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

Advancements in transmission electron microscopy (TEM) have revolutionized the study of interfaces and nanostructured materials. Innovations like aberration correctors, pixelated direct electron detectors, and monochromators have enabled atomic-resolution scanning transmission electron microscopy (STEM) and electron energy-loss spectroscopy (EELS), facilitating investigations into local structure, properties, and dynamic behaviors. Using a space- and angle-resolved vibrational EELS technique, we have recently observed red shifts and intensity changes in acoustic vibration modes near a single stacking fault in cubic silicon carbide, and nanoscale composition-induced red shifts in Si optical modes in SiGe quantum dots. We also developed a method for differentially mapping phonon momenta revealing the interplay between diffuse and specular reflection. In this talk, I present a novel approach, employing dark-field monochromated electron energy-loss spectroscopy for momentum-selective vibrational spectroscopy. This technique allows us to map phonon polarization vectors. When applied to centrosymmetric cubic-phase strontium titanate, we discover two types of oxygen atoms with contrasting vibrational anisotropies below and above 60 meV, based on mean-squared displacements. These transformations are supported by theoretical models, revealing the transition from oblate ellipsoids at low energies to prolate ellipsoids at high energies. These frequency-dependent thermal ellipsoids provide insights into the thermal and optical behaviors associated with acoustic and optical phonons. Our method enables the visualization of phonon eigenvectors at specific crystalline sites, opening new avenues for exploring dielectric, optical, and thermal properties with exceptional spatial resolutions.