Pseudospin-phonon pretransitional dynamics in lead halide hybrid perovskites

The low frequency lattice vibrations and relaxations are investigated in single crystals of the four 3D hybrid organolead perovskites, MAPbBr$_3$, FAPbBr$_3$, MAPbI$_3$, and $\alpha$-FAPbI$_3$, at the Brillouin zone center using Raman and Brillouin scattering and at the zone boundary using inelastic neutron scattering. The temperature dependence of the PbX$_6$ lattice modes in the four compounds can be renormalized into universal curves, highlighting a common vibrational dynamics at the cubic to tetragonal transition. In particular, no soft vibration is observed excluding a displacive-like transitional dynamics. The reorientational (pseudospin) motions of the molecular cations exhibit a seemingly order-disorder character recalling that of plastic crystals, but attributed to a secondary order-parameter. At ultra-low frequency, a quasi-elastic component evidenced by Brillouin scattering and associated to the unresolved central peak observed in neutron scattering, is attributed to center of mass anharmonic motions and rattling of the molecular cations in the perovskite cavities. Its partially unexpressed critical behavior at the transition points toward the general importance of defects in HOPs preventing the net divergence of order parameter correlations at the critical temperatures.