Anharmonic Effects in KTaO3: Ferroelectric Mode, Thermal Expansion,and Compressibility

The effects of temperature and pressure on the static dielectric constant and lattice parameter of KTa${\mathrm{O}}_3$ have been measured. Combined with literature data, the present results allow a determination of the pressure and temperature dependence of the soft-ferroelectric-mode frequency ${\omega }_f$ over a wide temperature range (0-500°K). The isobaric anharmonic self-energy shift of ${\omega }_f$ is separated into its pure-volume (thermal-strain) and pure-temperature contributions. Though small, the thermal-strain contribution is not negligible, amounting to 7% of the measured frequency at 300°K and 10% at 500°K. It acts to reduce the influence of the pure-temperature anharmonicities. The soft-mode Grüneisen parameter ${\gamma }_f$ is very large at low temperatures (460 at 4°K) and decreases rapidly with increasing temperature—unique properties of the soft mode. It is estimated that the strictly harmonic frequency ${\omega }_0$ of the soft mode is just barely imaginary, and thus all of the stabilization of ${\omega }_f$ at 0°K (≥21±4 ${\mathrm{cm}}^{-1\mathrm{}}$) is provided by zero-point anharmonicities. At high pressure, ${\omega }_0$ becomes real. Interpreted in terms of the perturbation and self-consistent phonon treatments, the high-temperature stabilization of ${\omega }_f$ is dominated by quartic anharmonicities, but the nonlinear high-temperature ${\omega }_f^2\mathrm{}\left(T\right)\mathrm{}$ response suggests the importance of higher-order anharmonicities.