Abstract
The vibrational energy of crystals is known to propagate in a fixed number of phonon branches allowed by symmetry. In the realm of nonlinear dynamics, however, additional nonlinear propagating modes are possible. Nonlinear propagating modes have unique properties that are important in many disciplines including optical communications, conducting polymers, biology, magnetism, and nuclear physics. Yet, despite the crucial importance of crystal lattice vibrations in fundamental and applied science, such additional propagating modes have not been observed in ordinary crystals. Here, we show that propagating modes exist beyond the phonons in fluorite-structured thoria, urania, and natural calcium fluoride using neutron scattering and first-principles calculations. These modes are observed at temperatures ranging from 5 K up to 1200 K, extend to frequencies 30–40% higher than the maximum phonon frequency, and travel at velocities comparable to or higher than the fastest phonon. The nonlinear origin of the modes is explained in part via perturbation theory, which approximately accounts for nonlinearity. Given that these modes are still clearly observed at 5 K, they are likely an inherent feature of the quantum ground state. The existence of these waves in three-dimensional crystals may have ramifications for material properties.
Highlights
The vibrational energy of crystals is known to propagate in a fixed number of phonon branches allowed by symmetry
There is some evidence that crystals support anharmonicity-driven intrinsic localized modes (ILMs)[11], which are stationary vibrations confined to just a few atoms
Inelastic scattering results are compared to density functional theory (DFT) calculations of the phonons in Fig. 1
Summary
The vibrational energy of crystals is known to propagate in a fixed number of phonon branches allowed by symmetry. The nonlinear origin of the modes is explained in part via perturbation theory, which approximately accounts for nonlinearity Given that these modes are still clearly observed at 5 K, they are likely an inherent feature of the quantum ground state. The existence of these waves in three-dimensional crystals may have ramifications for material properties. A foundational study of nonlinear systems by Fermi, Pasta, and Ulam (FPU or Fermi–Pasta–Ulam) considered a one-dimensional lattice of particles coupled by nonlinear springs[8] This simulation was expected to tend towards an equipartition of energy among all degrees of freedom after a large number of time steps, demonstrating the ergodicity of the system. It is likely that some features of fluorite structure are essential to the observation of these modes
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
