Visualizing Thermal Vibrations and Phonon Mode Softening in Real Space

Lattice vibrations lie at the very heart of exotic phases in quantum materials, either directly as in the case of phonon mode softening that drives the polarization in ferroelectrics or indirectly as in the phonon mediated interaction that creates Cooper pairs in superconductors. Typical methods for characterizing phonons like infrared or Raman spectroscopy and neutron scattering provide only spatially averaged measurements. Although vibrational electron energy loss spectroscopy offers high spatial resolution, the measurements often require detailed theoretical models for interpretation. Here, we demonstrate the capability of electron ptychography^1,2 as a novel detection tool to directly visualize lattice vibrations in real space.<br/><br/>We illustrate the capability of the technique to directly visualize the thermal ellipsoid of metal atoms that are intercalated in the van-der Waals gap of layered materials. The in-plane vibrational modes of the intercalants have a larger amplitude in comparison to the quenched out-of-plane mode³ and is reflected in the anisotropic thermal blur of the intercalant columns. We also show how ptychography enables us to study lattice distortions associated with a spatially localized phonon mode that is on the verge of softening in barium hexaferrite, a candidate material for quantum paraelectricity and room temperature multiferroicity⁴. By analysing the potential landscape associated with this near-soft phonon mode in three dimensions, we detect the presence of nanometer-scale polar regions⁵ from short-range ordering in the material.<br/><br/><u>References</u><br/>^1. Y. Jiang et al., Nature 559, 343–349 (2018)<br/>^2. Z. Chen et al., Science 372, 826-831 (2021)<br/>^3. S. Fan et al., Nano Lett. 21, 1, 99–106 (2021)<br/>^4. P. S. Wang and H. J. Xiang, Phys. Rev. X 4, 011035 (2014)<br/>^5. H. K. P. et al., Microscopy and Microanalysis, 28(S1), 476-478 (2022)