Microscopicspin Hamiltonian approaches for 3d8 and 3d2 ions ina trigonal crystal field - perturbation theory methods versuscomplete diagonalization methods

Abstract

In this paper, we critically review the existing microscopicspin Hamiltonian (MSH) approaches, namely the completediagonalization method (CDM) and the perturbation theorymethod (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 ourcrystal-field analysis (CFA) package for 3dN ions isdeveloped for numerical calculations. Our method takes intoaccount the contribution to the SH parameters (D,g∥ and g⊥) from all 45 CF states for 3d8(3d2) ions and is based on the completediagonalization of the Hamiltonian including the electrostaticinteractions, the CF terms (in the intermediate CF scheme) andthe spin-orbit coupling. The CFA/MSH package enables us to studynot only the CF energy levels and wavefunctions but also the SHparameters as functions of the CF parameters (B20,B40 and B43 or alternatively Dq, v and v') for3d8(3d2) ions in trigonal symmetry. Extensivecomparative studies of other MSH approaches are carried outusing the CFA/MSH package. First, we check the accuracyof the approximate PTM based on the `quasi-fourth-order' perturbation formulae developed by Petrosyan andMirzakhanyan (PM). The present investigations indicate that thePM formulae for the g-factors (g∥ andg⊥) indeed work well, especially for the cases of small v and v' and large Dq, whereas the PM formula forthe 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 b162 193) is then revisited. Second, we carry out an extensive comparison of the results of the present CFA/MSHpackage and those of other CDMs based on the strong- and weak-CFschemes. The CF energy levels and the SH parameters for3d2 and 3d8 ions at C3v symmetry sites inseveral crystals are calculated and analysed. Our investigationsreveal 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 LiNbO3crystals. The correctness of our CFA/MSH package is verified bycomparing 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 appearsthat the two independent approaches show perfect agreement withour approach, unlike those of Zhou et al and Li, which turnout to be unreliable. Our results reveal that the contributionsto the ZFS parameter from the higher excited states cannot beneglected; also, the ZFS parameter is very sensitive toslight changes of the crystal structure. Hence our CFA/MSHpackage, which takes into account the contributions to the ZFSparameter from the higher excited states, can provide reliableresults and proves to be a useful tool for the studies of theeffect of the lattice distortions, defects and structuraldisorder on the spectroscopic properties of 3d2 and3d8 ions at trigonal symmetry sites in crystals.