Studies on the Local Angular Distortion and Spin Hamiltonian Parameters for the Trigonal Co<sup>2+</sup> Center in MgCl<sub>2</sub>

The local angular distortion and spin Hamiltonian parameters (g factors g_∥, g_⊥ and the hyperfine structure constants) for the trigonal Co²⁺ center in MgCl₂ are theoretically studied by diagonalizing the 6 × 6 energy matrix of ground ⁴T₁ state for a trigonally distorted octahedral 3d⁷ cluster. Based on the cluster approach, the contributions from the admixtures of various J (= 1/2, 3/2, 5/2) states and the ligand orbital and spin–orbit coupling interactions are taken into account in a uniform way. The local impurity–ligand bond angle in the Co²⁺ center is found to be about 3.44^○ larger than the host metal–ligand bond angle in the pure crystal due to substitution of smaller Mg²⁺ by bigger Co²⁺, inducing a further compressed ligand octahedron. The calculated spin Hamiltonian parameters using the above local angular distortion are in good agreement with the experimental data. The present studies on the local structure and the spin Hamiltonian parameters for Co²⁺ in MgCl₂ are tentatively extended to a more general case by comparing the relevant impurity behaviours for Co²⁺ in various trigonal environments.