Theoretical studies of the spin-Hamiltonian parameters for the rhombic Mo5+ tetrahedral centres in ZrSiO4 crystal from a two-mechanism model

Abstract

The high-order perturbation formulas of spin-Hamiltonian parameters (g factors gi and hyperfine structure constants Ai, i = x, y, z) based on the two-mechanism model for d1 ions in rhombic tetrahedral clusters with the ground state are derived in this paper. In the model, besides the contributions to spin-Hamiltonian parameters due to the crystal-field (CF) mechanism in the widely applied CF theory, those due to the charge-transfer (CT) mechanism are taken into account. From these formulas, the six spin-Hamiltonian parameters gi and Ai for the rhombic Mo5+ tetrahedral centres in ZrSiO4 crystal are calculated with four adjustable parameters. The calculated results are in reasonable agreement with the experimental values. The calculations show that for the exact and complete calculations of spin-Hamiltonian parameters of the high valence state dn ions in crystals, the contributions due to CT mechanism should not be neglected. Some information on the defect structure of Mo5+ impurity centres in ZrSiO4 crystal is also acquired from the calculations. The results are discussed.