The far infrared spectral region (∼10−100 cm−1) corresponds to kT for T=15−150°K or βH for H=105−106 oe. Materials with characteristic temperatures or fields of these orders of magnitude may have interesting far infrared spectra. We have studied far infrared resonance spectra in antiferromagnetic and in ferromagnetic rare-earth iron garnets. Antiferromagnets have a resonance frequency which depends on the exchange and anisotropy fields, HE and HA. If HE is found from χ⊥, HA can be found from ω0, and compared with theory. We have done this with FeF2, MnO, and NiO, which have resonances for T≈0 at frequencies of 52.7 cm−1, 27.5 cm−1, and 36.6 cm−1, respectively. As the temperature is raised, these frequencies fall, reaching zero at TN. When a magnetic field is applied along the easy axis of FeF2, there is a first-order Zeeman splitting, from which a g value of 2.25 was determined. In MnO and NiO, however, there is an easy (111) plane. In this case the resonant mode is nondegenerate and hence the Zeeman effect is second-order and unobservably small. The exchange coupling between the rare earth and iron ions in garnets is typically of order 20 cm−1 (30°K), while the iron ions are coupled strongly together, corresponding to their Curie temperature of about 550°K. Because anisotropy breaks down selection rules, transitions in which a single rare-earth ion spin flips in the exchange field of the iron may be observed at far infrared frequencies. We also observe Kaplan-Kittel exchange resonances, in which the entire sublattice of rare-earth ions precess together and induce a corresponding precession of the iron sublattice. Since the frequency of such a resonance depends on the rare earth sublattice magnetization, it is quite temperature dependent, in contrast to the single ion absorptions. To obtain quantitative agreement with experiment, the Kaplan-Kittel theory must be generalized to take account of anisotropy energy. In YbIG at 2°K, with the magnetization along the [111] easy direction, we find single ion resonances at 23.4 and 26.4 cm−1 and an exchange resonance at 14.1 cm−1. The latter rises in frequency as the temperature is raised, whereas the former frequencies are nearly constant up to 60°K, where the intensity becomes too low for observation. The corresponding frequencies at low temperatures in ErIG are 18.2, 21.6, and 10.0 cm−1, whereas in SmIG the exchange resonance occurs at 33.5 cm−1 and decreases with increasing temperature. The small temperature dependence of the single ion exchange splittings suggests a rare earth-rare earth coupling (perhaps via spin waves in the iron sublattice) of magnitude ∼4% of the iron-rare earth coupling.
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