Abstract
The effect of the spin–orbit interactions of both the ground and excited configurations of Pr3+ ions on the magneto-optical (MO) effect induced by the Pr3+ ions in two crystals (Pr-substituted yttrium iron garnet and PrF3) has been studied based on the quantum theory. It is found that, in both Pr:YIG and PrF3, the influence of the spin–orbit coupling strength of the ground configuration on Faraday rotation (FR) is large; however the FR does not scale linearly with the spin–orbit coupling. It is surprising that the influence of the spin–orbit coupling strength of the excited configuration on FR is small except when the light frequency is near a MO resonance frequency. It is demonstrated that, contrary to widespread ideas, spin–orbit interactions of both the ground and excited configurations are not always needed to produce a FR. For PrF3, when spin–orbit interactions of both the ground and excited configurations are absent, the FR will be even larger than that under normal conditions. It is also shown that certain aspects of the effect of spin–orbit coupling on FR are related to the symmetry of the crystal field acting on magnetic ions.
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