Theoretical analysis of the magnetization and of the paramagnetic and diamagnetic magneto-optical effects in Pr-substituted yttrium iron garnets using quantum theory

By using quantum theory, the magneto-optical (Faraday rotation, Faraday ellipticity) properties at photon energies below 6 eV and the magnetic properties of the ${\mathrm{Pr}}^{3+}$ ion in the ${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$ garnet are analyzed in the 50--300 K temperature range. The strong enhancement of the Faraday rotation induced by the Pr presence originates mainly from the intraionic electrical dipole transitions between the split ${4f}^{2}$ and $4f5d$ levels. It is shown that the most important factor is the Pr-Fe superexchange interaction: if there is no Zeeman effect, no magneto-optical (MO) effects exist. The ``paramagnetic'' and ``diamagnetic'' contributions to the MO properties are discussed in detail: if only the Zeeman effect on the ground state is taken into account, the paramagnetic term which is strongly temperature dependent is obtained; on the contrary, if only the Zeeman effect on the excited configuration is considered, the diamagnetic contribution which is temperature insensitive is present. The observed MO properties result from these two components but are mainly determined by the paramagnetic one; the MO resonance frequencies are related to the energies of the multiplets of the ground term and of the excited configuration and to the crystal-field splitting of all these multiplets. Using this approach, the theoretically calculated results of both Pr magnetization and MO effects are in good agreement with experimental data. It is shown that the simultaneous treatment of the magnetic and MO phenomena is a powerful tool to prove the correctness of the approach and of the so-determined parameters. Finally, it is demonstrated that the mixing of the different multiplets of the ground term has a great influence on both magnetic and MO properties.