Imaging of nanoscale polar textures in quantum paraelectric SrTiO₃.

Abstract

When cooling towards a ferroelectric phase transition, collective atomic motions (phonons) slow down (soften) until a static atomic displacement pattern forms, giving rise to spontaneous polarization throughout the material¹. However, in quantum paraelectrics such as strontium titanate (SrTiO₃), long-range ferroelectric order does not develop at low temperatures due to persistent quantum fluctuations of ionic positions^2,3. In SrTiO₃, quantum paraelectricity emerges below T_q ≈ 40 K refs. ^4-6 and is preceded by anomalous phonon dynamics: a transverse acoustic phonon mode partially softens at a finite wavevector, hinting at a modulated state at the nanoscale^7-12. The precise real-space structure of SrTiO₃ at low temperature, however, has remained unresolved despite decades of study. Here we directly image the low-temperature polar structure of a SrTiO₃ lamella using cryogenic scanning transmission electron microscopy down to 20 K. High-resolution imaging reveals a spatially fluctuating landscape of nanoscale domains. Below about 105 K, short-range polar domains initially self-organize into a periodic structure extending over tens of nanometres; however, upon entering the quantum paraelectric regime below T_q, the process reverses and the periodically ordered polar nanodomains fragment into smaller clusters. Quantum paraelectricity in SrTiO₃ underlies remarkable properties, including large dielectric permittivity^13,14, proximity to ferroelectricity^15,16, multiferroicity¹⁷ and unconventional superconductivity^18-20. Our visualizations suggest that these phenomena may be linked to complex ordering and disordering of polar nanodomains at low temperature.