Atomic-Level Visualization of Frequency- and Symmetry-Dependent Vibrational Anisotropies Using Momentum-Selective Electron Microscopy

Studying vibrational anisotropies for individual phonon modes is essential for understanding intriguing optical, thermal, and mechanical phenomena in a wide range of crystalline materials. The averaged vibrational anisotropies of distinct elements are traditionally estimated by several optical and diffraction methods, which encountered critical drawbacks of lacking sufficient spatial resolution and energy resolutions. Here, I will present a novel momentum-selective dark-field monochromated electron energy-loss spectroscopy technique in a scanning transmission electron microscope to visualize the atomic-level vibrational anisotropies. By applying to SrTiO₃ and BaTiO₃, we first mapped out the energy-filtered vibrational signals with atomic resolution, matching with simulation results. We further observed two types of oxygen vibrations that exhibit contrasting anisotropies below and above a certain transition energy (60 meV for SrTiO₃ and 52 meV for BaTiO₃) due to their frequency-linked thermal ellipsoids. Unexpectedly, our results unveil that the weak tetragonality in BaTiO₃ lead to an asymmetric modulation of vibrational signals between apical and equatorial oxygen sites near 55 meV. This method establishes a new pathway to visualize phonon eigenvectors, thus delving into uncharted realms of various dielectric properties with unprecedented spatial resolutions.