Polar-Displacement Mechanism for Negative Poisson's Ratio in Ferroelectric Perovskites

Negative Poisson's ratio (NPR) is rare in crystalline solids, and its microscopic origin in oxide perovskites remains elusive. Here we use first-principles calculations to investigate the auxetic response of prototypical ferroelectrics PbTiO_{3} and BaTiO_{3} (BTO). We show that NPR is governed by local polar ionic displacements, which stabilize cation-anion bonding environment under deformation and can reverse the sign of the Poisson's ratio. In particular, NPR in both the tetragonal and cubic phases of BTO emerges only in structures exhibiting local Ti off centering along the ⟨111⟩ directions, whereas the conventional [001]-polarized tetragonal phase and the high-symmetry cubic structure display positive Poisson's ratios. Our results establish local polarization as the microscopic origin of NPR in ferroelectrics and highlight it as a tunable parameter for designing auxetic functionality in perovskite oxides.