  Hybrid lead halide perovskites (LHPs) are a class of semiconductor with novel
properties that are distinctively governed by structural fluctuations.
Diffraction experiments sensitive to average, long-range order reveal a cubic
structure in the device-relevant, high-temperature phase. Local probes find
additional short-range order with lower symmetry that may govern the
structure-function relationships of LHPs. However, the dimensionality,
participating atoms, and dynamics of this short-range order are unresolved,
impeding our understanding of technologically relevant properties including
long carrier lifetimes and facile halide migration. Here, we determine the true
structure of two prototypical hybrid LHPs, CH$_3$NH$_3$PbI$_3$ and
CH$_3$NH$_3$PbBr$_3$, using a combination of single-crystal X-ray and neutron
diffuse scattering, neutron inelastic spectroscopy, and molecular dynamics
simulations. The remarkable collective dynamics we found are not suggested by
previous studies and consist of a network of local two-dimensional, circular
pancake-like regions of dynamically tilting lead halide octahedra (lower
symmetry) that induce longer range intermolecular correlations within the
CH$_3$NH$_3^+$ sublattice. The dynamic local structure can introduce transient
ferroelectric or antiferroelectric domains that increase charge carrier
lifetimes, and strongly affect the halide migration, a poorly understood
degradation mechanism. Our approach of co-analyzing single-crystal X-ray and
neutron diffuse scattering data with MD simulations will provide unparalleled
insights into the structure of hybrid materials and materials with engineered
disorder.
