Relaxor study in high-entropy ferroelectrics and Vogel-Fulcher analysis of composition-dependent symmetry

The design of high-entropy perovskite relaxor ferroelectrics has emerged as a promising strategy to enhance the performance of high-energy storage materials. However, the dynamics of dipole moments in the relaxor ground state remain unclear. To address this issue, we studied and compared the dielectric spectra of noncentrosymmetric, $P4mm$ (Ba1/4Pb1/4Bi1/4K1/4)TiO₃, (Ba1/5Pb1/5Bi1/5Ca1/5K1/5)TiO₃, and (Ba1/2Pb1/8Bi1/8Ca1/8K1/8)TiO₃ and centrosymmetric, Pm3̄m (Ba1/5Pb1/5Sr1/5RE1/5K1/5)TiO₃ with RE=La, Nd, and Sm high-entropy compounds. Upon cooling, noncentrosymmetric compounds show a sharp ferroelectric transition (TC) and an ergodic-to-paraelectric transition at the Burns temperature (TB). In contrast, centrosymmetric compounds exhibit broader, diffuse dielectric peaks without a signal of long-range ferroelectric order. These features, arising from compositional disorder, are the fingerprint of relaxor ferroelectrics. Our analysis reveals that crystal symmetry correlates strongly with the dynamics of dipoles within polar nanoregions (PNRs). We studied PNRs dynamics using the Vogel-Fulcher (VF) model, fitting both the frequency f of the permittivity peak maximum at the temperature Tₘ and the characteristic relaxation time τc derived from the permittivity spectra (ε^' and ε^''), using a Debye-like function. For noncentrosymmetric compounds, the VF model was fitted to the frequency f only in the paraelectric state, while the relaxation time τc does not show VF-type behavior. On the other hand, for centrosymmetric compounds, it was found that the relaxation time τc can be described with physically meaningful parameters, whereas fitting the frequency f yielded fiscally unfeasible results using the VF model. These results define two distinct pathways in complex and highly disordered systems. On cooling, the symmetry breaking (Pm3̄m-P4mm) is associated with a ferroelectric-ergodic-paraelectric transition, where PNRs freeze at TC, characteristic of a relaxor ferroelectric, whereas the preservation of global symmetry (Pm3̄m) correlates with an ergodic-nonergodic state at very low temperatures, where the PNRs become static below TVF, defining a canonical relaxor. The existence and nanoscale heterogeneity of PNRs were directly confirmed via piezoresponse force microscopy.