Atomic-scale imaging of frequency-dependent phonon anisotropy

Xingxu Yan, Paul M. Zeiger, Yifeng Huang, Haoying Sun, Jie Li, Chaitanya A. Gadre, Hongbin Yang, Ri He, Toshihiro Aoki, Zhicheng Zhong, Yuefeng Nie, Ruqian Wu (), Ján Rusz () and Xiaoqing Pan ()
Additional contact information
Xingxu Yan: University of California
Paul M. Zeiger: Uppsala University
Yifeng Huang: University of California
Haoying Sun: Nanjing University
Jie Li: University of California
Chaitanya A. Gadre: University of California
Hongbin Yang: University of California
Ri He: Chinese Academy of Sciences
Toshihiro Aoki: University of California
Zhicheng Zhong: Chinese Academy of Sciences
Yuefeng Nie: Nanjing University
Ruqian Wu: University of California
Ján Rusz: Uppsala University
Xiaoqing Pan: University of California

Nature, 2025, vol. 645, issue 8082, 893-899

Abstract: Abstract Directly visualizing vibrational anisotropy in individual phonon modes is essential for understanding a wide range of intriguing optical, thermal and elastic phenomena in materials1–5. Although conventional optical and diffraction techniques have been used to estimate vibrational anisotropies, they fall short in achieving the spatial and energy resolution necessary to provide detailed information4–7. Here, we introduce a new form of momentum-selective electron energy-loss spectroscopy, which enables the element-resolved imaging of frequency- and symmetry-dependent vibrational anisotropies with atomic resolution. Vibrational anisotropies manifest in different norms of orthogonal atomic displacements, known as thermal ellipsoids. Using the centrosymmetric strontium titanate as a model system, we observed two distinct types of oxygen vibrations with contrasting anisotropies: oblate thermal ellipsoids below 60 meV and prolate ones above 60 meV. In non-centrosymmetric barium titanate, our approach can detect subtle distortions of the oxygen octahedra by observing the unexpected modulation of q-selective signals between apical and equatorial oxygen sites near 55 meV, which originates from reduced crystal symmetry and may also be linked to ferroelectric polarization. These observations are quantitatively supported by theoretical modelling, which demonstrates the reliability of our approach. The measured frequency-dependent vibrational anisotropies shed new light on the dielectric and thermal behaviours governed by acoustic and optical phonons. The ability to visualize phonon eigenvectors at specific crystallographic sites with unprecedented spatial and energy resolution opens new avenues for exploring dielectric, optical, thermal and superconducting properties.

Date: 2025
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DOI: 10.1038/s41586-025-09511-z

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