Elastic and Anelastic Properties of Ferroelectric ${\mathrm{SrTi}}^{18}{\mathrm{O}}_3$ in the kHz-MHz Regime

Resonant ultrasound spectroscopy has been used to follow elastic softening in ${\mathrm{SrTi}}^{18}{\mathrm{O}}_3$ in the frequency range $\sim 0.2–1\mathrm{MHz}$. A dramatic softening of $C_{44}$ occurs as the Curie temperature $T_c=24\mathrm{K}$ is approached from above or below, which correlates with the development of a central peak in Raman and Brillouin spectra. This is attributed to strong coupling between the acoustic mode and the central peak mode. A weaker anomaly is seen in a resonance mode which is believed to be controlled by $\frac{1}{2}(C_{11}-C_{12})$. Significant attenuation accompanies this softening and an additional dissipation peak has also been observed at $\sim 80–90\mathrm{K}$. This extends earlier work by a factor of $150000\times$ from the 30 GHz regime and helps address the question as to whether the ferroelectricity is stimulated primarily by a soft mode into a homogeneous ground state or by clustering of rhombohedral nanoregions into an inhomogeneous ground state.

Figure 1

Selected RUS spectra at approximately 5 K intervals, collected in a heating sequence. The left-hand axis should be amplitude, but the spectra have been shifted in proportion to the temperature at which they were collected and the axis labeled as temperature. The $\mathrm{\text{cubic}}\to \mathrm{\text{tetragonal}}$ transition is marked by the disappearance of most resonance peaks. The peak which persists near 1 MHz is instrumental in origin, as are peaks below $\sim 0.2\mathrm{MHz}$ which show little temperature dependence. A sample peak is visible showing variations with temperature between $\sim 0.13$ and $\sim 0.18\mathrm{MHz}$, and an additional broad resonance peak appears in spectra collected between 10 and 35 K.

Figure 2

Data for resonance frequency $f$ and inverse quality factor $Q^{-1}$ obtained by fits to the sample peak near 0.15 MHz in the stability field of the low symmetry structure and to peaks near 0.45, 0.55, 0.6 MHz from the stability field of the cubic phase. The broken line represents the transition point, which has been placed at 106.5 K in view of the steep increase in $Q^{-1}$ which occurs below 107 K. In comparison with ${\mathrm{SrTi}}^{16}{\mathrm{O}}_3$, elastic softening as $T\to T_c$ from above is limited both in magnitude and the temperature range over which it occurs.

Figure 3

Variations of $f^2$ (filled circles) and $Q^{-1}$ (open circles) from fits to the broad peak which is clearly visible in low-temperature spectra shown in Fig. 1.