Polarization Fluctuations near a Ferroelectric Phase Transition

Abstract

Critical polarization fluctuations in the nonpolar phase of a ferroelectric have been determined self-consistently using a correlated effective-field theory of ferroelectricity. Static correlations take the form of highly developed ferroelectric chains along an incipient polar direction, with interchain correlations being relatively very weak and of either sign. Neither interchain nor interchain correlations exhibit an exponential decay at large distances and a unique definition of correlation length is correspondingly difficult to obtain. The new statistical theory is able to describe phase transitions of both displacement and order-disorder character and predicts a paraelectric susceptibility divergence as $t=T\ensuremath{-}{T}_{C}\ensuremath{\rightarrow}0$ of the form $\frac{[\mathrm{ln}(\frac{1}{t})]}{t}$ and a specific heat going as $A\ensuremath{-}[\frac{{B}^{\ensuremath{'}}}{\mathrm{ln}(\frac{1}{t})}]$, where $A$ and ${B}^{\ensuremath{'}}$ are constants. These forms are to be compared with the Curie-Weiss susceptibility and the logarithmic divergence of specific heat which follow from the commonly used random-phase approximation.