Analysis on the local structures for 3d¹ impurities (Ti³⁺ and V⁴⁺ ) in KTiPO₄

Making use of the perturbation formulae for 3d¹ ions (Ti³⁺ and V⁴⁺ ) under orthorhombically compressed octahedra, the spin Hamiltonian parameters (g factors: g_x , g_y , g_z and hyperfine structure constants: A_x , A_y , A_z ) and local structures of the 3d¹ impurity centres C₁ , C₂ , and C₃ in KTiOPO₄ crystals are theoretically analyzed in a consistent way. The remarkable local distortions (i.e., the relative axial compression ratios 11.2%, 7.0%, and 5.5% along Z axis and the relative planar bond length variation ratios 15.9%, 7.0%, and 6.0%) are obtained for the [Ti2O₆ ]^9- cluster on Ti2 site and [VO₆ ]^8- clusters on Ti1 and Ti2 sites, respectively, in view of the Jahn-Teller effect. The above local orthorhombic distortion parameters in the impurity centres are found to be more significant than the host Ti1 and Ti2 sites in pure KTiOPO₄ . The sequences (C₁  > C₂  > C₃ ) of the local orthorhombic distortion parameters ρ and τ are in accordance with those of the axial and perpendicular anisotropies Δg and δg of g factors, respectively.