Tunneling in NaBr:F−: Thermal and Dielectric Properties

The existence of a large dipole moment and low-lying energy levels associated with the fluorine impurity ion in NaBr has been shown by measurements of paraelectric cooling, dielectric susceptibility, and low-temperature specific heat. Equilibrium orientations for the dipoles along the directions have been deduced from measurements of the dielectric constant under applied stress and high-field polarization. Thermal-conductivity measurements indicate a rather long impurity-lattice relaxation rate. This has been confirmed by dielectric-relaxation measurements which give a relaxation rate which varies linearly with temperature below 5 K with a value of ${10}^5$ ${\sec }^{-1\mathrm{}}$ at 2 K. These observations are explained by means of a model in which the impurity ion tunnels between potential minima displaced from the lattice site, somewhat similar to the tunneling observed in KCl: ${\mathrm{Li}}^{+}$. Two major differences with the data for KCl: ${\mathrm{Li}}^{+}$, namely, a much broader specific-heat contribution and slower relaxation rate, necessitate a modification of the simple tunneling model used in describing KCl: ${\mathrm{Li}}^{+}$. By taking into account the effect of lattice strains on the tunneling motion, good agreement is obtained with the data for NaBr: ${\mathrm{F}}^{-}$. Using this model a value of 8.7 mK is calculated for the tunneling matrix element. Thus NaBr: ${\mathrm{F}}^{-}$ represents a tunneling system in the limit of a small tunneling matrix element while KCl: ${\mathrm{Li}}^{+}$ is characteristic of a large tunneling matrix element. Evidence is cited for other systems which might fit the strained tunneling model. These systems are RbCl: ${\mathrm{Ag}}^{+}$, RbCl: O${\mathrm{H}}^{-}$, and KCl: O${\mathrm{H}}^{-}$.