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

Abstract

The spin-Hamiltonian (SH) parameters (g factors g _∥, g _⊥ and hyperfine structure constants A _∥, A _⊥) of tetragonal (M_I = 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 ΔZ_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 by ΔZ_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 ΔZ_I (which is about twice the displacement ΔZ_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.

Keywords:

• Mo^5 +
• W^5 +
• crystal field
• defect structures
• electron paramagnetic resonance
• inorganic materials
• spectroscopy