Elastic softness of hybrid lead halide perovskites

Much recent attention has been devoted towards unravelling the microscopic optoelectronic properties of hybrid organic-inorganic perovskites (HOP). Here we investigate by coherent inelastic neutron scattering spectroscopy and Brillouin light scattering, low frequency acoustic phonons in four different hybrid perovskite single crystals: MAPbBr$_3$, FAPbBr$_3$, MAPbI$_3$ and $\alpha$-FAPbI$_3$ (MA: methylammonium, FA: formamidinium). We report a complete set of elastic constants caracterized by a very soft shear modulus C$_{44}$. Further, a tendency towards an incipient ferroelastic transition is observed in 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 $\alpha$-FAPbI$_3$.