Critical Dynamics at Structural Transitions forT≥Tc

Abstract

We develop a theory of critical dynamics for the rotations of the $B{\mathrm{O}}_{6}$ octahedra in $\mathrm{AB}{\mathrm{O}}_{3}$ perovskites at $T\ensuremath{\ge}{T}_{c}$. Given a soft mode, we derive, using the third longtime approximation of Mori's continued-fraction representation, an approximate expression for the dynamic order-parameter form factor. This description leads, close to ${T}_{c}$, to the correct three-pole structure around $\ensuremath{\omega}=0$, including the central peak and the resonances of the conventional soft mode. The central peak is predicted to appear whenever the conventional soft-mode frequency and the isothermal phonon frequency differ considerably. This gives support to Feder's prediction. Given a soft acoustic mode, the theory also accounts for a central peak, as does the phenomenological theory of Shirane and Axe. Our theory, which leads by construction to a correct three-pole structure around $\ensuremath{\omega}=0$, justifies and clarifies the phenomenological expressions for the dynamic order-parameter form factor, as proposed by Schwabl and Shirane and Axe.