Slow and fast relaxation times of quantum lattice model with local multi-well potentials: phenomenological dynamics for Sn$_{2}$P$_{2}$S$_{6}$ ferroelectric crystals

TL;DR

This paper develops a phenomenological model combining statistical equilibrium and thermodynamics to analyze the slow and fast relaxation times in a quantum lattice model of ferroelectric crystals with multi-well potentials, focusing on phase transition behavior.

Contribution

It introduces a new framework linking dipole polarization and volume deformation as fluxes and forces, deriving rate equations with two relaxation times near equilibrium.

Findings

Identification of two distinct relaxation times ($ au_{S}$ and $ au_{F}$) near phase transitions.

Behavior of relaxation times varies significantly around ferroelectric phase transitions.

The model provides insights into irreversible dynamics in ferroelectric lattice systems.

Abstract

As a continuation of the previously published work [Velychko O. V., Stasyuk I. V., Phase Transitions, 2019, 92, 420], a phenomenological framework for the relaxation dynamics of quantum lattice model with multi-well potentials is given in the case of deformed Sn$_{2}$P$_{2}$S$_{6}$ ferroelectric lattice. The framework is based on the combination of statistical equilibrium theory and irreversible thermodynamics. In order to study these dynamics in a connected way we assume that the dipole ordering or polarization ($\eta$) and volume deformation ($u$) can be treated as fluxes and forces in the sense of Onsager theory. From the linear relations between the forces and fluxes, the rate equations are derived and characterized by two relaxation times ($\tau_{S}, \tau_{F}$) which describe the irreversible process near the equilibrium states. The behaviors of $\tau_{S}$ and $\tau_{F}$ in the vicinity of ferroelectric phase transitions are studied.