  Freestanding ferroelectric oxide membranes emerge as a promising platform for
exploring the interplay between topological polar ordering and dipolar
interactions that are continuously tunable by strain. Our investigations
combining density functional theory (DFT) and deep-learning-assisted molecular
dynamics simulations demonstrate that DFT-predicted strain-driven morphotropic
phase boundary involving monoclinic phases manifest as diverse domain
structures at room temperatures, featuring continuous distributions of dipole
orientations and mobile domain walls. Detailed analysis of dynamic structures
reveals that the enhanced piezoelectric response observed in stretched
PbTiO$_3$ membranes results from small-angle rotations of dipoles at domain
walls, distinct from conventional polarization rotation mechanism and adaptive
phase theory inferred from static structures. We identify a ferroelectric
topological structure, termed "dipole spiral," which exhibits a giant intrinsic
piezoelectric response ($>$320 pC/N). This helical structure, possessing a
rotational zero-energy mode, unlocks new possibilities for exploring chiral
phonon dynamics and dipolar Dzyaloshinskii-Moriya-like interactions.
