Coupling of GHz Phonons to Ferroelastic Domain Walls in ${\mathrm{SrTiO}}_3$

We study the linear and nonlinear acoustic response of ${\mathrm{SrTiO}}_3$ across its ferroelastic transition at $T_a=105\mathrm{K}$ by time domain Brillouin scattering. Above $T_a$ we observe that for a strain amplitude of $\sim 0.18\%$ the sound velocity for compressive strain exceeds the tensile strain velocity by 3%. Below $T_a$ we find a giant slowing down of the sound velocity by 12% and attribute this to the coupling of GHz phonons to ferroelastic twin domain walls. We propose a new mechanism for this coupling on the ultrafast time scale, providing an important new test ground for theories used to simulate atomic motion in domain forming crystals.

Figure 1

Transient reflectivity change at room temperature for high excitation fluences, plotted for different probe wavelengths. The curves are shifted vertically for clarity.

Figure 2

Transient reflectivity traces for (a) $T=300\mathrm{K}$ and (b) $T=25\mathrm{K}$ and two different strain amplitudes evaluated at $\lambda =528\mathrm{nm}$ ($\nu =71\mathrm{GHz}$). The curves are shifted vertically for clarity.

Figure 3

(a) Sound velocity distribution extracted from the Fourier transform of the transient reflectivity data shown in Fig. 2, for 0.18% strain amplitude in STO at selected temperatures generated by excitation of an LSMO transducer. (b) Extracted maxima from panel (a) as a function of temperature. Red open and full circles: sound velocities in STO for the LSMO transducer; black stars: sound velocities in STO for the SRO transducer. For strain amplitude refer to legend.

Figure 4

(a) Schematic of the STO crystal in the tetragonal phase near a kink in a twin wall according to literature [2, 3, 7, 8]. Tetragonal distortion and twinning angle are exaggerated. The shaded grey region highlights the strain field near the kink. (a) Black line: twin wall with kink. Grey rectangles: unit cells of tetragonal phase. Details of these unit cells are shown with oxygen octahedra as enlarged insets. For slow vertical expansion the kink would move along the thin black arrow. (b) Snapshot for ultrafast uniaxial expansive strain along ${\mathbf{k}}_{\mathrm{ph}}$ with amplitude exceeding the original tetragonal distortion (see text). No contraction perpendicular to ${\mathbf{k}}_{\mathrm{ph}}$ can occur for this time scale. Blue narrow arrows: compressive forces that counteract the external uniaxial expansion.