Strain-induced two-dimensional relaxor ferroelectrics in Se-doped PbTe

Triggered by external fields, typical ferroelectrics (FEs) undergo a sharp phase transition from the nonpolarized paraelectric (PE) phase, which induces the emergence of spontaneous electric polarization. It is widely accepted that by introducing a large number of point defects, conventional FEs can be transformed into relaxor FEs, which exhibit unique physical properties, such as polar nanoregions (PNRs) and a corresponding gradual phase transition. In recent years, the discovery of two-dimensional (2D) FEs has attracted significant interest driven by the increasing demand for miniaturized nanoelectronics. Despite the identification of various 2D FE materials, there has been no report on 2D relaxor FEs so far. In this study, we explore the strain-induced FE phase transitions in a Se-doped PbTe monolayer through molecular dynamics simulations utilizing a developed deep-learning potential. Our findings reveal the gradual emergence of PNRs during the strain-induced FE phase transition of $\mathrm{P}{\mathrm{b}}_{50}\mathrm{T}{\mathrm{e}}_{50\ensuremath{-}x}\mathrm{S}{\mathrm{e}}_{x}$ ($x\ensuremath{\ge}4$). Additionally, we showcase the dynamic nature of the PNRs through a comparison between the instantaneous and time-averaged dynamic pair distribution functions. Furthermore, we demonstrate that the evolution of the PNRs' size and percolation strength with increasing strain can be well fitted by power laws derived from the percolation theory, which is a key characteristic of the relaxor-to-FE phase transition. Finally, a strain-temperature PE-relaxor-FE phase diagram for $\mathrm{P}{\mathrm{b}}_{50}\mathrm{T}{\mathrm{e}}_{46}\mathrm{S}{\mathrm{e}}_{4}$ is presented, which provides valuable insights for potential applications involving 2D Se-doped PbTe.