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

Abstract

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, due to the other three mechanisms exceeds DSO. Although |DSOO| is quite small, the combined |DSO−SOO| is appreciable. The SO-based perturbation theory (PT) works generally well for the g-factors: and , while it fails for D in the vicinity of vc and for large and v>0. The high percentage discrepancy ratio δD = 2020% for vc 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 are tentatively studied, but appear to be quite small.