Electrical Switching of Strain Gradients and 90° Domain Walls via Hidden Polar-Acoustic Coupling in PbTiO_{3}

Although strain gradients hold great promise for tailoring emergent functionalities, their flexible global control remains a fundamental challenge. Here, we address this concern in PbTiO_{3} under biaxial tensile strain by uncovering the spontaneous appearance of strain gradients and 90° ferroelectric domain walls and demonstrating their electric control. Combining symmetry analysis and first-principles calculations, we reveal hidden polar-acoustic instabilities within conventionally assumed ground states. We further demonstrate that the trilinear coupling among the modulated polar mode, acoustic mode with modulated strain, and uniform polar mode spontaneously stabilizes a lower-energy a_{1}/a_{2} 90° domain structure with Pmc2_{1} symmetry and intrinsic strain gradients. Remarkably, we discover similar polar-acoustic coupling that governs both the c/a domain patterns and their dramatic piezoelectric enhancement. Leveraging these strong lattice couplings, we develop a unified framework for describing and electrically switching spatially varying strain and polarization fields. Our Letter resolves long-standing cross-scale discrepancies in the strain phase diagrams of PbTiO_{3}, reveals a new phonon-mediated mechanism for giant piezoelectricity, and provides the atomistic foundation for the electrical control of strain gradients and domain walls.