  In hybrid perovskites, the organic molecules and inorganic frameworks exhibit
distinct static and dynamic characteristics. Their coupling will lead to
unprecedented phenomena, which have attracted wide research interests. In this
paper, we employed Deep Potential molecular dynamics (DPMD), a large-scale MD
simulation scheme with DFT accuracy, to study $\mathrm{FA/MAPbI_3}$ hybrid
perovskites. A spontaneous hybrid nano-domain behavior, namely multiple
molecular rotation nano-domains embedded into a single $\mathrm{[PbI_6]^{4-}}$
octahedra rotation domain, was firstly discovered at low temperatures. The
behavior originates from the interplay between the long range order of
molecular rotation and local lattice deformation, and clarifies the puzzling
diffraction patterns of $\mathrm{FAPbI_3}$ at low temperatures. Our work
provides new insights into the structural characteristics and stability of
hybrid perovskite, as well as new ideas for the structural characterization of
organic-inorganic coupled systems.
