Spin-Lattice Relaxation in Some Rare-Earth Salts. I. Temperature Dependence

Abstract

We report measurements of the spin-lattice relaxation rate ${{T}_{1}}^{\ensuremath{-}1}$ for several magnetically dilute rare-earth ions in the temperature range $1.2\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\leqq}T\ensuremath{\leqq}5\ifmmode^\circ\else\textdegree\fi{}$K, using the transient recovery of the microwave paramagnetic resonance in the frequency range $8\ensuremath{\leqq}\ensuremath{\nu}\ensuremath{\leqq}18$ Gc/sec. Data are given for ${\mathrm{Sm}}^{3+}$ and ${\mathrm{Dy}}^{3+}$ in the double nitrate ${\mathrm{La}}_{2}$${\mathrm{Mg}}_{2}$${(\mathrm{N}{\mathrm{O}}_{3})}_{12}$.24${\mathrm{H}}_{2}$O; for ${\mathrm{Pr}}^{3+}$, ${\mathrm{Sm}}^{3+}$, and ${\mathrm{Er}}^{3+}$ in the ethyl sulfate La${({\mathrm{C}}_{2}{\mathrm{H}}_{5}\mathrm{S}{\mathrm{O}}_{4})}_{3}$.9${\mathrm{H}}_{2}$O; and for ${\mathrm{Ce}}^{3+}$, ${\mathrm{Nd}}^{3+}$, ${\mathrm{Pr}}^{3+}$, ${\mathrm{Sm}}^{3+}$, ${\mathrm{Er}}^{3+}$, and ${\mathrm{Tb}}^{3+}$ in the ethyl sulfate Y${({\mathrm{C}}_{2}{\mathrm{H}}_{5}\mathrm{S}{\mathrm{O}}_{4})}_{3}$.9${\mathrm{H}}_{2}$O. We observe the temperature dependence for the direct process ${{T}_{1}}^{\ensuremath{-}1}\ensuremath{\propto}T$; for the Orbach process ${{T}_{1}}^{\ensuremath{-}1}\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\Delta}}{T})$; and for the Raman process ${{T}_{1}}^{\ensuremath{-}1}\ensuremath{\propto}{T}^{7} or {T}^{9}$. The magnitudes of the processes are in reasonable agreement with simple theoretical estimates. The observed rates are shown to be independent of paramagnetic ion concentration in the range 0.1 to 1%. For Pr in the ethyl sulfate, we observe, as expected, a phonon bottleneck rate ${{T}_{b}}^{\ensuremath{-}1}\ensuremath{\propto}{T}^{2}$ rather than the direct process. In several cases the Orbach process determines a previously unknown value of the crystal-field splitting $\ensuremath{\Delta}$, while in some cases it shows that the value of $\ensuremath{\Delta}$ in the dilute salt is significantly different from the value determined optically in the concentrated salt.