Real-Space Visualization of Frequency-Dependent Anisotropy of Atomic Vibrations

Abstract: The underlying dielectric properties of materials, intertwined with intriguing phenomena such as topological polariton modes and anisotropic thermal conductivities, stem from the anisotropy in atomic vibrations. Conventionally, X-ray diffraction techniques have been employed to estimate thermal ellipsoids of distinct elements, albeit lacking the desired spatial and energy resolutions. Here we introduce a novel approach utilizing the dark-field monochromated electron energy-loss spectroscopy for momentum-selective vibrational spectroscopy, enabling the cartographic delineation of variations of phonon polarization vectors. By applying this technique to centrosymmetric cubic-phase strontium titanate, we successfully discern two types of oxygen atoms exhibiting contrasting vibrational anisotropies below and above 60 meV due to their frequency-linked thermal ellipsoids. This method establishes a new pathway to visualize phonon eigenvectors at specific crystalline sites for diverse elements, thus delving into uncharted realms of dielectric, optical, and thermal property investigations with unprecedented spatial resolutions.