Soft Polar-Acoustic Excitations Reveal an Incipient Modulated Phase in SrTiO3

Enhanced fluctuations are one of the hallmarks of continuous phase transitions, however in some cases these fluctuations inhibit long-range order down to zero temperature. Even when not fully ordered, the associated elementary excitations of the system inherit properties of the underlying ``hidden order''. Here we study quantum paraelectric SrTiO₃, a quintessential example of such frustrated orders. We use ultrafast x-ray scattering at a free electron laser, together with a novel approach to probe inversion symmetry breaking using intense terahertz pulses, to resolve the polar excitations of SrTiO₃. We find that the relevant low-energy excitations at low temperature are polar-acoustic and particularly soft at the tens of nanometer lengthscale. These soft polar-acoustic modes indicate precursor fluctuations of an incipient polar state in which the polarization and strain are spatially modulated, and is distinct from the known homogeneous ferroelectric state. Our results provide a glimpse into potential modulated phases of SrTiO₃ and highlight the importance of probing fluctuations with atomic resolution both in equilibrium and at ultrafast timescales.