Rare-Earth Ion Relaxation Time andGTensor in Rare-Earth-Doped Yttrium Iron Garnet. I. Ytterbium

Microwave-resonance measurements at 9.3 and 16.8 Gc/sec between 1.5 and 300°K in the principal crystallographic directions of a single-crystal of yttrium iron garnet (YIG) doped with 5.1% Yb are compared with the predictions of the longitudinal (so-called "slow relaxing ion") mechanism of relaxation, which is briefly reviewed. Except for the low-temperature anomaly in the [110] direction, excellent agreement is found. A quantitative analysis allows deduction of the tensor $G$ describing the anisotropic exchange splitting of the ground-state Kramers doublet of the Yb ion. We obtain $G_1=31.9\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$; $G_2=22.4\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$; $G_3=8.5\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, which is a similar result to that reported from spectroscopic measurements on ytterbium iron garnet. The small differences probably reflect the different lattice dimensions in the two cases. We also deduce $\tau$, the relaxation time of the Yb ion in the YIG environment. The results are most extensive and accurate in the [111] direction, where the temperature dependence for $T<\mathrm{}60\mathrm{}$ °K indicates the dominance of a direct process as described by ${\left(\frac{1}{\tau }\right)}_D={\left(\frac{1}{{\tau }^0}\right)}_{D}coth\left(\frac{\delta }{2kT}\right)$ with ${\left(\frac{1}{{\tau }^0}\right)}_D=2.1\mathrm{}\times {10}^9$ ${\sec }^{-1\mathrm{}}$ for ${\delta }_{111}=21.0\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. Taking into account that the measured relaxation time in this direction is a weighted average of the two relaxation times associated with the two values of the doublet splitting, we find that the observed direct process is well described by spin-magnon relaxation, which also gives a more consistent evaluation of the $G$ tensor than does spin-lattice relaxation. At higher temperatures, the temperature dependence of the observed relaxation time follows that expected for the Raman process, viz., ${\left(\frac{1}{\tau }\right)}_R=A{J}_8{T}^9$, with $A=4.5\mathrm{}\times {10}^{-12\mathrm{}}$ ${\sec }^{-1\mathrm{}}$ ${\left(\mathrm{°}\mathrm{K}\right)}^{-9\mathrm{}}$ for a Debye temperature of 550°K. This is in excellent agreement with the Raman-process relaxation time reported for Yb in yttrium gallium garnet, though it is some 5 orders of magnitude shorter than the theoretical estimate. The Orbach process is found to be unimportant over the temperature range covered.