Theoretical investigations of the local distortion and electron paramagnetic resonance parameter for CdCl₂:V²⁺ and CsMgX₃:V²⁺ (X=Cl, Br) systems

This paper systematically investigates the local distortion and electron paramagnetic resonance (EPR) parameter for CdCl₂:V²⁺ and CsMgX₃:V²⁺ (X=Cl, Br) systems on the basis of the complete energy matrix, in which not only the contributions due to the spin--orbit coupling of the central ions but also that of the ligands are considered. To describe the difference of overlapping between d-orbits and p orbit, two spin--orbit coupling coefficients are introduced. By simulating the crystal field parameter and EPR parameter, the local distortion parameters are studied and the relationships between the EPR parameter and the spin--orbit coupling coefficients as well as divergent parameter are discussed. These results show that the local structures exhibit compression distortion for CdCl₂:V²⁺ and elongation distortions for CsMgX₃:V²⁺ (X = Cl, Br), respectively. It notes that the empirical formula R \approx R_\rm H + (r_\rm i - r_\rm h ) / 2 is not suitable for CdCl₂:V²⁺ and CsMgX₃:V²⁺ (X = Cl, Br) systems. The contributions of ligand to spin--orbit coupling interaction cannot be neglected for strong covalent systems, especially for V²⁺ doped in CsMgBr₃:V²⁺.