Quantum theory of the magneto-optical effect and magnetization of Nd-substituted yttrium iron garnet

The magneto-optical and magnetic properties of Nd3+ ions in Y3Fe5O12 garnet are analyzed by using quantum theory. In the spontaneous state, tile magne to-optical effects: originate mainly from tile intra-ionic electric dipole transitions between tile 4f(3) and 4f(2)5d states split by tho spin-orbit, crystal field, and superexchange interactions. For tile excited configurati on, tile coupling scheme of Yanase is extended to tire Nd3+ ion. The magnet o-optical resonance frequencies are mainly determined by the splitting of t he 5d states: induced Ly the crystal field. Tile theoretical results of bot h Nd magnetization and Faraday rotation are in good agreement with experime nts. Tile observed Faraday rotation is proved to Le of tile paramagnetic ty pe. Although the value uf tile magneto-optical resonance frequency derived from a macroscopic analysis is approximately confirmed by our theoretical s tudy, a new assignment about the transitions associated with this resonance is unambiguously determined. Tile spin-orbit coupling of tile ground confi guration has a great influence on both the Faraday rotation and magnetizati on, but, unlike tile theoretical results obtained in some metals and alloys , the relation between tile Faraday rotation and the spin-orbit coupling st rength is more complex than a linear one. The magnitude of tile magneto-opt ical coefficient increases as the spin-orbit interaction strength of tile g round configuration decreases when tile strength is not very weak. Finally, the temperature dependence oi tire magneto-optical coefficient and the eff ect of tile mixing of different ground-term multiplets induced by tile crys tal field are analyzed.