Lattice Dynamics above Structural Phase Transitions: SrTiO3

The temperature dependence of the soft mode ${\omega }_0$, the central peak $S(\overrightarrow{\mathrm{q}}, \omega =0)$, and the electron-paramagnetic-resonance (EPR) linewidth $\Delta H$ above a continuous structural phase transition driven by a soft $R$-corner mode is calculated. In the noncritical region the important self-energy terms leading to a central peak at $\overrightarrow{\mathrm{q}}={\overrightarrow{\mathrm{q}}}_R$ are shown to be the chain diagrams. This is due to a particular feature of the lowest transverse phonon branch giving rise to a two-phonon density of states ${\rho }_0(\overrightarrow{\mathrm{q}}, \omega )$ which is nonzero for $\overrightarrow{\mathrm{q}}\cong {\overrightarrow{\mathrm{q}}}_R$, $\omega \cong 0$. The exponents of $T-T_c$ found for ${\omega }_0$, $S({\overrightarrow{\mathrm{q}}}_R, \omega =0)$, and $\Delta H$ are, respectively, +½, -2, and -½, the first being the same as that obtained in the mean-field theory of Pytte and Feder, and the second agreeing with a result of Cowley.