Origin of reentrant relaxor formation in ferroelectric solid solutions

Nanoscale compositional heterogeneity created by doping in ferroelectric systems leads to the formation of conventional relaxors in most cases, but reentrant relaxors in some unusual cases. It has remained a long-standing puzzle why reentrant relaxors rather than conventional relaxors form in these unusual cases. In this study, we use a binary ferroelectric system having a solid solution of a ferroelectric with cubic (C) to tetragonal (T) transition at one end and a ferroelectric with C to rhombohedral (R) transition at the other end, with nanoscale compositional heterogeneities, to reveal the origin of the reentrant relaxor transition. Our phase field simulations based on Landau theory demonstrate that the reentrant relaxor transitions in such a system are manifested by the formation of R nanodomains in the T microdomains upon cooling at compositions near the T/R phase boundary, which is accompanied by frequency-dependent permittivity peaks below ${T}_{\mathrm{C}}$. We found that the difference in phase transition sequence at different local compositions near the T/R phase boundary created by point defect doping is essential for the formation of reentrant relaxors. This work unravels the general conditions for the formation of reentrant relaxors and may shed light on the origin of other reentrant ferroic glasses.