New Features in Phonon Spectra from Highly Anharmonic Crystals Found by Inelastic Neutron Scattering

Textbook phonons are bosonic quasiparticles that populate vibrational modes of a crystal. Classical dynamics is often used to find the vibrational modes, which are then quantized in units of hv, where v is frequency and h is Planck's constant. This approach is extended to "quasiharmonic" theory, where v is a function of volume, and to "anharmonic" theory, where a phonon self-energy depends on interactions with other phonons through cubic or quartic perturbations to the potential. Larger deviations of the potential from harmonic can be accommodated by molecular dynamics simulations. Combining these simulations with inelastic neutron scattering (INS) experiments revealed two new types of nonlinear vibrational behavior. Both are interpreted with the quantum Langevin equation.<br/>A phonon potential with forces that depart from linearity produces spectral features found in other nonlinear media, such as crystals for nonlinear optics. Our INS measurements on rocksalt NaBr found intermodulation phonon sidebands (IPS) at frequencies approximately equal to the sum and difference of strongly-interacting TA and TO phonon modes [1]. The "input-output theory" of quantum optics [2] was successful for predicting the intensities and shapes of the intermodulation sidebands, although the wavevector dependence of phonons adds complexity. Very recent measurements on NaBr show frequency doubling at elevated temperatures.<br/>A second nonlinear phenomenon was found in cuprite, Cu2O. At temperatures above room temperature, a diffuse inelastic intensity (DII) replaced the optical modes. Again, the Schrödinger-Langevin equation could predict the general appearance and perhaps the shape of the DII. It originates with phase shifts in the oscillations of oxygen atoms caused by slower movements of neighboring Cu atoms. The DII requires both anharmonicity and some temporal randomness in the nonlinear forces between neighboring atoms.<br/>Experiments to isolate the IPS and DII were performed with single crystals on a direct-geometry Fermi chopper spectrometer, ARCS, at the Spallation Neutron Source. Background removal was a challenge, but the experiments could not have been done without the low background, high flux, and detector efficiency of the ARCS spectrometer. Advances in experimental capabilities will allow other studies of nonlinear phenomena in phonon physics, and new insights into phonon anharmonicity.<br/><br/>[1] DOI: 10.1103/PhysRevB.103.134302<br/>[2] DOI: 10.1103/PhysRevA.31.3761<br/>This work is supported by DOE BES award No. DE-FG02-03ER46055.