Revealing the Anisotropy of Frequency- and Symmetry-Dependence of Atomic Vibrations in Oxides by Electron Energy-Loss Spectroscopy

The underlying dielectric properties of materials, along with intriguing optical, thermal, and elastic phenomena, stem from the anisotropy of atomic vibrations. Traditionally, diffraction techniques have been used to estimate the average thermal ellipsoids of distinct elements, though they lack the desired spatial and energy resolutions. Here, we present a novel dark-field monochromated electron energy-loss spectroscopic approach for momentum-selective vibrational spectroscopy, enabling the cartographic delineation of frequency- and symmetry-dependent phonon eigenvectors. In centrosymmetric strontium titanate, we distinguish between two types of oxygen vibrations exhibiting contrasting anisotropies: oblate thermal ellipsoids below 60 meV and prolate ones above 60 meV, due to their local symmetry, supported by theoretical modeling. Furthermore, the tetragonality of non-centrosymmetric barium titanate and accompanying cation displacements generate an unexpected modulation of thermal ellipsoids between apical and equatorial oxygen sites near 55 meV, along with soft-phonon modes. These frequency-linked thermal ellipsoids offer insights into diverse dielectric behaviors strongly correlated with acoustic and optical phonons. Our method establishes a new pathway to visualize phonon eigenvectors at specific crystalline sites for various elements, delving into uncharted realms of dielectric, optical, thermal, elastic, and superconducting property investigations with unprecedented spatial and energy resolutions.