The zero-field splitting D of the 8 S 7/2 ground singlet for the tetragonal Gd 3+ center in La 2-x Sr x CuO 4 is theoretically studied from the superposition model. Meanwhile, the g factor is also quantitatively investigated from the approximation formula including admixture of the ground 8 S 7/2 and the excited 6 L 7/2 ( L=P , D, F, G) states via the spin-orbit coupling interactions. The calculated zero-field splitting and g factor are in reasonable agreement with the experimental data. It is found that the significant zero-field splitting can be ascribed to the average impurity-ligand bonding angles [≈ (θ1 + θ2)/2 ≈ 62°] related to the four-fold axis larger than that (≈ 54.74°) of the cubic case. Nevertheless, the experimental g factor close to 2 may be largely due to the very slight admixture of the ground 8 S 7/2 and the excited 6 L 7/2 states via the spin-orbit coupling interactions.
