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In this paper, the high-order perturbation formulas of spin-Hamiltonian (SH) parameters (g factors g(parallel to), g(perpendicular to) and zero-field splitting D), including both the crystal-field (CF) and for the first tune charge-transfer (CT) mechanisms, are established for 3d(8) ions in trigonal octahedral clusters. By using these formulas, the SH parameters of Ni2+ ions in CSMgX3 (X = Cl, Br, 1) crystals are calculated. The results are consistent with the experimental values. The calculations suggest that the sign of Q(CT) (Q = Delta g(parallel to), Delta g(perpendicular to) or D, where the g-shift Delta g(i) = g(i)-g(e), g(e)approximate to 2.0023 is the value of free-electron) due to CT mechanism is the same as that of the corresponding Q(CF) due to CF mechanism, and the relative importance of CT mechanism (characterized by Q(CT)/Q(CF)) increases with the increasing atomic number of ligand X. So, for the 3d(n) MLm clusters with ligand having large atomic number, the reasonable theoretical explanations of all SH parameters should take both CF and CT tnechanisms into account. The defect structure of (NiX6)(4-) impurity centers in CSMgX3:Ni2+ crystals is also considered in our model. (c) 2007 Elsevier B.V. All rights reserved.