Microscopic theory of glassy disordered crystals: (KBr)1-x(KCN)x

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Abstract
Lack of information about the local structure of glasses has severely hindered He-tailed understanding of their universal properties. The glassy behavior found in the crystalline systems discussed here is therefore a very exciting theoretical opportunity. In particular, there are no successful microscopic models for the tunneling centers in glasses (which are responsible for the low temperature properties); thus little predictive information about the distribution of tunneling center parameters is available, and sharp tests of the theory are not possible. We have identified the microscopic tunneling centers in the glassy crystal (KBr)1_x(KCN)x. Thus for the first time we predict the quantitative experimental behavior of a glassy material starting from a microscopic model. There are three important experimental features in this system. First, KBr:KCN undergoes a transition into a low temperature state where the cyanide axes are frozen into a disordered configuration. Second, it shows a very broad log-normal dielectric loss peak associated with 180 degree flips of the cyanide orientations. Third, it exhibits all the universal low temperature properties of glasses. We develop a mean field theory for this material, modeling static fluctuations in the number of cyanide neighbors with a Gaussian random coupling constant. We explain the breadth, form and temperature dependence of the low frequency dielectric loss peaks using our model. We identify the tunneling centers with those cyanide ions whose couplings to the mean field are small enough to allow quantum tunneling to flip them within the measuring time scale. We determine the tunneling center parameter distributions using high temperature experiments, and predict low temperature time dependent specific heats which agree with experiments within a factor of two.