applications and hold promise for the design of future high-density nonvolatile memories and multifunctional nanodevices. The functionality of the ferroelectric-based devices depends strongly on the structures of ferroelectric domains with different polarization orientations. Advanced imaging techniques based on aberration-corrected transmission electron microscopy (TEM) or scanning transmission electron microscopy (STEM) have been a powerful method to study the domain structures in ferroelectric thin films, allowing nanoscale polarization states to be resolved unambiguously with sub-Angstrom resolution. It has been shown that nanoscale ferroelectric structures under special boundary conditions may exhibit unusual polarization patterns that challenge the conventional understanding of ferroelectric polar states, and possess functional properties that can be useful for new applications1. In recent years, several new techniques based on aberration-corrected TEM have been under developing, including the STEM scanning diffraction method that allows the electric field distribution in thin foils to be measured at atomic scale2, the atomic electron tomography (AET) that allows the 3D coordinates of all the atoms in a nanosystem to be reconstructed accurately3, and the low-energy electron energy-loss spectroscopy (or vibrational spectroscopy, with energy resolution < 10 meV) that allows the local vibrational spectrum of TEM specimens to be probed with high spatial resolution4. These techniques provide new opportunities for the study of fundamental physics in ferroelectric nanostructures. Here, we demonstrate the capability of these techniques for the characterization of emergent phenomena in ferroelectric heterostructures. The obtained results provide insights into 1) the effects of polarization bound charge, interface built-in field, free charge compensation, and magnetoelectric coupling on polarization structures across domain walls and different types of interfaces; 2) the 3D polarization structures of domain walls, domain states induced by surface reconstruction, or exotic polarization states such as vortices; and 3) the interaction between the polarization and the lattice vibration (phonon modes) of ferroelectric materials.
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 Y. S. Yang, et al., Nature 542, 75 (2017).
 O. L. Krivanek, et al., Nature 514, 209 (2014).