Schubert, M. et al. Anisotropy, phonon modes, and free charge carrier parameters in monoclinic β-gallium oxide single crystals. Phys. Rev. B 93, 125209 (2016).
Ma, W. L. et al. In-plane anisotropic and ultra-low-loss polaritons in a natural van der Waals crystal. Nature 562, 557–562 (2018).
Kim, S. E. et al. Extremely anisotropic van der Waals thermal conductors. Nature 597, 660–665 (2021).
Bubnova, R., Volkov, S., Albert, B. & Filatov, S. Borates—crystal structures of prospective nonlinear optical materials: high anisotropy of the thermal expansion caused by anharmonic atomic vibrations. Crystals 7, 93 (2017).
Lin, I. C. et al. Extraction of anisotropic thermal vibration factors for oxygen from the Ti L2,3-edge in SrTiO3. J. Phys. Chem. C 127, 17802–17808 (2023).
Abramov, Y. A., Tsirelson, V. G., Zavodnik, V. E., Ivanov, S. A. & Brown, I. D. The chemical bond and atomic displacements in SrTiO3 from X-ray diffraction analysis. Acta Crystallogr. B 51, 942–951 (1995).
Gong, Y. et al. Polarized Raman scattering of in-plane anisotropic phonon modes in α-MoO3. Adv. Opt. Mater. 10, 2200038 (2022).
Jauch, W. & Reehuis, M. Electron-density distribution in cubic SrTiO3: a comparative gamma-ray diffraction study. Acta Crystallogr. A 61, 411–417 (2005).
Yan, X., Gadre, C. A., Aoki, T. & Pan, X. Probing molecular vibrations by monochromated electron microscopy. Trends Chem. 4, 76–90 (2022).
Krivanek, O. L. et al. Vibrational spectroscopy in the electron microscope. Nature 514, 209–212 (2014).
Hage, F. S., Radtke, G., Kepaptsoglou, D. M., Lazzeri, M. & Ramasse, Q. M. Single-atom vibrational spectroscopy in the scanning transmission electron microscope. Science 367, 1124–1127 (2020).
Xu, M. et al. Single-atom vibrational spectroscopy with chemical-bonding sensitivity. Nat. Mater. 22, 612–618 (2023).
Yan, X. et al. Single-defect phonons imaged by electron microscopy. Nature 589, 65–69 (2021).
Qi, R. et al. Measuring phonon dispersion at an interface. Nature 599, 399–403 (2021).
Gadre, C. A. et al. Nanoscale imaging of phonon dynamics by electron microscopy. Nature 606, 292–297 (2022).
Zeiger, P. M. & Rusz, J. Simulations of spatially and angle-resolved vibrational electron energy loss spectroscopy for a system with a planar defect. Phys. Rev. B 104, 094103 (2021).
Hoglund, E. R. et al. Direct visualization of localized vibrations at complex grain boundaries. Adv. Mater. 35, e2208920 (2023).
Haas, B. et al. Atomic-resolution mapping of localized phonon modes at grain boundaries. Nano Lett. 23, 5975–5980 (2023).
Hage, F. S., Kepaptsoglou, D. M., Ramasse, Q. M. & Allen, L. J. Phonon spectroscopy at atomic resolution. Phys. Rev. Lett. 122, 016103 (2019).
Venkatraman, K., Levin, B. D. A., March, K., Rez, P. & Crozier, P. A. Vibrational spectroscopy at atomic resolution with electron impact scattering. Nat. Phys. 15, 1237–1241 (2019).
Sirenko, A. A. et al. Soft-mode hardening in SrTiO3 thin films. Nature 404, 373–376 (2000).
Huang, J. K. et al. High-kappa perovskite membranes as insulators for two-dimensional transistors. Nature 605, 262–267 (2022).
Nova, T. F., Disa, A. S., Fechner, M. & Cavalleri, A. Metastable ferroelectricity in optically strained SrTiO3. Science 364, 1075–1079 (2019).
Gao, W. et al. Real-space charge-density imaging with sub-ångström resolution by four-dimensional electron microscopy. Nature 575, 480–484 (2019).
Casella, L. & Zaccone, A. Soft mode theory of ferroelectric phase transitions in the low-temperature phase. J. Phys. Condens. Matter 33, 165401 (2021).
Burns, G. & Dacol, F. H. Lattice modes in ferroelectric perovskites. III. Soft modes in BaTiO3. Phys. Rev. B 18, 5750–5755 (1978).
Tian, Z. et al. Preparation of nano BaTiO3‐based ceramics for multilayer ceramic capacitor application by chemical coating method. J. Am. Ceram. Soc. 92, 830–833 (2009).
Jeong, D. S. et al. Emerging memories: resistive switching mechanisms and current status. Rep. Prog. Phys. 75, 076502 (2012).
Ji, D. et al. Freestanding crystalline oxide perovskites down to the monolayer limit. Nature 570, 87–90 (2019).
Sun, H. et al. Nonvolatile ferroelectric domain wall memory integrated on silicon. Nat. Commun. 13, 4332 (2022).
