Studies of the spin-Hamiltonian parameters and defect structures for Gd 3+ ions in zircon-structure silicates MSiO 4 (M = Zr, Hf, Th)

Abstract

The spin-Hamiltonian parameters ( g factors g ∥, g ⊥ and zero-field splittings b 2 0 , b 4 0 , b 4 4 , b 6 0 , b 6 4 ) for 4f 7 ion Gd 3+ at the tetragonal M 4+ site of zircon-structure silicates MSiO 4 (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 8 S 7/2 and the excited multiplets 6 L 7/2 ( L = P, D, F, G, H, I). The defect structures of Gd 3+ centers in the three MSiO 4 crystals are yielded from the calculation. The results are discussed.