Ultrasonic Attenuation by Interaction with the Soft Optic Mode in KTaO3

Abstract

Ultrasonic attenuation and velocity in KTa${\mathrm{O}}_3$ have been measured from 180-900 MHz over the temperature range 2-300°K. Both longitudinal and transverse waves were studied. While for transverse waves the attenuation and velocity behaved normally, for longitudinal waves they showed a rapid temperature dependence at low temperature. The longitudinal attenuation was much larger than the transverse attenuation and showed a large peak at ∼30°K. At 4.2°K it varied as the square of the ultrasonic frequency (at low frequency). These observations are explained, quantitatively at low temperature and qualitatively over the entire range, in terms of an Akhieser-type interaction with the soft optic mode. The Grüneisen constant and k=0 frequency for the soft mode are obtained from the analysis. Also, some information about the soft-mode dispersion is obtained. The Grüneisen constant so determined is in fair agreement with that determined from a phenomenological theory using electrostrictive constants. The k=0 soft-mode frequency is in excellent agreement with Raman and infrared results. The effective relaxation time for the interaction is shown to involve both acoustic- and optic-mode relaxation times.