Hypersonic Attenuation by Low-Frequency Optical Phonons in SrTiO3Crystals

Hypersonic attenuation above the structural phase transition temperature $T_a\simeq 103$°K has been measured from 0.4 to 1 GHz in SrTi${\mathrm{O}}_3$. Studies were made for both polarizations in - and -oriented single crystals. For temperatures above 150°K, the attenuation of shear waves is temperature-independent, while that of longitudinal waves is monotonically increasing with decreasing temperature. As $T\to T_a$ from above, the attenuation of both longitudinal and transverse waves shows a striking increase that continues until $T\simeq T_a$, when hypersonic transmission in the medium stops. These observations are explained qualitatively in terms of Akhieser damping of the hypersonic waves by interactions with thermally excited phonons of the acoustic and soft optic modes in SrTi${\mathrm{O}}_3$. It is found that for $(T-T_a)>\mathrm{}40\mathrm{}$ >°K, the temperature dependence of the attenuation of longitudinal waves is given by $\frac{T}{{(T-T_c)}^m}$ with $T_c=43\mathrm{}$ °K and $m$ ranging from 1 to 1.4. In the interval $10°\mathrm{K}<(T-T_a)<\mathrm{}30\mathrm{}°\mathrm{K}$, the temperature dependence is well described by ${(T-T_a)}^{-n}$; the exponent $n$ ranges from 0.9 to 1.2 for longitudinal waves, but it is between 1.9 and 2.2 for transverse waves.