Spin-Lattice Relaxation of ${\mathrm{Tm}}^{2+}$ in Ca${\mathrm{F}}_2$, Sr${\mathrm{F}}_2$, and Ba${\mathrm{F}}_2$

Measurements were made of the spin-lattice relaxation time of the ground state of ${\mathrm{Tm}}^{2+}$ in Ca${\mathrm{F}}_2$, Sr${\mathrm{F}}_2$, and Ba${\mathrm{F}}_2$ over the magnetic field range of 1 to 12 kG and temperature range of 1.3 to 20°K. The one-phonon relaxation process was unambiguously identified by its characteristic fourth-power dependence on frequency and its linear temperature dependence. The Raman process with its $T^9$ dependence begins to dominate the relaxation above 5°K. The angular dependence of the relaxation permitted the separation of the effect of the two local modes, $E_g$ and $T_{2g}$, on the one-phonon process. Calculations were in good agreement with theory, and they showed that the second-order terms of the orbit-lattice interaction dominate the relaxation process. Continuous measurement of the relaxation over this magnetic field range was made possible by a technique which is independent of any microwave sources. The detection was done by monitoring the magnetic circular dichroism of the broad optical absorption bands.