Theoretical investigations of the Jahn–Teller distortions for V 3+ and Cr 4+ in α-Al 2O 3

Abstract

The spin Hamiltonian parameters (zero-field splittings D, g factors g // and g ⊥, the hyperfine structure constants and the spin–lattice coupling coefficients | G –|, | G 15|, | G 51| and | G 44|) for V 3+ and Cr 4+ in α-Al 2O 3 are theoretically investigated from the perturbation formulas of these parameters for a 3d 2 ion under trigonally distorted octahedra. In these formulas, the contributions from the dynamical Jahn–Teller effect, the configuration interactions and the ligand orbital and spin–orbit coupling interactions are quantitatively taken into account in a uniform way based on the ligand field model. The impurity-ligand bond angles related to the C 3 axis are found to experience the variations of about 1.5–1.9° due to the dynamical Jahn–Teller nature, yielding more regular octahedra around the 3d 2 impurities. In addition, the size mismatching substitution of the smaller host Al 3+ by the larger impurities may also bring forward some contributions to the local angular distortions. All the calculated spin Hamiltonian parameters based on the above angular variations show reasonable agreement with the experimental data for both centers. The improvements are achieved in this work by adopting the uniform model and formulas and much fewer adjustable parameters as compared with the previous treatments.