We first consider the effects of the crystal field on both the 4f ground state and the 5d excited state of a Ce3+ ion in the paramagnetic medium CeF3, and further take account of the splitting of the crystalfield ground-state levels caused by the effective superexchange field Hv and the applied field He; then, with a model of a double transition that includes ground-state splitting, we calculate quantitatively the specific Faraday rotation θF, the Verdet constant V, the magnetic susceptibility X, and their temperature dependences in CeF3. Theoretical calculations show that the magneto-optical effect and its temperature dependence in CeF3 are closely related to the superexchange interaction between Ce3+ ions. V-1 is linearly dependent on T and V/X=-18353(1+63.01/T) in the temperature range 60<T≤300K. The theory is in good agreement with the experimental results.

In ferrimagnetic media, besides originating from the splitting of the excited state resulting from the spin-orbit interaction, magneto-optical effects also arise from the splitting of the ground state caused by the superexchange interaction and applied field. A theoretical calculation according to this view shows that the Faraday rotation 0 depends linearly on sublattice magnetization Mi (i=1,2,..., l) in both the low-temperature and high-temperature regimes for the medium with high Curie temperature, while in the normal-temperature regime, 0 depends nonlinearly on each Mi and T. The theory is in good agreement with experimental results.

Having used the classical electromagnetic field theory and combined it with the effective-field conception, in this paper we show that: 1) The real part θ of Faraday rotation φ in any kind of the magneto-optical (MO) material can be expressed in the fundamental form of θ=VLHi. 2) The differences in the MO properties of the different kinds of the MO media mainly result from both the characteristics and the size of their effective field Hi and especially, the different temperature properties in various media are discussed. 3) The relationship between the real part θ and the imaginary part ψ of φ can be described by the effective extinction coefficient η*. 4) The other MO properties are predicted. It is proved that the effective field Hv, which is concerned in both the spin-orbital interaction and the exchange interaction (or the indirect exchange interaction) in media, can be expressed in the form of Hv=vM (or E1=1viMi). Some theoretical results are verified by experiments.

In ferromagnetic media, besides originating from the splitting of the excited state resulting from the spin-orbit interaction, magneto-optical effects also arise from the splitting of the ground state caused by both the exchange interaction and the applied field. In view of the standpoint mentioned above, it is shown by calculation that the Faraday rotation 0 depends linearly on magnetization M in both the regions of T<T, (Curie temperature) and of high temperature for the medium with high T c, but nonlinearly on M and Tin the usual temperature region between the above two regions.

In some paramagnetic media, the effective field Hi, which includes an effective exchange field and an applied field, can cause a splitting of the ground level. In the temperature region T>Tc (Tc is the Curie temperature), there are certain probability distributions of electrons on two energy levels due to ground-state splitting. This induces the ground level for a double transition. It is shown that there are several temperature behaviors for the magneto-optical Faraday effect in paramagnetic media. If the applied field is not too large, the ratio of the Verdet constant to the magnetic susceptibility is V/x=A (1+BT) in some media, or V/x=A (1+B/T) in other media. It is also indicated that both the real part θ' and imaginary part θ" of the Faraday rotation are proportional to the effective field Hl, and show similar temperature behaviors beyond the region of optical absorption.