Elastic Softness of Hybrid Lead Halide Perovskites

Much recent attention has been devoted towards unraveling the microscopic optoelectronic properties of hybrid organic-inorganic perovskites. Here we investigate by coherent inelastic neutron scattering spectroscopy and Brillouin light scattering, low frequency acoustic phonons in four different hybrid perovskite single crystals: ${\mathrm{MAPbBr}}_{3}$, ${\mathrm{FAPbBr}}_{3}$, ${\mathrm{MAPbI}}_{3}$, and $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{FAPbI}}_{3}$ (MA: methylammonium, FA: formamidinium). We report a complete set of elastic constants characterized by a very soft shear modulus ${C}_{44}$. Further, a tendency towards an incipient ferroelastic transition is observed in ${\mathrm{FAPbBr}}_{3}$. We observe a systematic lower sound group velocity in the technologically important iodide-based compounds compared to the bromide-based ones. The findings suggest that low thermal conductivity and hot phonon bottleneck phenomena are expected to be enhanced by low elastic stiffness, particularly in the case of the ultrasoft $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{FAPbI}}_{3}$.