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 Ni 2+ (3d 8 ) ions in a trigonal type I symmetry (C 3v , D 3d , D 3 ) 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 D SO to the zero-field splitting (ZFS) parameter D change sign. For the trigonal CFP, v c ≈ 1200 cm −1 D due to the other three mechanisms exceeds D SO . 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: g and g ⊥ , while it fails for D in the vicinity of v c and for large |v | and v > 0. The high percentage discrepancy ratio δ D = 2020% for v c indicates unreliability of D SO (in PT). Applications to Ni 2+ ions at trigonal symmetry sites in LiNbO 3 , α-LiIO 3 , and Al 2 O 3 , are provided. The theoretical SH parameters are in good agreement with the experimental data. The low symmetry (C 3 ) effects induced by the angle ϕ are tentatively studied, but appear to be quite small.

Alternative zero-field splitting (ZFS) parameter sets and standardization for Mn2+ ions in various hosts exhibiting orthorhombic site symmetry

“…The origin of the fine structure as resulting "from the crystal field and the spin-spin interactions" is not quite correct since as recent microscopic spin Hamiltonian studies [73,74] reveal the spin-orbit interactions contribute dominantly to ZFS, whereas the contribution from the spin-spin interactions is rather minor. The determination of the direction cosines of the distortion axis using the method of Rao and Subramanian [75] used in [72] appears to be valid only for the cases of axial distortions of sixfold nearly cubic ML 6 complexes.…”

Spin-Spin and Spin-Other-Orbit Interactions of Spin-Hamiltonian Parameters for 3d2(8)Ions in Al2O3Crystals

“…(3d 8 ) ions in some crystals [13,[18][19][20]. They found that, for 3d 2 and 3d 8 ions at trigonal symmetry sites, although the SO mechanism is the most important one, the SS and SOO interactions were found important.…”

“…By taking into account the SS and SOO interactions, the total Hamiltonian of a 3d 2(8) ion in trigonal crys- * corresponding author; e-mail: weiaqun@163.com tal field (CF) in intermediate scheme can be written as [13,[18][19][20]: [23,26], and hence play a key role in the CF studies.…”

“…∆g (= g − g e ) = ∆g ⊥ (= g ⊥ − g e ) = 0, whereas considering the magnetic interactions and trigonal CF simultaneously yields D = 0, ∆g = 0 and ∆g ⊥ = 0 [18]. So, to study the relative contribution to SH parameters, we should calculate the departure of g factors from g e rather than g factors themselves.…”

Research on the Spin-Hamiltonian Parameters and Local Structure for the Tetragonal Mo5+Centers in CaWO4Crystal

“…where B kl are the CF parameters in Wybourne notation [31,32].Ā k (R) (k = 2, 4) are the intrinsic parameters. For 4d n ions in crystals, the ratiō A 2 (R)/Ā 4 (R) ≈ 6 ± 2 was found [29, n clusters is about 1.5(1) times that of the isoelectronic 3d n clusters [19].…”