Microscopic spin Hamiltonian approaches for 3d8 and 3d2 ions in a trigonal crystal field - perturbation theory methods versus complete diagonalization methods

Abstract

In this paper, we critically review the existing microscopic spin Hamiltonian (MSH) approaches, namely the complete diagonalization method (CDM) and the perturbation theory method (PTM), for 3d8(3d2) ions in a trigonal (C3v, D3, D3d) symmetry crystal field (CF). A new CDM is presented and a CFA/MSH computer package based on our crystal-field analysis (CFA) package for 3dN ions is developed for numerical calculations. Our method takes into account the contribution to the SH parameters (D, g∥ and g⊥) from all 45 CF states for 3d8(3d2) ions and is based on the complete diagonalization of the Hamiltonian including the electrostatic interactions, the CF terms (in the intermediate CF scheme) and the spin-orbit coupling. The CFA/MSH package enables us to study not only the CF energy levels and wavefunctions but also the SH parameters as functions of the CF parameters (B20, B40 and B43 or alternatively Dq, v and v') for 3d8(3d2) ions in trigonal symmetry. Extensive comparative studies of other MSH approaches are carried out using the CFA/MSH package. First, we check the accuracy of the approximate PTM based on the `quasi-fourth-order' perturbation formulae developed by Petrosyan and Mirzakhanyan (PM). The present investigations indicate that the PM formulae for the g-factors (g∥ and g⊥) indeed work well, especially for the cases of small v and v' and large Dq, whereas the PM formula for the zero-field splitting (ZFS) exhibits serious shortcomings. Earlier criticism of the PM approach by Zhou et al (Zhou K W, Zhao S B, Wu P F and Xie J K 1990 Phys. Status Solidi b 162 193) is then revisited. Second, we carry out an extensive comparison of the results of the present CFA/MSH package and those of other CDMs based on the strong- and weak-CF schemes. The CF energy levels and the SH parameters for 3d2 and 3d8 ions at C3v symmetry sites in several crystals are calculated and analysed. Our investigations reveal serious inconsistencies in the CDM results of Zhou et al and Li (Li Y 1995 J. Phys.: Condens. Matter 7 4075) based on the strong-CF scheme for Ni2+ ions in LiNbO3 crystals. The correctness of our CFA/MSH package is verified by comparing our results with the predictions of Ma et al (Ma D P, Ma N, Ma X D and Zhang H M 1998 J. Phys. Chem. Solids 59 1211, Ma D P, Ma X D, Chen J R and Liu Y Y 1997 Phys. Rev. B 56 1780) and Macfarlane (Macfarlane R M 1964 J. Chem. Phys. 40 373) for α-Al2O3 : V3+(3d2) and MgO : Ni2+(3d8). It appears that the two independent approaches show perfect agreement with our approach, unlike those of Zhou et al and Li, which turn out to be unreliable. Our results reveal that the contributions to the ZFS parameter from the higher excited states cannot be neglected; also, the ZFS parameter is very sensitive to slight changes of the crystal structure. Hence our CFA/MSH package, which takes into account the contributions to the ZFS parameter from the higher excited states, can provide reliable results and proves to be a useful tool for the studies of the effect of the l...

A Unified Calculation of the Optical and EPR Spectral Data for the Trigonal Cr3+Center in Cr3+-Doped α-RbAl(SO4)2·12H2O Alum Crystal

“…where B and C are the Racah parameters, B kl are the CF parameters in the Wybourne notation [25,26] (the relationships between the Wybourne notation and Ballhausen's conventional notation in Ref. [17] for CF parameters are given in Ref.…”

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.…”

Investigation of the Spin-Hamiltonian Parameters and the Local Structure of Ni2+ Ions in CsMgX3 (X = Cl, Br, I) Crystals

“…where B kq are the CF parameters and B 43 = −B [14,29], taking into account the ZFS and Zeeman terms [14,15,29], can be written as [17] …”

“…The MSH theory enables to correlate optical spectroscopy and structural data with the spin-Hamiltonian (SH) parameters extracted from the EPR spectra. Hence, the MSH studies of transition metal ions in crystals can provide a great deal of microscopic insight concerning the crystal structure, structural disorder, phase transitions and pressure behaviour as well as the observed magnetic and spectroscopic properties [17]. To study these properties, using the perturbation method (PTM), Pereosyan and Mirzakhanyan [18], Shang et al [19], and Huang [20] obtained a high-order perturbation formula for the SH parameters of d 8 ions at trigonal symmetry, including spin-orbit (SO) interaction only.…”

“…To study these properties, using the perturbation method (PTM), Pereosyan and Mirzakhanyan [18], Shang et al [19], and Huang [20] obtained a high-order perturbation formula for the SH parameters of d 8 ions at trigonal symmetry, including spin-orbit (SO) interaction only. The accuracy of the approximate PTM developed by Pereosyan and Mirzakhanyan has been checked in [17] by using the complete diagonalization method (CDM). This investigation indicated that the PTM formulas for the g-factors indeed work well, whereas the PTM formula for zero-field splitting (ZFS) of the ground 3 A 2 state exhibits serious shortcomings.…”