Ferroic Polarization from Nonpolar Phonons

Born effective charge, a fundamental quantity in lattice dynamics and ferroelectrics, provides a quantitative measure of linear polarization response to ionic displacements. However, it does not account for higher-order effects, which can play a significant role in certain materials, such as fluorite HfO$_2$. In this letter, we use the second-order mode effective charges defined with the second-order atomic dynamical charges as a measure of the dipole moments generated by nonpolar lattice distortions. Using first-principles calculations, we demonstrate that specific combinations of nonpolar phonons in many oxides can induce strongly aligned second-order polarizations, reaching magnitudes comparable to those of intrinsically polar modes even in the zero frequency limit, broadening the understanding of second-order effects, which have historically been emphasized for their dynamical effects at specific frequency ranges. Through a symmetry-based analysis of the charge density, we elucidate the microscopic origin of these effects, tracing them to variations in bond covalency and local electronic rearrangements. We also demonstrate large second-order mode effective charge in well-studied perovskites, highlighting the generality of these phenomena. Our results offer new insights into the design principles of next-generation ferroelectric, piezoelectric and multifunctional materials from the higher-order contribution to polarization in crystalline solids.