Anomalous Excitations in Glasses in the FAR Infrared

Abstract

An intriguing feature of amorphous dielectrics is the presence of low frequency anharmonic modes, these are qualified as “anomalous” since they contribute to large deviations from the expected crystalline behavior. The first clear evidence that these anomalous modes represented a general phenomenon in glassy materials was obtained from the low temperature specific heat and thermal conductivity measurements of Zeller and Pohl [1]. For a variety of glassy materials they found a linear temperature dependence of the specific heat and a thermal conductivity whose temperature dependence and magnitude were the same for all glasses. Extensive measurements of the specific heat [2] of a large number of glasses have confirmed the presence of anomalous excitations in the energy range below a few cm−1. Additional evidence for such low frequency excitations comes from ultrasonic attenuation experiments [3]. Finally the observation of boundary scattering in small glass fibers has shown that Debye-like phonons carry the heat (as in a crystalline solid) and that the excess excitations observed in specific heat measurements do not themselves carry heat through the crystal [4]. To account for these special modes a localized tunneling model [5,6] has been proposed in which atoms, ions or groups of particles quantum mechanically tunnel between two or more equivalent sites. The linear dependence of the specific heat has been obtained from this model by including a statistical distribution of barrier heights and asymmetries for the local potential. One straightforward prediction which this model makes is that the temperature dependence of the far infrared absorption coefficient should be determined by the occupation numbers of a small number of energy levels associated with the tunneling manifold. For example a distribution of infrared-active two-level systems will produce an infrared absorption which decreases with increasing temperature in a well-defined way. In this talk, we shall discuss a variety of measurements of the temperature-dependent absorption coefficient of amorphous dielectrics in the far infrared. In one restricted temperature and frequency regime a decrease in absorption coefficient with increasing temperature is observed as expected while in another temperature and frequency range the absorption coefficient increases with increasing temperature [7]. A complete mapping of the absorption coefficient versus frequency and temperature for a number of glasses demonstrates that both ground state and excited state transitions are observed in the far infrared. In addition the results are consistent with the presence of widely spaced manifolds of energy levels. All of these results can be explained with an asymmetric tunneling potential model. At frequencies above 10 cm−1 a modest temperature dependence indicates that resonant mode transitions are being measured. Apparently the spatial inhomogeneities in glass provide a natural habitat not only for Debye-like phonons but also for localized modes, resonant modes and tunneling states - excitations which in the past were associated exclusively with slightly perturbed single crystals [8].