Soft-mode nonlinearities away from ferroelectric phase transition
The interplay between ionic and electronic subsystems dictates the behavior of structural phase transitions in polar dielectrics, a coupling mediated by soft optical phonon modes. In incipient ferroelectrics such as SrTiO$_3$ (STO), strong local-field effects can drive the lattice into a non-perturbative regime near the phase boundary. However, disentangling the distinct contributions of local fields from those of spontaneous macroscopic polarization remains an experimental challenge. Here, we isolate these mechanisms by probing paraelectric STO deep within its symmetric phase, where macroscopic spontaneous polarization is suppressed. Linear terahertz (THz) spectroscopy reveals that the soft mode exhibits a hybrid character, predominantly driven by electronic polarizability. Utilizing two-dimensional THz spectroscopy, we map the underlying nonlinear signals, demonstrating that the system persists in a perturbative regime characterized by robust local-field coherence. By implementing a microscopic model of coupled electronic and lattice degrees of freedom mediated by local fields, we qualitatively reproduce these multidimensional coherent signatures. Our findings highlight that while local fields are necessary to initiate non-perturbative lattice dynamics, they are insufficient on their own. This reveals that spontaneous polarization plays a deterministic role in dictating soft-mode nonlinearities in strongly correlated polar dielectrics.