A combined theoretical and experimental study of the phase coexistence and morphotropic boundaries in ferroelectric-antiferroelectric-antiferrodistortive multiferroics

The physical nature of the ferroelectric (FE), ferrielectric (FEI) and antiferroelectric (AFE) phases, their coexistence and spatial distributions underpins the functionality of antiferrodistortive (AFD) multiferroics in the vicinity of morphotropic phase transitions. Using Landau-Ginzburg-Devonshire (LGD) phenomenology and a semi-microscopic four sublattice model (FSM), we explore the behavior of different AFE, FEI, and FE long-range orderings and their coexistence at the morphotropic phase boundaries in FE-AFE-AFD multiferroics. These theoretical predictions are compared with the experimental observations for dense Bi_1-yR_yFeO₃ ceramics, where R is Sm or La atoms with the fraction 0 ≤ y ≤ 0.25, as confirmed by the X-ray diffraction (XRD) and Piezoresponse Force Microscopy (PFM). These complementary measurements were used to study the macroscopic and nanoscopic transformation of the crystal structure with doping. The comparison of the measured and calculated AFE/FE phase fractions demonstrate that the LGD-FSM approach well describes the experimental results obtained by XRD and PFM for Bi_1-yR_yFeO₃. Hence, this combined theoretical and experimental approach provides further insight into the origin of the morphotropic boundaries and coexisting FE and AFE states in model rare-earth doped multiferroics.