Harmonic Phonon Excitations in Sodium Iodide Crystals: Unveiling Intrinsically Localized Modes

This study investigates the formation of Intrinsically Localized Modes (ILMs) in Sodium Iodide (NaI) crystals, focusing on a pair of harmonic phonons along the [111] lattice direction. ILMs' propensity to form at a specific center-of-mass momentum q and relative momentum vector k is attributed to van-Hove singularities in the non-interaction two-phonon density of states continuum. As q approaches the high-symmetry point L=q(π/a,π/a,π/a), k stabilizes at (π/2a,π/2a,π/2a) for a defined q threshold, converging at the upper edge of the two-phonon density of states spectrum with heightened degeneracy in critical energy. Our findings underscore the energetic degeneracy of harmonic phonon pairs beyond the threshold q towards L at the invariant vector k, signaling a robust presence of ILMs. Calculated ILMs manifest at critical energies of 19.2 meV and 25.2 meV for optic and acoustic modes, respectively. These correspond to nearest-neighbor K₁ and next-nearest-neighbor K₂ spring coupling constants, with K₂/K₁ ratios approximately equal to 0.598 and 0.202 optic and acoustic modes, respectively. Notably, prior Inelastic Neutron Scattering experiments at 555 K identified one-phonon breather excitations at 10.2 meV. Our study posits that anharmonic interactions lifting degeneracies enhance ILM formation, revealing multi-phonon bound states. This exploration contributes insights into harmonic phonon dynamics, providing a nuanced understanding of ILM mechanisms in NaI crystals.