Sublattice Magnetization in Yttrium and Lutetium Iron Garnets

The temperature dependence of the $a$ and $d$ sublattice magnetization in yttrium iron garnet (YIG) and lutetium iron garnet (LuIG) has been observed by means of the NMR of ${\mathrm{Fe}}^{57}$ between 4 and 373°K, with special emphasis on the temperature range where the spin-wave theory is expected to hold. An analysis of these results in terms of the spin reversals due to acoustical and optical spin-wave modes has been carried out. From a comparison of theory and experiment in YIG, the value of the dispersion parameter $D=30.0\mathrm{}\pm 0.6$ ${\mathrm{cm}}^{-1\mathrm{}}$ is obtained. A resonable estimate of the separate exchange parameters is $J_{\mathrm{ad}}=22.5\mathrm{}\pm 1$ ${\mathrm{cm}}^{-1\mathrm{}}$, $J_{\mathrm{dd}}=2.0\mathrm{}\pm 0.5$ ${\mathrm{cm}}^{-1\mathrm{}}$, and $J_{\mathrm{aa}}=0.5\mathrm{}\pm 0.5$ ${\mathrm{cm}}^{-1\mathrm{}}$, subject to the constraint that their linear combination gives $D=30\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. The agreement between experiment and theory is improved when a small transferred hyperfine interaction from the $d$ sites to the $a$ sites (and vice versa) is postulated. For LuIG one obtains a value $D=27.3\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. The values of $D$ and of the exchange parameters $J_{\mathrm{ij}}$ for YIG and LuIG are compared with those from other experiments. In YIG, the magnetic field dependence of the sublattice magnetizations has been observed up to 10 kG at 63 and 77°K, and there is good agreement with the results from spin-wave theory. It is believed that this is the first such investigation in a ferrimagnet. In the course of these experiments, the gyromagnetic ratio of ${\mathrm{Fe}}^{57}$ was determined to be $\frac{\gamma }{2\pi }=137.4\mathrm{}\pm 0.2$ Hz/G. In LuIG a broad spectrum of resonances between about 40 and 76 MHz was observed at 4.2°K. This is attributed to the resonance of ${\mathrm{Lu}}^{175}$ and ${\mathrm{Lu}}^{176}$ in a transferred hyperfine field (∼100 kG) broadened by quadrupole interaction. In ${\mathrm{Y}}^{89}$ in YIG, this transferred field seems to be smaller than ∼10 kG, from NMR and specific-heat evidence.