Magnetic Field Dependence of Spin-Lattice Relaxation in Neodymium Ethylsulfate

Relaxation times for neodymium ethylsulfate have been derived from dispersion curves of the Casimir-duPré form, measured by an audio-frequency self-inductance bridge method at temperatures between 2.4 and 4.2 K and in magnetic fields between 150 and 2870 Oe parallel to the crystal $c$ axis. The temperature dependence of the relaxation rate is described by ${\mathrm{DT}}^2+{\mathrm{BT}}^9$. The magnetic field dependence of $B$ is satisfactorily fitted by Orbach's theoretical expression $B\left(H\right)=B_{\infty }\frac{(H^2+\mu H_n^2+\frac{1}{2}{\mu }^{\prime }{H}_d^2)}{(H^2+H_n^2+\frac{1}{2}{H}_d^2)}$, with $B_{\infty }=(5.8\mathrm{}\pm 0.4)\times {10}^{-5\mathrm{}}$ ${\sec }^{-1\mathrm{}}$ ${\mathrm{K}}^{-9\mathrm{}}$ and ${10}^{-4\mathrm{}}\times (\mu H_n^2+\frac{1}{2}{\mu }^{\prime }{H}_d^2)=151\mathrm{}\pm 13$ ${\mathrm{Oe}}^2$. Various approximation schemes for estimating the dynamic crystal-field parameters have been used to calculate values of $B_{\infty }$ and $\mu H_n^2+\frac{1}{2}{\mu }^{\prime }{H}_d^2$. Orbach's scheme, with Huang's factors added, gives a better account of the variation of the Raman relaxation rate at low fields and intermediate fields. At high fields either the Orbach-Huang or the Scott-Jeffries approximation schemes give reasonable Raman relaxation rates. A normal-mode theory fails to give agreement with experiment at either high or low fields, probably due to its use of a point-charge model for the crystal field. The direct process is found to be bottlenecked, but neither Orbach's nor Scott and Jeffries's scheme gives a rate coefficient large enough to satisfy the condition for a bottleneck. The bottlenecked direct-process coefficient shows a field dependence, decreasing by a factor of 2 as $H$ increases.