Atomic-Scale Visualization of Phonon Anisotropy in Perovskite Oxides

Recently, there has been growing interest in studying phonon anisotropy, referring to the variation of phonon spectra along different crystallographic directions of low-symmetry materials. Directly visualizing vibrational anisotropy in individual phonon modes is essential for understanding dielectric, optical, thermal, and superconducting phenomena in materials. Although conventional diffraction techniques have been used to estimate phonon anisotropies, they fall short in achieving the spatial and energy resolution necessary to provide detailed information. Here, I will introduce a momentum-selective electron energy-loss spectroscopy (q-selective EELS) technique to visualize directional atomic vibrations by choosing the momentum exchange of collected electrons. In perovskite oxides, we mapped out vibrational signals in different energy ranges, showing atomic resolution features and matching simulation results. By comparing the mapping results between two orthogonal directions, oxygen atoms undergo oblate thermal ellipsoids at low energies and prolate ones at high energies. Intriguingly, our results revealed that the ferroelectric polarization and oxygen octahedral distortion in the tetragonal BaTiO₃ give rise to asymmetric modulations between apical and equatorial oxygen near 55 meV. Our method establishes a new pathway to visualize phonon eigenvectors at different sites for exploring various properties with unprecedented spatial and energy resolution.