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

Abstract

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

Keywords

• INLINE
• HTTP
• WWW.W3.ORG/1998/MATH/MATHML
• MATH XMLNS
• SPLITTING
• MSUP

This publication has 7 references indexed in Scilit:

• Paramagnetic Resonance of Trivalent Holmium Ions in Calcium Tungstate
  Physical Review B, 1965
• Ferrimagnetic Resonance Linewidth in Rare-Earth-Doped YIG at Low Temperatures
  Journal of Applied Physics, 1965
• Energy Levels and Crystal-Field Calculations of Neodymium in Yttrium Aluminum Garnet
  Physical Review B, 1964
• Spin-Magnon Relaxation in Rare-Earth Iron Garnets
  Physical Review B, 1964
• Crystal Field for Yb3+ in Garnets
  The Journal of Chemical Physics, 1964
• Spin-lattice relaxation in rare-earth salts
  Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1961
• Analysis of the Solid-State Spectra of Trivalent Neodymium and Erbium
  The Journal of Chemical Physics, 1960

Cited by 21 articles