Studies of the tetragonal distortion due to Jahn-Teller effect for the Cu2+ centres in trigonal ZnMF6 ·6H2 O (M = Si, Ti, Zr) crystals from the calculations of spin-Hamiltonian parameters

Abstract

The spin-Hamiltonian (SH) parameters (g -factors g∥, g⊥ and hyperfine structure constants A∥, A⊥) of the tetragonal Cu(H2O)62+ centres (which are caused by the static Jahn–Teller effect) in trigonal ZnMF6·6H2O (M = Si, Ti, Zr) crystals are calculated from two theoretical methods, the perturbation theory method (PTM) and the complete diagonalization (of energy matrix) method (CDM). In the calculations, the required crystal-field parameters are estimated from the superposition model which enables correlation of the crystal-field parameters and hence the SH parameters with the tetragonal distortion (characterized by ΔR = R∥ – R⊥, where R∥ and R⊥ denote the metal–ligand distances parallel with and perpendicular to the tetragonal axis) of Cu(H2O)62+ centres. The calculated SH parameters from both methods are in reasonable agreement with the experimental values, suggesting that both PTM and CDM can explain satisfactorily the SH parameters of 3d9 ions in crystals. The tetragonal distortion of the Cu(H2O)62+ centres in ZnMF6·6H2O crystals are also obtained from the calculations. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)