Defect model and spin-Hamiltonian parameters for the tetragonal Mo5+ and W5+ centers in Cs2ZrCI6 and Cs2HfCI6 crystals

The spin-Hamiltonian (SH) parameters (g factors g(parallel to), g(perpendicular to) and hyperfine structure constants A(parallel to), A(perpendicular to)) of tetragonal MIC16- (M-I = Mo, W) centers in cubic Cs2MCl6 (M = Zr, Hf): M-I(5+) 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 MIC16- centers. In model I, one Cl- ion shifts towards the M-I(5+) impurity by Delta Z(I) 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 M-I(5+) by Delta Z(II) 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 Delta Z(I) (which is about twice the displacement Delta Z(II)) 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.