Polar nanoregions and reentrant-like ferroelectric behavior in SrTiO$_3$

Abstract

Recent real-space imaging in quantum paraelectric SrTiO$_3$ [Nature 656, 54 (2026)] reveals that local polar textures do not continuously grow upon cooling, but reach a maximum intensity at intermediate temperatures around 60-65~K and weaken again toward the quantum paraelectric ground state. Such a reentrant-like weakening of local polar textures challenges the conventional paradigm in which ordering tendencies generally strengthen as thermal fluctuations are suppressed. Here we employ a self-consistent phase-field theory showing that this anomalous behavior naturally arises from the interplay between intrinsic polar and antiferrodistortiv (AFD) fluctuations. We demonstrate that flexoelectric-like coupling strongly hybridizes the polar and AFD modes. As the uncoupled polar and AFD modes cross near 52~K, their hybridization is maximized, driving the lower hybridized branch to develop a minimum on a finite-wave-vector shell. This finite-$q$ softening triggers a Brazovskii-type instability, strongly enhancing polarization correlations and producing nanoscale polar textures. Away from the crossing temperature, the two modes become increasingly detuned, weakening their hybridization and the associated finite-$q$ softening. These results reaveal the origin of the formation of polar nanoregions in SrTiO$_3$, naturally explaining the unexpected confinement to an intermediate-temperature window and providing a mechanism beyond the quantum-fluctuation-based interpretation suggested by experiment. Furthermore, we predict an unconventional reentrant-like sequence in weakly strained SrTiO$_3$, evolving from ferroelectric to paraelectric, polar-nanoregion, and eventually paraelectric regimes upon heating from zero temperature.