Domain Wall Damping and Elastic Softening in ${\mathrm{SrTiO}}_3$: Evidence for Polar Twin Walls

A marked change in anelastic properties, namely, elastic softening accompanied by increased damping, has been observed in a single crystal of ${\mathrm{SrTiO}}_3$ below $\sim 50\mathrm{K}$ by resonant ultrasound spectroscopy. This correlates with other subtle changes in structure and properties which have been explained in the past in terms of a novel quantum state and the formation of polar clusters in an incipient ferroelectric structure. Comparison of the new data, obtained at frequencies near 1 MHz, with mechanical spectroscopy data collected at a few Hz or a few kHz, reveals a distinct dispersion with frequency and is interpreted in terms of an acoustic loss mechanism which depends primarily on the mobility under stress of ferroelastic twin walls. In most ferroelastic materials, it is found that the twin walls become immobile below some low-temperature interval due to the pinning effects of defects. It is proposed instead for ${\mathrm{SrTiO}}_3$ that associated with the local atomic displacements within the incipient ferroelectric clusters is a change in structure of the twin walls such that their mobility becomes enhanced. We propose that the structural change is not correlated with structural changes of the bulk material but relates to increasing polarity of the walls. This interpretation implies that ferroelastic domain walls in ${\mathrm{SrTiO}}_3$ become ferroelectric at low temperatures.

Figure 1

Temperature evolution of RUS resonances over a small frequency interval near 1 MHz. The spectra have been offset up the $y$ axis in proportion to the temperature at which they were collected during a heating sequence between 9 K (bottom spectrum) and 291 K (top spectrum). The spectrum shown in green at the boundary between closely spaced and more widely spaced spectra was collected at 105.6 K and is the first to show sharp resonances typical of the cubic structure. Each peak represents a resonance mode of the sample. In spite of strong attenuation in the stability field of the tetragonal structure, two broad peaks remain clearly visible down to low temperatures.

Figure 2

Temperature dependence of the squared resonance RUS frequency (left axis, red, steep decrease below $\sim 106\mathrm{K}$) and damping (right axis, blue, steep increase below $\sim 106\mathrm{K}$) for a peak near 1 MHz which probably depends substantially on $C_{44}$. The ferroelastic phase transition at 105 K appears as sudden softening and increasing acoustic loss. Low-temperature anomalies are comparably large but are unrelated to any macroscopic structural instability.

Figure 3

Integral damping of the entire RUS spectrum, obtained by autocorrelation analysis in the manner described by Salje and Carpenter [26].

Figure 4

Selected resonance peaks showing marked asymmetry (Fano profiles) in spectra from the ferroelastic phase of ${\mathrm{SrTiO}}_3$.