We consider a standard Ginzburg-Landau model of a ferroelectric whose electrical polarization is coupled to gradients of elastic strain. At the harmonic level, such flexoelectric interaction is known to hybridize acoustic and optic phonon modes and lead to phases with modulated lattice structures that precede the state with spontaneously broken inversion symmetry. Here, we use the self-consistent phonon approximation to calculate the effects of thermal and quantum polarization fluctuations on the bare hybridized modes to show that such long-range modulated order is unstable at all temperatures. We discuss the implications for the nearly ferroelectric ${\mathrm{SrTiO}}_3$ and ${\mathrm{KTaO}}_3$, and we propose that these systems are melted versions of an underlying modulated state that is dominated by nonzero momentum thermal fluctuations except at the very lowest temperatures.

• Received 21 August 2022
• Revised 24 April 2023
• Accepted 25 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.046801