ESR and uniaxial stress study of a freely librating elastic dipole

Uniaxial stress along $〈110〉$ lifts the degeneracy of the three tunneling orientations of the restricted interstitial motion of the $H_A\left({\mathrm{Li}}^{+}\right)$ center in KCl:${\mathrm{Li}}^{+}$. This phonon-assisted tunneling motion possesses $C_{3\nu }$ symmetry around $〈111〉$. These experiments yield two differential stress coupling coefficients, which is not sufficient for a determination of the elastic dipole tensor. Uniaxial stress along $〈100〉$ changes the $H_A\left({\mathrm{Li}}^{+}\right)$ orientation in a continuous fashion along a well-defined path. An interpretation of the $〈110〉$ and $〈100〉$ data is presented. To this end the concept of a free elastic dipole in a stress field is introduced and the statistics of these dipoles are calculated. This permits an interpretation and analysis of the $〈100〉$ stress data and a third independent linear stress coupling coefficient is obtained. The resulting elastic dipole tensor has a principal axis close to $〈111〉$. The free elastic dipole model implies that at zero applied stress the $\mathrm{Cl}_2^{}{}_{}{}^{-}$ of $H_A\left({\mathrm{Li}}^{+}\right)$ librates freely over a large angle, i.e., that all positions along the path are equally probable. A careful reanalysis of the ESR spectra has confirmed the existence of this librational motion. The $\mathrm{Cl}_2^{}{}_{}{}^{-}$ librates freely with respect to a {110} plane along an almost quadrant of a cone around $〈100〉$ whose apex angle is 2 × 28.2°. The libration frequency is fast enough to result in a motionally averaged but still anisotropic ESR spectrum.