Acoustic properties of amorphous metals at very low temperatures: Applicability of the tunneling model

Studies of the relative change of sound velocity Delta upsilon/upsilon and internal friction Q(-1) of a metallic glass (PdSiCu) in the temperature ran ge 0.2 mK less than or equal to T < 0.5 R and at kHz frequencies reveal sig nificant deviations from the predictions of the tunneling model for both ac oustic properties. At the lowest temperatures, the logarithmic temperature dependence of Delta upsilon/upsilon is no longer observed, and in addition, the sound-velocity variation strongly depends on the applied acoustic inte nsity. In clear contrast to the predicted "plateau" in the internal frictio n, we observe Q(-1) proportional to ln T throughout the whole temperature r ange investigated, the magnitude of Q(-1) being dependent on the applied st rain, too. The apparent discrepancy between experimental data and tunneling model is traced back to different considerations of strain-dependent effec ts: in contrast to the experiment, the tunneling model is linear in strain and thus does not account for any strain dependence. As a consequence, comp arison between experimental results and tunneling model should be possible for zero-strain values of Delta upsilon/upsilon and Q(-1) which have been d etermined by detailed investigations of the acoustic intensity dependence o f both acoustic properties at different constant temperatures. The main res ult of this work is that the tunneling-model behavior is unveiled only in t he limit of zero strain. Thus, for the first time the behavior expected wit hin the tunneling model for an amorphous metal has been scrutinized: we rep ort a logarithmic temperature dependence for Delta upsilon/upsilon at T>0.2 mK and a temperature-independent plateau of Q(-1) at T>0.5 mK.