Crystal field and microscopic spin Hamiltonians approach including spin–spin and spin–other-orbit interactions for d 2 and d 8 ions at low symmetry C3 symmetry sites: V 3+ in Al 2O 3

Abstract

A new module has been developed within the CFA/MSH computer package, which is applicable for d 2 and d 8 ions at sites of trigonal symmetry type I ( C 3 v , D 3, D 3 d ) and type II ( C 3, C 3 i ), including the ‘imaginary’ CF term. For the first time the spin–spin (SS) and spin–other-orbit (SOO) interactions have also been included in the Hamiltonian. This module enables to study the contributions to the energy levels and the spin Hamiltonian parameters, i.e. zero-field splitting D and g-factors: g ∥ and g ⊥. The contributions arising from the spin–orbit (SO), SS, and SOO interaction as well as those due to the low symmetry CF effects induced by the distortion angle ϕ, which describes the difference between C 3 and C 3 v symmetry, can be studied. As an application of the new module, calculations have been carried out for V 3+(3d 2) ions in α-Al 2O 3 crystal, taking into account for the first time the SS and SOO interactions, and the low symmetry CF effects. The results show that (i) the contributions from the SS and SOO interactions to the energy levels are larger for free V 3+ ions than those for V 3+ ions in α-Al 2O 3 crystal, (ii) both the contributions to the SH parameters and the energy levels arising from the SOO interaction are larger than those arising from the SS interaction, (iii) the contributions due to the low symmetry CF effects induced by the distortion angle ϕ are in general significant, (iv) D and g ⊥ are sensitive to the distortion angle ϕ, whereas g ∥ is insensitive to ϕ, and (v) the influence of the lattice distortions on the spectroscopic properties of V 3+ ion in α-Al 2O 3 is pronounced. It appears important for similar ion-crystal cases to consider the lattice distortions in detailed calculations, which take into account the relevant contributions from the SO, SS and SOO interactions. A good agreement between the theoretical and experimental results has been obtained.