Temperature Dependence of the Soft Ferroelectric Mode in KTaO3

The lattice dynamics of the perovskite-type ferroelectric KTa${\mathrm{O}}_3$ has been studied by inelastic neutron-scattering techniques. In particular, the temperature dependence of the soft ferroelectric mode, namely a transverse optical mode at $q=0\mathrm{}$, has been studied between 4 and 295°K. At 295°K, the phonon energy of this mode is 10.7±0.3 meV (86.3±2.5 ${\mathrm{cm}}^{-1\mathrm{}}$), in excellent agreement with the optical measurement of Miller and Spitzer. The square of the energy of the soft mode follows closely the temperature dependence of $\frac{1}{\epsilon }$ down to 15°K (the extrapolated Curie temperature is 2-4°K). The deviation of the dielectric constant $\epsilon$ from a Curie-Weiss law, at the high- and low-temperature extremes, is faithfully reflected in the temperature dependence of the soft mode. Anomalous behavior was observed at 4.3°K in this mode as well as in other modes. A tentative explanation for this anomalous behavior is that a phase transition has set in at approximately 10°K.