Theoretical study on local lattice structure distortion for octahedral Fe3+ center in several germanate garnets

Local lattice structure distortion study of octahedral Fe3+ center in garnets Ca3M2Ge3O12 (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 d5 configuration ion in a trigonal ligand field. From the EPR calculation, the local structure distortion parameters ΔR and Δθ 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 Fe3+ center in garnets Ca3M2Ge3O12 (M = Al, Ga, Sc, In, Lu) are in good agreement with the experimental findings. Although the local lattice structures around the M3+ (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 Fe3+ in garnets Ca3M2Ge3O12 (M = Al, Ga, Sc, In, Lu).