Relaxor study in high-entropy ferroelectrics and Vogel-Fulcher analysis of composition-dependent symmetry
Phys. Rev. Materials 10, 084402 – Published 6 August, 2026
DOI: https://doi.org/10.1103/cmbp-8sw3
Abstract
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, , , and and centrosymmetric, with , Nd, and Sm high-entropy compounds. Upon cooling, noncentrosymmetric compounds show a sharp ferroelectric transition () and an ergodic-to-paraelectric transition at the Burns temperature (). 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 of the permittivity peak maximum at the temperature and the characteristic relaxation time derived from the permittivity spectra ( and ), using a Debye-like function. For noncentrosymmetric compounds, the VF model was fitted to the frequency only in the paraelectric state, while the relaxation time does not show VF-type behavior. On the other hand, for centrosymmetric compounds, it was found that the relaxation time can be described with physically meaningful parameters, whereas fitting the frequency 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 () is associated with a ferroelectric-ergodic-paraelectric transition, where PNRs freeze at , characteristic of a relaxor ferroelectric, whereas the preservation of global symmetry () correlates with an ergodic-nonergodic state at very low temperatures, where the PNRs become static below , defining a canonical relaxor. The existence and nanoscale heterogeneity of PNRs were directly confirmed via piezoresponse force microscopy.