Theoretical study on local lattice structure distortion for octahedral Fe 3+ center in several germanate garnets

Abstract

Local lattice structure distortion study of octahedral Fe 3+ center in garnets Ca 3M 2Ge 3O 12 (M = Al, Ga, Sc, In, Lu) has been performed systematically based on the diagonalization of the complete energy matrices of the electron–electron repulsion, the spin–orbit coupling and the trigonal ligand–field interaction for a d 5 configuration ion in a trigonal ligand field. From the EPR calculation, the local structure distortion parameters Δ R and Δ θ are determined, respectively. These results illuminate a microscopic origin of various ligand field parameters used empirically for the interpretation of electron paramagnetic resonance experiments. It is found that the theoretical results of the electron paramagnetic resonance spectra for Fe 3+ center in garnets Ca 3M 2Ge 3O 12 (M = Al, Ga, Sc, In, Lu) are in good agreement with the experimental findings. Although the local lattice structures around the M 3+ (M = Al, Ga, Sc, In, Lu) ions are obviously different, the local lattice structures around the dopants are rather similar. Moreover, it is noted that the empirical impurity–ligand distance R ≈ R H + 1 2 ( r i - r h ) is not suitable for Fe 3+ in garnets Ca 3M 2Ge 3O 12 (M = Al, Ga, Sc, In, Lu).