Phenomenological explanation of the anomalous dielectric behavior of alums with pseudo-spin-lattice coupled-mode model

Abstract

With the use of the pseudo-spin-lattice coupled-mode (PLCM) model and the statistical Green's-function technique a phenomenological explanation of the hitherto unexplained ferroelectric phase transitions in (C${\mathrm{H}}_{3}$N${\mathrm{H}}_{3}$)Al${(\mathrm{S}{\mathrm{O}}_{4})}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}12${\mathrm{H}}_{2}$O (MASD) and (N${\mathrm{H}}_{4}$)Fe${(\mathrm{S}{\mathrm{O}}_{4})}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}12${\mathrm{H}}_{2}$O (AFeSD) alums has been given. The pseudospins assumed to be associated with the protons of the monovalent methylammonium group and the ammonium groups, respectively, in MASD and AFeSD alums undergo ordering at low temperatures. From our calculations the expression for the electrical susceptibility ($\ensuremath{\chi}$) comes out to be of the form $\ensuremath{\chi}={A}_{0}^{\ensuremath{'}}+{B}_{0}^{\ensuremath{'}}+{C}_{0}^{\ensuremath{'}}+\ensuremath{\cdots}$, where ${A}_{0}^{\ensuremath{'}}$ is a temperature-independent term and ${B}_{0}^{\ensuremath{'}}$ is a measure of the contribution from phonon-phonon interaction. The third term ${C}_{0}^{\ensuremath{'}}$ arises from the rotation of the monovalent ions. For ferroelectric alums ${C}_{0}^{\ensuremath{'}}$ is found to be highly temperature dependent, and for other nonferroelectric alums both ${B}_{0}^{\ensuremath{'}}$ and ${C}_{0}^{\ensuremath{'}}$ show negligibly small dependences on temperature. A single set of model parameters (Blinc---de Gennes parameters) has been calculated for AFeSD from fitting the experimental data of dielectric constant ($\ensuremath{\epsilon}$), Curie-Weiss constant ($C$) and transition temperature (${T}_{C}$) with the corresponding theoretical expressions. However, in the case of MASD alum, we must vary the renormalized phonon frequency ${\overline{\ensuremath{\omega}}}_{0}[={\ensuremath{\omega}}_{0}+{\overline{A}}^{\ensuremath{'}}(0, T)]$ with temperature to fit the entire $\ensuremath{\epsilon}\ensuremath{-}T$ curve with a single set of model parameters. This is due to the presence of strong phonon-phonon interaction in MASD alum, causing the strongly temperature-dependent anharmonicity parameter ${\overline{A}}^{\ensuremath{'}}(0, T)$. The present success of the PLCM model for explaining the phase transitions in alums definitely indicates the unified character of this model, which may also be applied to many other crystals.