Investigation of Tunneling States Using the Spin-Phonon Interaction. I. Experiment

Phonons in KCl doped with small amounts of LiCl or KCN are known to be strongly scattered at discrete energies by tunneling states of the impurity ions. The effect of a magnetic field on the low-temperature thermal conductivity of doped KCl containing $R$ centers was used to study this resonant scattering of phonons by C${\mathrm{N}}^{-}$ and ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_{}^{+}{}_{}{}^{}$ impurity ions. By means of this technique it was possible to resolve the tunneling resonance in KCl:C${\mathrm{N}}^{-}$ into two components. The resonant energies were 1.1 and 2.0 ${\mathrm{cm}}^{-1\mathrm{}}$. The resonances in K${\mathrm{C}\mathrm{l}:}^6$Li were found to consist of three components: 1.0, 1.72, and 2.70 ${\mathrm{cm}}^{-1\mathrm{}}$. The effect of an applied electric field in the direction on the tunneling resonances of the Li ion was measured in fields of up to 12 kV/cm. The Devonshire model with potential minima for orientations was applied to C${\mathrm{N}}^{-}$ ions in KCl. Good agreement between the predicted and measured tunneling energies was obtained with model parameters which also agree with the results of studies using other techniques. The observed tunneling energies of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ion were compared with the $X{Y}_8$ tunneling model of Gomez, and values of the tunneling parameters were deduced from the measured energies. The variations which were observed in the level spacing imply that although tunneling along the cube edge predominates, a significant amount takes place through the center of the unit cell, but that face-diagonal tunneling is negligible within experimental error. Using certain approximations to calculate the tunneling parameters from specific model potentials, agreement could be obtained between the measured energy levels and the levels of the $X{Y}_8$ tunneling model. Agreement with the observed levels could not be obtained using an elliptical potential well. The measured effects of an electric field on the resonances of the K${\mathrm{C}\mathrm{l}:}^6$Li system are consistent within experimental error with the predictions of the $X{Y}_8$ tunneling model and with the results of measurements using other techniques.