Atomic-Level Observation of Frequency-Dependent Phonon Eigenvectors and Vibrational Anisotropies*

Phonon anisotropy gives rise to the orientation dependence of dielectric, optical, and thermal properties of materials [1, 2]. At the atomic level, the vibration of individual atoms, known as thermal ellipsoids, could exhibit strong anisotropies due to the local point group symmetry. The averaged thermal ellipsoids can be traditionally estimated by many diffraction methods [3], which encountered critical drawbacks of lacking atomic resolution and energy resolution. The missing frequency-dependency is crucial for understanding their thermal and photonic responses. The state-of-the-art monochromated electron energy-loss spectroscopy (EELS) reaches a combination of few-meV energy resolution and sub-nm spatial resolution and enables the detection of local phonon modes at various crystalline imperfections [4, 5]. We further developed a novel dark-field EELS technique with desired momentum exchanges and applied this approach to a centrosymmetric SrTiO₃. We spatially mapped out the energy-filtered vibrational signals with atomic resolution from 10 to 110 meV. We also discerned 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, thus delving into uncharted realms of dielectric, optical, and thermal property investigations with unprecedented spatial resolutions.