Theoretical Investigations And Applications Of The Zero-field Splitting And G Factors Of The Ground State And Low-lying States For Transition Metal Ions In Crystals

By using complete diagonalization method (CDM), the spin-Hamiltonian (SH) parameters of ground state and excited states for d3 ions and d2/8 ions at trigonal and tetragonal symmetry are studied, based on crystal field theory. The main contents and innovations are as follows:Firstly, by analyzing the crystal field potential, the concepts of crystal field parameters are illustrated. The three models adopted to calculate CF parameters are compared and analyzed. In the development of CF theory, various CF notations are used, this result in confusion to researchers. In this thesis, the physical meanings of various CF notations are illustrated, the relations between various CF notations are analyzed, and the confusions are clarified. The spectra fine structure of dN ions at trigonal and tetragonal symmetry are deduced by group theory.Secondly, in the intermediate crystal field coupling scheme, the complete energy matrices for transition metal (TM) ions are constructed. In addition to general spin-orbit (SO) interactions, the slight magnetic interactions including spin-spin (SS), spin-other-orbit (SOO) and orbit-orbit (OO) interactions are taken into account. Formulas of SH parameters of ground state and excited states are deduced, and the corresponding computer program are developed.Thirdly, by using the theory and the program developed in this thesis, the contribution to SH parameters of ground state from excited states of d3 ions are investigated. For trigonal and tetragonal symmetry, these results are obtained:(a) The ground state is 4F, contributions from spin doublets are appreciable. For g factors, there are almost no contributions from spin doublets, (b) The contributions from SS and SOO mechanisms mainly depend on spin quartets, and the contributions from spin doublets are appreciable. (c) The contribution to g factors from SS mechanism almost is zero, but the contribution to g factors from SOO mechanism is appreciable, and this contribution depends on spin quartets only.Fourthly, the influence to SH parameters of ground state of d2/8 ions from excited states at trigonal symmetry are studied. It is shown that, the contribution from SO mechanism is dominant, in which, the contributions from spin triplets are mainly. The contributions to ZFS of ground state from SS, SOO and SO-SS-SOO combined mechanisms are mainly due to spin triplets. The contribution to g factors from SS mechanism almost is zero, but the contribution to g factors from SOO mechanism is appreciable, and this contribution depends on spin triplets only. Contributions to g factors from 00 mechanism are depending on spin triplets only.Fifthly, the theory of ZFS of excited states have been established. The ZFS of low-lying states for d3 ions at trigonal symmetry have been studied, the misprint in reference are pointed out. The formulas of ZFS of 4T2,4T1a,2T1a and 2T2a have been defined. It is shown that, the ZFS of 4T2 and 4T1a terms are mainly depend on trigonal CF. The contribution to ZFS of low-lying states from spin-orbit mechanism is dominant, and the contributions from other mechanisms are slight. The energy integrals ofδ1(2T1α)andδ1(2T2α) depend on magnetic interactions, and the energy integrals ofδ2(2T1α) andδ2(2T2α)depend on trigonal CF.Sixthly, the convergence of PTM formulas of 4T2 and 4T1a terms for d3 ions at tetragonal symmetry has been analyzed. The results show that, the convergence of PTM formulas is better in the cases of stronger CF.Seventhly, the g factors of 2E state of d3 ions at trigonal symmetry have been investigated. The g factors 2E state of Al2O3:Mn4+ and Al2O3:Cr3+ systems have been explained theoretically. It is found that, there exists combined mechanism. And the relative magnitude of various magnetic mechanisms has been studied. The contributions to ZFS of ground state from slight magnetic interactions are considerable. But the contributions to ZFS of 2E state from slight magnetic interactions are small. For g factors, the contributions to g factors of the ground state and E'(2E) state from SS, SOO and 00 magnetic interactions can not be omitted, but are slight to the g factors of E"(2E) state. The experimental values of g factors of 2E state of ZnGa2O4:Cr3+ systems have been explained. The values of g factors of 2E state for MgAl2O4:Cr3+ system have been predicted theoretically.Eighthly, the local structure of Al2O3:V2+, Al2O3:Cu3+, CsMgX3:V2+(X=Cl,Br,I) systems and LiNbO3:Ni2+ systems have been studied by using ligand plane displacement model, center ions displacement model and double displacement model, respectively. The coincidence between the calculated results and the experimental results shows that the models we adopted are reasonable.