Theoretical studies of the g factors and local structures of the Ni3+ centers in Na2 Zn(SO4 )2 ·4H2 O and K2 Zn(SO4 )2 ·6H2 O crystals

The local structures and the g factors g_i (i = x, y, z) for Ni³⁺ centers in Na₂ Zn(SO₄ )₂ ·4H₂ O (DPPH) and K₂ Zn(SO₄ )₂ ·6H₂ O (PHZS) crystals are theoretically studied by using the perturbation formulas of the g factors for a 3d⁷ ion with low spin (S = 1/2) in orthorhombically compressed octahedra. In these formulas, the contributions to g factors from both the spin-orbit coupling interactions of the central ion and ligands are taken into account, and the required crystal-field parameters are estimated from the superposition model and the local geometry of the systems. Based on the calculations, the Ni-O bonds are found to suffer the axial compression δz (or Δz) of about 0.111 Å (or 0.036 Å) along the z-axis for Ni³⁺ centers in DPPH (or PHZS) crystals. Meanwhile, the Ni-O bonds may experience additional planar bond length variation δx (≈0.015 Å) along x- and y-axes for the orthorhombic Ni³⁺ center in DPPH. The theoretical g factors agree well with the experimental data. The obtained local structural parameters for both Ni³⁺ centers are discussed.