The spin-Hamiltonian parameters (g factors g∥, g⊥ and zero-field splittings b2(0), b4(0), b4(4), b6(0), b6(4)) for 4f7 ion Gd3+ at the tetragonal M4+ site of zircon-structure silicates MSiO4 (M=Zr, Hf, Th) are calculated from a diagonalization (of energy matrix) method. The Hamiltonian concerning this energy matrix contains the free-ion, crystal-field interaction and Zeeman interaction terms and the 56×56 energy matrix is constructed by considering the ground multiplet 8S7/2 and the excited multiplets 6L7/2 (L=P, D, F, G, H, I). The defect structures of Gd3+ centers in the three MSiO4 crystals are yielded from the calculation. The results are discussed.
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