Rare-Earth Ion Relaxation Time andGTensor in Rare-Earth-Doped Yttrium Iron Garnet. II. Neodymium

We present ferrimagnetic-resonance linewidth measurements at 9.3 Gc/sec and 16.9 Gc/sec between 1.5 and 250°K in the principal crystallographic directions for a single crystal of yttrium iron garnet (YIG) doped with 0.82% Nd. These results are compared with the linewidth predicted by the longitudinal (so-called "slow relaxing ion") mechanism of relaxation for a single Kramers doublet. We find that the temperature and frequency dependences of the linewidths are in good agreement with the predictions, but that the anisotropic exchange splitting of the ground-state Kramers doublet is not accurately described by a tensor $G$, according to ${(G_1^{}{}_{}{}^2{\mathbf{i}}^2+G_2^{}{}_{}{}^2{\mathbf{j}}^2+G_3^{}{}_{}{}^2{\mathbf{k}}^2)}^{\frac{1}{2}}$, probably through the admixture of higher states into the ground doublet. However, the tensor $G_1\sim 40$ ${\mathrm{cm}}^{-1\mathrm{}}$; $G_2\sim 20$ ${\mathrm{cm}}^{-1\mathrm{}}$; $G_3\sim 80$ ${\mathrm{cm}}^{-1\mathrm{}}$ describes the basic topology of the splitting. We also deduce $\tau$, the relaxation time of the ${\mathrm{Nd}}^{3+}$ ion in the YIG environment. The results are somewhat limited except in the [111] direction, where they suggest that for $T<\mathrm{}40\mathrm{}$°K a direct process dominates, and is given by ${\left(\frac{1}{\tau }\right)}_D={\left(\frac{1}{{\tau }^0}\right)}_{D}coth\left(\frac{{\delta }_{111}}{2kT}\right)$ with ${\left(\frac{1}{{\tau }^0}\right)}_D\sim 4\times {10}^{10}$ ${\sec }^{-1\mathrm{}}$ for the average splitting in the [111] direction ${\delta }_{111}$ equal to 61.3 ${\mathrm{cm}}^{-1\mathrm{}}$. We cannot say whether this observed direct process is predominantly spinmagnon or spin-lattice, for a rough estimate shows that both processes could conceivably be of the observed order of magnitude. At higher temperatures, the temperature dependence of the observed relaxation time follows that expected for the Orbach or resonance process, as described by ${\left(\frac{1}{\tau }\right)}_O=\frac{B}{\left[\exp \right(\frac{\Delta }{\mathrm{kT}})-1]}$ with