Dielectric susceptibility and thermal conductivity of tunneling electric dipoles in alkali halides

A microscopic calculation is presented to obtain the dielectric susceptibility X(T,ω) and the thermal conductivity κ(T) at temperature T and frequency ω for dilute concentrations of multiorientational tunneling dipoles randomly distributed in a nondipolar medium. There are two contributions to X(T,ω): a discrete one arising from the near neighbors, and a quasicontinuous one from faraway neighbors. The continuous part of X(T,ω) exhibits a broad T dependence in its real and imaginary parts. The theory predicts a lnT term in the dc as well as in the ac susceptibility for low T. It also predicts a discrete and a continuous contribution to the specific heat $C_v$(T) and the thermal expansion α(T). Applying the derivations to ${\mathrm{Li}}^{+}$ ions in KCl, one obtains that κ(T)∝$T^2$ for low T with some important deviations from $T^2$ dependence for somewhat higher T. α(T) is primarily determined by the coupling of the phonons to the tunneling matrix element Δ, whereas κ(T) is determined by the coupling to the anisotropy energy ${\varepsilon }_a$. When these results are combined with calculations for the density of the excitation energies, the specific heat, and the thermal expansion, the model gives low-T properties (in all the variables mentioned above) that are very similar to those observed in glasses. This is the first solvable microscopic model which gives glasslike properties at low temperatures from fundamental considerations without the use of a mean-field theory.