Octahedral 3d 1 Ion Spin Hamiltonian Parameters Of The Theoretical Research

As important model systems, 3d¹ ions (Ti³⁺, V⁴⁺, Cr⁵⁺) have been extensivelyinvestigated by means of electron paramagnetic resonance (EPR), and manyexperimental data for spin Hamiltonian parameters g factors and the hyperfine structureconstants were also measured. As for the theoretical analyses, some experimental resultsfor 3d¹ ions in tetragonally and rhombically compressed octahedra were not been treated,and some others were not satisfasctorily interpreted. The weakness of the previousstudies lies in (ⅰ) adoption of the simple second-order perturbation formulas of the gfactors and (ⅱ) neglecting of the contributions from the ligand orbits and spin-orbitcoupling coefficients. In order to make further investigations on the spin Hamiltonianparameters for the above 3d¹ centers, they are quantitatively analyzed from theirhigh-order perturbation formulas for a 3d¹ ion in tetragonally and rhombicallycompressed octahedra. In these formulas, the contributions to the spin Hamiltonianparameters from the s- and p-orbital as well as the spin-orbit coupling of ligands aretaken into account based on the cluster approach. In addition, the information about thedefect structures of the 3d¹ impurity centers can be connected with the low symmetricaldistortions and thus the spin Hamiltonian parameters.(1) For the tetragonal VO²⁺ in (NH₄)₂SbCl₅, the contributions to the spin Hamiltonianparameters from the s- and p-orbital as well as the spin-orbit coupling of ligands arefound to be significant and cannot be neglected, and the signs of the experimentalhyperfine structure constants are also theoretically determined.(2) For the interstitial V⁴⁺ in anatase (TiO₂), the above contributions to the spinHamiltonian parameters are also taken into account and the quantitative interpretation tothe hyperfine structures A_i factors are carried out.(3) For the interstitial V⁴⁺ in rutile (TiO₂), stretching and contraction of the parallel andperpendicular bonding lengthes by about 0.28(?) and 0.14(?) compare to those in thehost is obtained for the impurity.(4) For the substitutional V⁴⁺ centers in rutile type MO₂(M=Ti,Ge,Sn), the (VO₆)^8-clusters change from elongation in the hosts to compression in the impurity centers due to the Jahn-Teller effect. In additon, the contributions from the ligand orbital andspin-orbit coupling contributions are not negligible because of the significant covalencyof the systems.and the liand ions become significant, because of the high valence stateof the impurity V⁴⁺. So contributions from the s- and p-orbital as well as the spin-orbitcoupling of ligands must be consider in theoretical studies on Spin Hamiltonianparameters of 3d¹ impurity centers. The second, local distortion octahedron consisted ofV⁴⁺ and ligands usually are compressed because of the Jahn-Teller effect and the groundstate is orbital singlet ²B_2g.