Spin-lattice relaxation at high gap energies using a pulsed tunable dye laser

Spin-lattice relaxation within the ${}_{}{}^5{}_{}{}^{}D_4^{}{}_{}{}^{}$ manifold for ${\mathrm{Tb}}^{3+}$ in Y${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_3$ has been investigated by optically pumping an individual excited state with a pulsed tunable dye laser and following the time evolution of the population of the revelant state from its emission using single-photon time correlation techniques. Relaxation between the two lowest states ($\mu =3^{+},2\mathrm{}$) was found to be primarily by direct single-phonon processes near 1 K. Above ∼ 7 K the observed relaxation rates can be adequately described in terms of an additional two-phonon Raman process. The observed decay rates, corrected to 0 K, followed the expected ${\left(\Delta E\right)}^3$ dependence on energy gap over the entire range studied (1.3-7 ${\mathrm{cm}}^{-1\mathrm{}}$). The effect of a phonon bottleneck was examined theoretically and shown to be unimportant in the present system, consistent with observation.