Anharmonic lattice dynamics in large thermodynamic ensembles with machine-learning force fields: CsPbBr₃, 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 the 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 CsPbBr3. 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 CsPbBr3 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 ∼0.8THz within the lead-bromide framework.