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

Abstract

Microwave-resonance measurements at 9.3 and 16.8 Gc/sec between 1.5 and 300\ifmmode^\circ\else\textdegree\fi{}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 ${G}_{1}=31.9$ ${\mathrm{cm}}^{\ensuremath{-}1}$; ${G}_{2}=22.4$ ${\mathrm{cm}}^{\ensuremath{-}1}$; ${G}_{3}=8.5$ ${\mathrm{cm}}^{\ensuremath{-}1}$, 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 $\ensuremath{\tau}$, 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 $Tl60$ \ifmmode^\circ\else\textdegree\fi{}K indicates the dominance of a direct process as described by ${(\frac{1}{\ensuremath{\tau}})}_{D}={(\frac{1}{{\ensuremath{\tau}}^{0}})}_{D}coth(\frac{\ensuremath{\delta}}{2kT})$ with ${(\frac{1}{{\ensuremath{\tau}}^{0}})}_{D}=2.1\ifmmode\times\else\texttimes\fi{}{10}^{9}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ for ${\ensuremath{\delta}}_{111}=21.0$ ${\mathrm{cm}}^{\ensuremath{-}1}$. 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., ${(\frac{1}{\ensuremath{\tau}})}_{R}=A{J}_{8}{T}^{9}$, with $A=4.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ ${(\mathrm{\ifmmode^\circ\else\textdegree\fi{}}\mathrm{K})}^{\ensuremath{-}9}$ for a Debye temperature of 550\ifmmode^\circ\else\textdegree\fi{}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.