Studies of the EPR g factors and the local structures for the orthorhombic Er3+ centers in garnets

The perturbation formulas of the EPR g factors gx, gy and gz for a 4f11 ion in orthorhombic symmetry are established. In these formulas, the contributions to the g factors arising from the second-order perturbation terms and the admixture of various states are taken into account. The above formulas are applied to the orthorhombic Er3+ centers in YAG, YGG and LuGG garnets. By analyzing their g factors, we find that the polar angles θj′ of the impurity-ligand bonds related to the Z axis of the crystals in these Er3+ centers are smaller than the host angles θj in pure crystals, whereas the azimuthal angles ϕj′ related to the X axis in the impurity centers are larger than the corresponding ϕj in the hosts. The g factors and their anisotropies Δg [= gz − (gx + gy)/2] and δg (= gx − gy) for Er3+ in the garnets based on the above local structural parameters are in good agreement with the observed values. In addition, the angular distortions Δθ (=θj′-θj) or Δϕ (=ϕj′-ϕj) obtained by analyzing the EPR data in this work are different from Δθ2 or Δϕ2 (for only the second set of ligands, i.e., j = 2) based on the superposition model crystal-field analysis in the previous work. The validity of the results is discussed.