  The long carrier lifetime and defect tolerance in metal halide perovskites
(MHPs) are major contributors to the superb performance of MHP optoelectronic
devices. Large polarons were reported to be responsible for the long carrier
lifetime. Yet microscopic mechanisms of the large polaron formation including
the so-called phonon melting, are still under debate. Here, time-of-flight
(TOF) inelastic neutron scattering (INS) experiments and first-principles
density-functional theory (DFT) calculations were employed to investigate the
lattice vibrations (or phonon dynamics) in methylammonium lead iodide
($\rm{MAPbI_3}$), a prototypical example of MHPs. Our findings are that optical
phonons lose temporal coherence gradually with increasing temperature which
vanishes at the orthorhombic-to-tetragonal structural phase transition.
Surprisingly, however, we found that the spatial coherence is still retained
throughout the decoherence process. We argue that the temporally decoherent and
spatially coherent vibrations contribute to the formation of large polarons in
this metal halide perovskite.
