Spin-Lattice Relaxation in Some Rare-Earth Salts. II. Angular Dependence, Hyperfine Effects, and Cross Relaxation

In this second part of a study of the spin-lattice relaxation rate ${T_1}^{-1\mathrm{}}$ in the temperature range $1.2\leqq T\leqq 5°$K of some trivalent rare-earth ions in the salts ${\mathrm{La}}_2$ ${\mathrm{Mg}}_3$ ${\left(\mathrm{N}{\mathrm{O}}_3\right)}_{12}$·24${\mathrm{H}}_2$O[LaMN], La${\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{S}{\mathrm{O}}_4\right)}_3$·9${\mathrm{H}}_2$O[LaES], and ${\mathrm{Y}\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{S}{\mathrm{O}}_4\right)}_3$·9${\mathrm{H}}_2$O[YES], we examine the dependence of ${T_1}^{-1\mathrm{}}$ on the angle $\theta$ between the crystal symmetry axis and the magnetic field H. Data are obtained from the transient recovery of the microwave paramagnetic resonance at $\nu \approx 9$ Gc/sec for Nd: YES, Nd: LaES, Nd: LaMN, Sm: LaMN, Sm: LaES, Sm: YES, Er: LaES, and Er: YES, all for isotopes of spin $I=0\mathrm{}$. There is a decided anisotropy of the direct process, as large as 15:1, which seems to be moderately well explained by the same simple theoretical procedure used in part I for the temperature dependence. The Raman process was found to be independent of $\theta$ and $H$, as expected theoretically; likewise for the Orbach process, except for Nd: LaMN, where a small anisotropy is observed and explained. The data for the phonon-bottlenecked cases Ce: LaMN and Pr: LaMN indicate that the spins interact only with the phonons within the paramagnetic-resonance linewidth. The direct process for the various hyperfine lines of ${\mathrm{Er}}^{167}$ in Er: YES and ${\mathrm{Nd}}^{143}$ in Nd: LaMN is measured and found to exhibit a dependence on $M_I$ and $H$ in accordance with the theory of Baker and Ford, showing the importance of "forbidden" relaxation transitions $\Delta M_S=1\mathrm{}$, $\Delta M_I=\pm 1$. In a study of relaxation in (Er, Ce): LaES we find that the Er relaxation rate is quite well explained in its dependence on both temperature and Ce concentration by resonance cross relaxation with Ce ions in the excited state at $\Delta =5.7\mathrm{}°$K.