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Abstract

The nature of the "failed" ferroelectric transition in SrTiO₃ has been a long-standing puzzle in condensed matter physics. A compelling explanation is the competition between ferroelectricity and an instability with a mesoscopic modulation of the polarization. These polarization density waves, which should become especially strong near the quantum critical point, break local inversion symmetry and are difficult to probe with conventional x-ray scattering methods. Here we combine a femtosecond x-ray free electron laser (XFEL) with THz coherent control methods to probe inversion symmetry breaking at finite momenta and visualize the instability of the polarization on nanometer lengthscales in SrTiO₃. We find polar-acoustic collective modes that are soft particularly at the tens of nanometer lengthscale. These precursor collective excitations provide evidence for the conjectured mesoscopic modulated phase in SrTiO₃.