Ultrasonic attenuation in metallic glasses at low temperatures

Results are reported of ultrasonic attenuation measurements on amorphous ${\mathrm{Pd}}_{0.40}$ ${\mathrm{Ni}}_{0.40}$ ${\mathrm{P}}_{0.20}$ at frequencies 25-450 MHz (transverse) and temperatures down to 0.3 K. The saturation behavior of attenuation as a function of ultrasonic amplitude is consistent with the prediction of the two-level-system tunneling theory. Contrary to the predictions of this theory, however, a linear frequency dependence and essentially no temperature dependence of the total saturable attenuation changes were observed at temperatures below about 1 K as in PdSi-based alloys reported previously. The frequency and temperature dependence of the completely saturated attenuation is described by $\omega \ln \left(\frac{T}{T_0}\right)$ at temperatures 0.3-2 K.