Theoretical investigations of the microscopic spin Hamiltonian parameters including the spin-spin and spin-other-orbit interactions for Ni²⁺(3d⁸) ions in trigonal crystal fields

The microscopic origin of the spin Hamiltonian (SH) parameters for Ni²⁺(3d⁸) ions in a trigonal type I symmetry (C₃ᵥ,D₃d,D₃) crystal field (CF) is studied. In addition to the spin–orbit (SO) interaction, we consider also the spin–spin (SS) and spin–other-orbit (SOO) interactions. The relative importance of the four (SO, SS, SOO, and combined SO–SS–SOO) contributions to the SH parameters is investigated using the CFA/MSH package and the complete diagonalization method (CDM). The SO mechanism is dominant for all CF parameter (CFP) ranges studied, except where the contributions Dₛₒ to the zero-field splitting (ZFS) parameter D change sign. For the trigonal CFP, υc ≈1200cm⁻¹ D due to the other three mechanisms exceeds Dₛₒ. Although | D ₛₒₒ| is quite small, the combined | D ₛₒ₋ₛₒₒ| is appreciable. The SO-based perturbation theory (PT) works generally well for the g-factors: gǁ and g⊥, while it fails for D in the vicinity of υc and for large |υ’|and υ>0. The high percentage discrepancy ratio δD = 2020% for υc indicates unreliability of Dₛₒ (in PT). Applications to Ni²⁺ ions at trigonal symmetry sites in LiNbO₃,α-LiIO₃, and Al₂O₃, are provided. The theoretical SH parameters are in good agreement with the experimental data. The low symmetry (C₃) effects induced by the angle φ are tentatively studied, but appear to be quite small. Copyright © 2004 IOP Publishing.