Lifetime-shortened acoustic phonons and static order at the Brillouin zone boundary in the organic-inorganic perovskite CH$_3$NH$_3$PbCl$_3$.

Lead halide hybrid perovskites consist of an inorganic framework hosting a molecular cation located in the interstitial space. These compounds have been extensively studied as they have been identified as promising materials for photovoltaic applications with the interaction between the molecular cation and the inorganic framework implicated as influential for the electronic properties. CH3NH3PbCl3 undergoes two structural transitions from a high temperature cubic unit cell to a tetragonal phase at 177 K and an orthorhombic transition at 170 K. We have measured the low-frequency lattice dynamics using neutron spectroscopy and observe an energy broadening in the acoustic phonon linewidth towards the symmetry point QX =(2,1/2,0) when approaching the transitions. Concomitant with these zone boundary anomalies is a hardening of the entire acoustic phonon branch measured near the (2, 0, 0) Bragg position with decreasing temperature. Measurements of the elastic scattering at the Brillouin zone edges QX = (2,1/2,0), QM = (3/2,1/2,0), and QR = (3/2,3/2,5/2) show Bragg peaks appearing below these structural transitions. Based on selection rules of neutron scattering, we suggest that the higher 177 K transition is displacive with a distortion of the local octahedral environment and the lower transition is a rigid tilt transition of the octahedra. We do not observe any critical broadening in energy or momentum, beyond resolution, of these peaks near the transitions. We compare these results to the critical properties reported near the structural transitions in other perovskites. We suggest that the simultaneous onset of static resolution-limited Bragg peaks at the zone boundaries and the changes in acoustic phonon energies near the zone center is evidence of a coupling between the inorganic framework and the molecular cation.