Spin-Lattice Relaxation in theE¯(E2)State ofd3Ions in Corundum

Abstract

A theoretical study of the spin-lattice relaxation in the excited $\overline{E}\left({}_{}{}^2{}_{}{}^{}E\right)$ state of ${\mathrm{Cr}}^{3+}$ in ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ is presented. The two-step resonant relaxation process involving the $2\overline{A}$ state is calculated. The appropriate orbit-lattice parameter appearing in the calculation is obtained from static strain measurements. The theoretical results are in very good agreement with experiment. The normal direct-process relaxation time in the $\overline{E}$ level, involving exchange of phonons whose energy is equal to the Zeeman splitting of $\overline{E}$, is shown to be considerably longer than the radiative lifetime of $\overline{E}$ for an external magnetic field parallel to the $c$ axis. This time can be shortened considerably by a magnetic-field component perpendicular to the $c$ axis. The theory presented is applicable to the corresponding $\overline{E}\left({}_{}{}^2{}_{}{}^{}E\right)$ states of ${\mathrm{V}}^{2+}$ and ${\mathrm{Mn}}^{4+}$ in ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ and with slight modification to the $\overline{E}$ state of these $d^3$ ions in other crystal hosts.