Defect model and spin-Hamiltonian parameters for the tetragonal Mo⁵⁺and W⁵⁺centers in Cs₂ZrCI₆and Cs₂HfCI₆crystals

The spin-Hamiltonian (SH) parameters (g factors g ∥, g ⊥ and hyperfine structure constants A ∥, A ⊥) of tetragonal (MI = Mo, W) centers in cubic Cs2MCl6 (M = Zr, Hf): crystals are calculated from high-order perturbation formulas based on a two-mechanism model. These contain the contributions to SH parameters from both the crystal-field (CF) mechanism concerning the CF excited states and the charge-transfer (CT) mechanism concerning the CT excited states. In the calculations, two possible defect models are suggested for the tetragonal centers. In model I, one Cl− ion shifts towards the impurity by ΔZI along the C 4 axis due to electrostatic repulsion between the Cl− ion and a neighboring charge compensator, monovalent anion, at the interstitial site. In model II, two Cl− ions are displaced towards by ΔZII along the C 4 axis due to the Jahn–Teller effect. The calculated results show that, to obtain a good fit between calculated and experimental SH parameters, the required displacement ΔZI (which is about twice the displacement ΔZII) is too large to be regarded as reasonable. Thus, model II seems more likely. The contributions of the CT mechanism to SH parameters are important and, for high valence state d n ions in crystals, the exact calculations of the SH parameters should take both CF and CT mechanisms (the latter is omitted in the widely used CF theory) into account.