Two-level systems in fluorite mixed crystals - a far-infrared study

Low-temperature far-infrared absorption measurements have been made on six different alkaline earth:rare earth fluoride mixed crystal systems at a number of concentrations. All of these chemically disordered crystals display a glass-like continuous distribution of two-level systems (TLS) throughout the millimetre wave spectral region. Much of this study has focused on LaF₃ doping where the effective density of states of the TLS initially increases with dopant concentration, reaching a maximum saturated value at a concentration of about 5 mol% for a CaF₂ host, 20% for SrF₂ and at least 35% for BaF₂. The magnitude of the saturated TLS optical density of states is system dependent, varying from roughly one-fifth to five times that found in a standard sodalime-silica glass. The optical strength indicates that only a small fraction, less than one in a thousand, of the dopant ions contribute to the TLS optical absorption. At submillimetre wavelengths it is found that both the fluorite mixed crystals and a standard glass exhibit a characteristic temperature-dependent absorption associated with transitions to excited levels above the ground-state TLS manifold. It is proposed that resonant phonon scattering by these excited state transitions is the cause of the plateau observed in the temperature dependence of the thermal conductivity of glasses.