Sublattice contributions to second-order magneto-optical effects in rare-earth iron garnets

The angular variation of second-order magnetooptical effects, as the crystal is rotated relative to the magnetization, is calculated for each sublattice of rare-earth iron garnets. The expressions are obtained by applying Tucciarone´s recently proposed AVIA (angular variation of induced anisotropy) method, which, in the approximation of axially symmetric garnet sites, gives the angular variation of a general garnet anisotropy property. The octahedral contribution vanishes when the magnetization lies along fourfold crystal axes, whereas the tetrahedral contribution vanishes when the magnetization lies along threefold axes or at an angle of 45° with respect to fourfold axes. All sublattice contributions are found to have in shape the same angular variation. The data of previous experiments are compared with theory and agree well with this behavior. On the basis of the theoretical expressions it is possible to analyze tha data and to distinguish, at different wavelengths and temperatures, the contributions to magnetic linear dichroism and birefringence coming from different sublattices. Finally, theory allows a new and simple interpretation for phenomenological macroscopical parameters, which were previously introduced in order to describe the crystallooptical behavior of cubic magnetic materials.