He, R. et al. Structural phase transitions in SrTiO3 from deep potential molecular dynamics. Phys. Rev. B 105, 064104 (2022).
van der Marel, D., Barantani, F. & Rischau, C. W. Possible mechanism for superconductivity in doped SrTiO3. Phys. Rev. Res. 1, 013003 (2019).
Niedermeier, C. A. et al. Phonon scattering limited mobility in the representative cubic perovskite semiconductors SrGeO3, BaSnO3, and SrTiO3. Phys. Rev. B 101, 125206 (2020).
Smith, J., Huang, Z., Gao, W., Zhang, G. & Chi, M. Atomic resolution cryogenic 4D-STEM imaging via robust distortion correction. ACS Nano 17, 11327–11334 (2023).
Zeiger, P. M. & Rusz, J. Efficient and versatile model for vibrational STEM-EELS. Phys. Rev. Lett. 124, 025501 (2020).
Zeiger, P. M. & Rusz, J. Frequency-resolved frozen phonon multislice method and its application to vibrational electron energy loss spectroscopy using parallel illumination. Phys. Rev. B 104, 104301 (2021).
Cancellieri, C. et al. Polaronic metal state at the LaAlO3/SrTiO3 interface. Nat. Commun. 7, 10386 (2016).
Krivanek, O. et al. Damage-free analysis of biological materials by vibrational spectroscopy in the EM. Microsc. Microanal. 26, 108–110 (2020).
Chen, Z. et al. Electron ptychography achieves atomic-resolution limits set by lattice vibrations. Science 372, 826–831 (2021).
Sun, H. et al. Signatures of superconductivity near 80 K in a nickelate under high pressure. Nature 621, 493–498 (2023).
Yang, H. et al. Phonon modes and electron–phonon coupling at the FeSe/SrTiO3 interface. Nature 635, 332–336 (2024).
Nelson, C. T. et al. Domain dynamics during ferroelectric switching. Science 334, 968–971 (2011).
Spiecker, E. Determination of crystal polarity from bend contours in transmission electron microscope images. Ultramicroscopy 92, 111–132 (2002).
Nord, M., Vullum, P. E., MacLaren, I., Tybell, T. & Holmestad, R. Atomap: a new software tool for the automated analysis of atomic resolution images using two-dimensional Gaussian fitting. Adv. Struct. Chem. Imaging 3, 9 (2017).
Yan, X. et al. Curvature-induced one-dimensional phonon polaritons at edges of folded boron nitride sheets. Nano Lett. 22, 9319–9326 (2022).
Culjak, I., Abram, D., Pribanic, T., Dzapo, H. & Cifrek, M. A brief introduction to OpenCV. In Proc. 35th International Convention MIPRO (ed. Biljanović, P.) 1725–1730 (IEEE, 2012).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).
Gonze, X. & Lee, C. Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory. Phys. Rev. B 55, 10355–10368 (1997).
Thompson, A. P. et al. LAMMPS – a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 271, 108171 (2022).
Carreras, A. phonoLAMMPS Documentation. GitHub https://github.com/abelcarreras/phonolammps (2023).
Carreras, A., Togo, A. & Tanaka, I. DynaPhoPy: a code for extracting phonon quasiparticles from molecular dynamics simulations. Comput. Phys. Commun. 221, 221–234 (2017).
Togo, A., Chaput, L., Tadano, T. & Tanaka, I. Implementation strategies in phonopy and phono3py. J. Phys. Condens. Matter 35, 353001 (2023).
Togo, A. First-principles phonon calculations with phonopy and phono3py. J. Phys. Soc. Jpn 92, 012001 (2023).
Zhang, Y. et al. DP-GEN: a concurrent learning platform for the generation of reliable deep learning based potential energy models. Comput. Phys. Commun. 253, 107206 (2020).
Barthel, J. Dr. Probe: a software for high-resolution STEM image simulation. Ultramicroscopy 193, 1–11 (2018).
Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011).
Servoin, J. L., Luspin, Y. & Gervais, F. Infrared dispersion in SrTiO3 at high temperature. Phys. Rev. B 22, 5501–5506 (1980).
Stirling, W. G. Neutron inelastic scattering study of the lattice dynamics of strontium titanate: harmonic models. J. Phys. C 5, 2711 (1972).
Zhou, J.-J., Hellman, O. & Bernardi, M. Electron-phonon scattering in the presence of soft modes and electron mobility in SrTiO3 perovskite from first principles. Phys. Rev. Lett. 121, 226603 (2018).
Scalabrin, A., Chaves, A. S., Shim, D. S. & Porto, S. P. S. Temperature dependence of the A1 and E optical phonons in BaTiO3. Phys. Status Solidi B 79, 731–742 (1977).
Hermet, P., Veithen, M. & Ghosez, P. Raman scattering intensities in BaTiO3 and PbTiO3 prototypical ferroelectrics from density functional theory. J. Phys. Condens. Matter 21, 215901 (2009).
Evarestov, R. A. & Bandura, A. V. First-principles calculations on the four phases of BaTiO3. J. Comput. Chem. 33, 1123–1130 (2012).
Ehsan, S., Arrigoni, M., Madsen, G. K. H., Blaha, P. & Tröster, A. First-principles self-consistent phonon approach to the study of the vibrational properties and structural phase transition of BaTiO3. Phys. Rev. B 103, 094108 (2021).
