Study of soft modes by temperature-derivative first- and second-order Raman spectroscopy

A study of soft modes in SrTi${\mathrm{O}}_3$ using a temperature-derivative Raman technique is reported. The $A_{1g}$ component of the mode which softens towards the phase transition at 108 K has been studied below the phase-transition temperature. The energy of the modes as a function of temperature was followed down to 4 ${\mathrm{cm}}^{-1\mathrm{}}$. The square of the energy of this mode deviates from the Landau behavior for $\frac{T}{T_c}>0.95\mathrm{}$ and follows a temperature dependence very similar to that of the rotation of the octahedra in SrTi${\mathrm{O}}_3$. The soft ferroelectric mode has been observed for the first time in second-order Raman. It is shown that two structures in the spectra correspond to a replica of the soft mode and to the simultaneous emission of the soft mode and the absorption of an acoustic mode close to the $\Gamma$ point.