Valence fluctuations in Sn(Pb)$_2$P$_2$S$_6$ ferroelectrics

TL;DR

This paper investigates valence fluctuations and charge disproportionation in Sn(Pb)$_2$P$_2$S$_6$ ferroelectrics, analyzing phase diagrams, phonon behavior, and dielectric properties through computational and theoretical models.

Contribution

It introduces a comprehensive analysis of valence fluctuations and phase transitions in Sn(Pb)$_2$P$_2$S$_6$ using GGA calculations and develops an anharmonic quantum oscillators model.

Findings

Identification of valence fluctuation mechanisms linked to ferroelectricity.

Phase diagrams showing tricritical points and quantum paraelectric states.

Evidence of phonon softening and increased dielectric susceptibility at low temperatures.

Abstract

The valence fluctuations which are related to the charge disproportionation of phosphorous ions $P^{4+} + P^{4+}\rightarrow P^{3+} + P^{5+}$ are the origin of ferroelectric and quantum paraelectric states in Sn(Pb)$_2$P$_2$S$_6$ semiconductors. They involve recharging of SnPS$_3$ or PbPS$_3$ structural groups which could be represented as half-filled sites in the crystal lattice. Temperature-pressure phase diagram for Sn$_2$P$_2$S$_6$ compound and temperature-composition phase diagram for (Pb$_y$Sn$_{1-y}$)$_2$P$_2$S$_6$ mixed crystals, which include tricritical points and where a temperature of phase transitions decrease to 0 K, together with the data about some softening of low energy optic phonons and rise of dielectric susceptibility at cooling in quantum paraelectric state of Pb$_2$P$_2$S$_6$, are analyzed by GGA electron and phonon calculations and compared with electronic correlations models. The anharmonic quantum oscillators model is developed for description of phase diagrams and temperature dependence of dielectric susceptibility.