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The low frequency lattice vibrations and relaxations are investigated insingle crystals of the four 3D hybrid organolead perovskites, MAPbBr$_3$,FAPbBr$_3$, MAPbI$_3$, and $\alpha$-FAPbI$_3$, at the Brillouin zone centerusing Raman and Brillouin scattering and at the zone boundary using inelasticneutron scattering. The temperature dependence of the PbX$_6$ lattice modes inthe four compounds can be renormalized into universal curves, highlighting acommon vibrational dynamics at the cubic to tetragonal transition. Inparticular, no soft vibration is observed excluding a displacive-liketransitional dynamics. The reorientational (pseudospin) motions of themolecular cations exhibit a seemingly order-disorder character recalling thatof plastic crystals, but attributed to a secondary order-parameter. Atultra-low frequency, a quasi-elastic component evidenced by Brillouinscattering and associated to the unresolved central peak observed in neutronscattering, is attributed to center of mass anharmonic motions and rattling ofthe molecular cations in the perovskite cavities. Its partially unexpressedcritical behavior at the transition points toward the general importance ofdefects in HOPs preventing the net divergence of order parameter correlationsat the critical temperatures.

Pseudospin-phonon pretransitional dynamics in lead halide hybrid perovskites