Thermal Conductivity of KCl: Li. Isotope and Electric Field Effects

The resonance scattering of phonons in KCl: Li has been studied through thermal-conductivity measurements of crystals containing ${\mathrm{Li}}^6$ and ${\mathrm{Li}}^7$, and also of crystals in which the tunneling states of the lithium ion were polarized through an applied electric field. In all cases the resonance scattering can be very well described phenomenologically with a single-resonance relaxation rate of the form $\frac{\left(\frac{\mathrm{nA}}{{{\omega }_0}^2}\right){\left(\frac{\omega }{{\omega }_0}\right)}^2}{{[1-{\left(\frac{\omega }{{\omega }_0}\right)}^2]}^2}$, where ${\omega }_0$ appears to be the weighted average of the tunneling frequencies. The lighter isotope causes an upward shift of ${\omega }_0$ by 45%, which agrees with the isotope effect observed for the tunnel splitting in specific-heat measurements. This is considered strong evidence that the phonon scattering is indeed caused by an interaction with the tunneling states. The electric-field-induced shift of ${\omega }_0$ also is consistent with the known Stark shifts of the tunneling states. The single resonance is explained with the picture that all tunneling states contribute to the scattering, and that the resolution of the thermal-conductivity measurements used for phonon spectroscopy is insufficient to resolve the scattering by the individual states. The scattering strength $A$, to a good approximation, is found to be proportional to ${{\omega }_0}^2$, regardless of whether ${\omega }_0$ is changed by applying electric fields or by changing the isotopic mass. This behavior is that of a classical oscillator which is damped by radiation at its resonance frequency ${\omega }_0$. It is concluded that the combined scattering by the tunneling states, as observed in thermal conductivity, is similar to that of a classical oscillator. For lithium concentrations in excess of 3×${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$, the thermal conductivity saturates below 1°K. This behavior is similar to that observed earlier in specific-heat measurements. The origin of this saturation is still not understood and requires further study.