Acoustic Behavior of the Jahn-Teller Ion ${\mathrm{Ni}}^{3+}$ in ${\mathrm{Al}}_2$${\mathrm{O}}_3$

We have measured the attenuation of 100- and 260-Mc/sec longitudinal acoustic waves in $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$ (corundum) containing a few ppm of ${\mathrm{Ni}}^{3+}$, and have compared our data with previous measurements at 2 Mc/sec. The attenuation as a function of temperature shows a relaxation-type behavior with a peak at 12°K for 100-Mc/sec waves and 14°K for 260-Mc/sec waves. From our data we can deduce a temperature-dependent relaxation time $\tau$ which is in reasonably good agreement with the relaxation time for the dynamic Jahn-Teller effect as observed in spin resonance. Above 12°K, we find $\tau =5\mathrm{}\times {10}^{-14\mathrm{}}{e}^{\frac{-130\mathrm{}}{T}}$ sec, the form expected for a thermal-activation process. At low temperatures, $\tau$ varies approximately linearly with temperature, as expected for phonon-assisted tunneling. Unexplained deviations from theory are observed below about 6°K at 2 Mc/sec, but we find no evidence for resonant absorption of acoustic phonons.