Theoretical investigations of the g factors and the local structures for the orthorhombic Nd3+ centers in the garnets

The EPR g factors gx, gy and gz and the local structures for the orthorhombic Nd3+ centers in YAG, YGG and LuGG garnets are studied by using the perturbation formulas of the g factors for a 4f3 ion in orthorhombic symmetry. In these formulas, the contributions to the g factors arising from the second-order perturbation terms and the admixture of various energy levels are considered. Based on the analyses of the g factors, we find that the polar angles θ′j of the impurity-ligand bonds related to the Z-axis of the crystals in these Nd3+ centers are smaller than the host angles θj in pure crystals, whereas the azimuthal angles ϕ′j related to the X-axis in the impurity centers are larger than the corresponding ϕj in the hosts. The calculated g factors, particularly their anisotropies Δg [= gz − (gx + gy)/2] and δg (= gx − gy) for Nd3+ in the garnets based on the above local angles show reasonable agreement with the observed values.