Anharmonic lattice dynamics in large thermodynamic ensembles with machine-learning force fields: CsPbBr$_{3}$ a phonon-liquid with Cs rattlers

The phonon dispersion relations of crystal lattices can often be well-described with the harmonic approximation. However, when the potential energy landscape exhibits more anharmonicity, for instance, in case of a weakly bonded crystal or when the temperature is raised, the approximation fails to capture all crystal lattice dynamics properly. Phonon-phonon scattering mechanisms become important and limit the phonon lifetimes. We take a novel approach and simulate the phonon dispersion of a complex dynamic solid at elevated temperatures with Machine-Learning Force Fields of near-first-principles accuracy. Through large-scale molecular dynamics simulations the projected velocity autocorrelation function (PVACF) is obtained. We apply this approach to the inorganic perovskite CsPbBr$_{3}$. Imaginary modes in the harmonic picture of this perovskite are absent in the PVACF, indicating a dynamic stabilization of the crystal. The anharmonic nature of the potential makes a decoupling of the system into a weakly interacting phonon gas impossible. The phonon spectra of CsPbBr$_{3}$ show the characteristics of a phonon liquid. Rattling motions of the Cs$^{+}$ cations are studied by self-correlation functions and are shown to be nearly dispersionless motions of the cations with a frequency of $\sim$0.8THz within the lead-bromide framework.