Theoretical studies of the local structures and the spin Hamiltonian parameters of the tetragonal Ru3+ centers in AgCl and AgBr

The local structures and the spin Hamiltonian parameters of the tetragonal Ru3+ centers in AgCl and AgBr are theoretically studied from the perturbation formulas of these parameters for a 4d5 ion in tetragonally distorted octahedra. In these formulas, the contributions from the spin–orbit coupling coefficient and the s- and p- orbitals of the ligands are taken into account from the cluster approach. Based on the studies, the impurity centers are attributed to the substitutional Ru3+ occupying the Ag+ site associated with one and two next nearest neighbouring cation vacancy VAg along the [1 0 0] (or C4) axis for AgCl and AgBr, respectively. Due to the electrostatic repulsion of the VAg, the halide ligand(s) intervening in the VAg and the impurity Ru3+ are found to displace away from the vacancy by an amount ΔZ ≈ 0.156 Å (or 0.185 Å) along the C4 axis for AgCl (or AgBr), respectively. The theoretical results based on the above defect models and the displacements ΔZ show good agreement with the experimental data. The contributions to the spin Hamiltonian parameters from the ligand orbitals and spin–orbit coupling coefficient are also discussed.