Dependence of Faraday rotation and magneto-optical figure of merit on dielectric tensor elements in materials with uniaxial symmetry

We derive the functional dependence of the specific Faraday rotation Theta, optical absorption alpha, and magneto-optical figure of merit F equivalent to vertical bar Theta vertical bar/alpha on the dielectric tensor elements of a uniaxial, magneto-optically active material in a wavelength regime of relative transparency. In addition, we calculate F as a function of omega < 2.2 eV for the diamagnetic transition of the octahedrally coordinated Fe3+ in bismuth doped yttrium iron garnet (omega(0)=3.15 eV) and show that F achieves a local maximum value in this frequency regime at omega=1.25 eV. We also discuss the implications of this result in rare-earth iron garnets for bulk magneto-optical isolators and in orthoferrites for thin film devices. Finally, we discuss the importance of controlling linear birefringence in thin film isolators and its impact on the usefulness of F.