Paraelectric and Ferroelectric States in a Model for Relaxor Ferroelectrics

TL;DR

This paper models relaxor ferroelectrics to reveal metastable paraelectric states, phase coexistence, and the effects of disorder, providing insights into experimental observations of these complex materials.

Contribution

It introduces a variational model incorporating correlations and disorder averaging to analyze the free energy landscape of relaxor ferroelectrics, highlighting metastable states and phase transitions.

Findings

Metastable paraelectric states exist down to zero temperature.

Phase diagram shows coexistence line ending at a critical point.

Distinct structure factors differentiate relaxor states from conventional ferroelectrics.

Abstract

We study the free energy landscape of a minimal model for relaxor ferroelectrics. Using a variational method which includes leading correlations beyond the mean-field approximation as well as disorder averaging at the level of a simple replica theory, we find metastable paraelectric states with a stability region that extends to zero temperature. The free energy of such states exhibits an essential singularity for weak compositional disorder pointing to their necessary occurrence. Ferroelectric states appear as local minima in the free energy at high temperatures and become stable below a coexistence temperature $T_c$. We calculate the phase diagram in the electric field-temperature plane and find a coexistence line of the polar and non-polar phases which ends at a critical point. First-order phase transitions are induced for fields sufficiently large to cross the region of stability of the metastable paraelectric phase. These polar and non-polar states have distinct structure factors from those of conventional ferroelectrics. We use this theoretical framework to compare and to gain physical understanding of various experimental results in typical relaxors.