8571 Observed optical and magnetooptical spectra of rare earth (RE) ions in crystals are associated mainly with electric dipole (ED) transitions [1-3], although contributions from magnetic dipole (MD) transitions to the Faraday rotation have been found in some RE garnet crystals in the infrared (IR) spectral range [4][5][6]. The theory for MD transitions is well established for the LS coupling scheme and has been used to explain the features observed in the optical spectra of RE compounds [7][8][9]. At the same time, Kittel et al.[10] and Chetkin et al. [5] have examined some inter esting aspects regarding the application of this theory for an explanation of the Faraday rotation features in crystals of paramagnetic garnets YbAG and HoAG [5, 6] and europium ethylsulphate [10]. These authors have shown that in the magnetooptical spectra of these paramagnets, there is a wavelength independent gyro magnetic Faraday effect that is determined by the non diagonal component μ xy of the magnetic permeability tensor [4-6, 10].A quantum mechanical description of the Faraday effect in paramagnets has been carried out in [5] that shows that if J is a "good" quantum number and the frequency ω of the light wave is considerably larger 1 The article is published in the original. µ than the frequencies of all the magnetooptically active MD transitions within the ground multiplet (i.e., tran sitions following the MD selection rules, ΔL = 0, ΔS = 0, ΔJ = 0, and Δm = ±1) including relaxation frequencies, then the corresponding expression for the gyromagnetic rotation (per unit of length), can be written as [4][5][6] ,where is the average index of refraction of the crys tal, β = e/2mc, M is the magnetization, and g Jj is the Lande' factor of the magnetoactive ions in j th sublat tice.At the same time, according to [10], at low temper ature the Faraday rotation observed in the spectra of Eu 3+ ions is caused by Van Vleck "mixing" of the wavefunctions of the ground state |J 0 = 0, M 0 = 0〉 with the first excited state |J 1 = 1, M 1 = 0〉 [11], and also by the Zeeman splitting of the states |J 1 = 1, M 1 = ±1〉. In this case, as the electromagnetic wave frequencies ω are considerably larger than the resonance frequencies of the MD transitions between the neighboring mul ( ) 2 m F J j j j n g M c π β α = ∑ Abstract-The Faraday effect (FE) of the rare earth (RE) paramagnetic garnet crystals associated with mag netic dipole (MD) transitions has been investigated theoretically over a wide temperature range 80 to 300 K. Over this temperature range, the "gyromagnetic" Verdet constant of the Eu 3 Ga 5 O 12 (EuGG) is not a lin ear function of the magnetic susceptibility χ measured along the [111] axis. We find that the nontrivial char acter of the temperature dependence of the MD Verdet constant is associated with the presence of a con tribution to the Faraday rotation of the Van Vleck "mixing" by an external magnetic field of the Eu 3+ elec tronic states. The optical absorption and magnetic circular dichroism (MCD) of Eu 3+ ion in EuGG at 85 K fo...

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