Far Infrared Spectra of Rare-Earth Iron Garnets

Abstract

Transmission measurements on a number of ferrimagnetic rare-earth iron garnets at low temperatures indicate that both collective and single-ion excitations are observable. Kaplan-Kittel exchange resonances, wherein a mutual precession of the iron and rare-earth sublattices occurs, have been observed at 2°K in YbIG (14.0 ${\mathrm{cm}}^{-1\mathrm{}}$), ErIG (10.0 ${\mathrm{cm}}^{-1\mathrm{}}$), SmIG (33.5 ${\mathrm{cm}}^{-1\mathrm{}}$), and HoIG (38.5 ${\mathrm{cm}}^{-1\mathrm{}}$). The exchange resonances are usually easily identified by their characteristic temperature dependence, which stems from the marked temperature dependence of the rare-earth sublattice magnetization. On the other hand, the single-ion transitions, resulting from transitions between rare-earth ion energy levels split by the crystalline electric field and the iron exchange field, are relatively independent of temperature below 70°K, because the iron sublattice producing the exchange field remains nearly completely ordered. The observation of single-ion transitions has permitted a rather detailed study of the fields acting on an individual rare-earth ion in the garnet structure. For example, measurement of the angular dependence and Zeeman shift of the exchange-split Kramers doublet of ${\mathrm{Yb}}^{3+}$ in YbIG indicates that both the spectroscopic $g$ values of the ground doublet and the exchange field acting on the doublet are anisotropic. Also, a slight temperature dependence of the single-ion splitting in both ErIG and SmIG suggests that a weak ferromagnetic rare-earth-rare-earth coupling exists. Further, single-ion transitions from the ground state of the rare-earth ion to higher crystal-field states as modified by the iron exchange field have been identified in ErIG and HoIG, but a detailed level assignment has not been possible. Finally, the absence of observable single-ion transitions in GdIG confirms the predicted dependence of these on crystal field-induced inequivalence of rare-earth ions, which is negligible for an $S$-state ion such as ${\mathrm{Gd}}^{3+}$.