Ultrasonic study of the charge-fluctuation compound

We have measured the ultrasonic velocity and attenuation coefficient of the rare-earth chalcogenide (Formula presented) to examine the valence-fluctuation effect due to the coexistence of (Formula presented) and (Formula presented) ions in the ratio of 1:2. The ultrasonic dispersion around 120 K indicates that the charge-fluctuation time obeys the activation-type temperature dependence (Formula presented) with a characteristic time (Formula presented) and an activation energy (Formula presented) The absence of the phase transition due to the charge ordering in (Formula presented) means a freezing of (Formula presented) and (Formula presented) ions in random distribution at low temperatures. We find an elastic softening with (Formula presented) dependence below 15 K down to a spin glass transition around 1.3 K. This striking behavior is attributed to a two-level system due to the tunneling of (Formula presented) electrons among randomly distributed (Formula presented) and (Formula presented) ions. This result is similar to the ionic tunneling in amorphous glass compounds. Employing the group-theoretical analysis, we show some aspects of charge-fluctuation modes in (Formula presented) and a possible mechanism for the charge glass state of (Formula presented) and (Formula presented) ions.