Theoretical Investigations Of The Spin Hamiltonian Parameters For 3d～3 Ions In Crystals From Two-mechanism (Crystal-field And Charge-transfer) Model

The performances of many valuable functional materials are to a large extent dependent on the electronic structure and defect structure of transition-metal or rare-earth ions in them. Electron paramagnetic resonance(EPR) spectrum is an effective tool to investigate the microscopic structure(such as electronic structure and defect structure),optical and magnetic properties of crystals and complexes doped with transition-metal or rare-earth ions. EPR experimental results are usually described by the spin Hamiltonian parameters, so, the spin Hamiltonian theory is the main part of the theory of electron paramagnetic resonance.However, in the conventional crystal-field(CF) theory only the contribution to EPR parameters due to the interactions of CF excited states with the ground state via the spin-orbit(SO) coupling parameter of the central 3d³ ion is included(it is therefore called one-SO-parameter model). Since in this model, the admixture between the d orbital of central 3dⁿ ion and the p orbital of ligand via covalency effect is not considered, the model is difficult to give a satisfactory explanation for transition-metal ions in strong-covalence crystals, especially, when the spin-orbit coupling coefficients of ligand ions are larger. Recently a two-SO-parameter model(where the contributions to EPR parameters via both the SO coupling parametersζ_d of 3d³ ion andζ_p of ligand are considered) was developed, and it has successfully explained some experimental results of EPR parameters which are difficult to be explained by the one-SO-parameter model in the cases of heavy-element ligand ions, e. g., the g-shiftâ–³g(=g-g_e, where, g_e=2.0023, the g-factor for free electron) of CsMgI₃: V²⁺is positive. However, the model is not effective to the explanation ofâ–³g for the high valence state 3dⁿ ions, e.g., the positive Ag in SrTiO₃: Fe⁵⁺. In fact, the excited states contain CF and charge-transfer(CT) excited states. So, the contributions to Ag come from the interactions of both CF excited states(CF mechanism) and CT excited states(CT mechanism) with the ground state via the SO coupling. However, in the above one-and two-SO-parameter models based on CF theory, only the contribution of CF mechanism is considered. The contributions to Ag and other EPR parameters from CT mechanism are not included. The cause of neglecting the contribution of CT mechanism may be due to the large energy difference between CT excited states and ground state, which results in the small interaction between them. As is known, for the isoelectronic 3dⁿ series in crystals, the above energy difference decreases with the increasing valence state(and hence with increasing atomic number) of 3dⁿ ion, it can be expected that the importance of CT mechanism toâ–³g and other EPR parameters should grow in the cases of high valence state 3d³ ion in crystals. In the thesis, the CT mechanism is considered and the ligand field theory(or semi-empirical LACO theory) is used to deduce the complete high-order perturbation formulae for EPR parameters of 3d³ ions in octahedral crystals. Thus, the formulae based on the two-mechanism model, which can be used to calculate the EPR parameters of 3d³ ion clusters in crystals from ionic to strong covalent, is established and applied to some materials. They are:1. For a cubic octahedral 3d3 ion cluster, the one-electron wave functions based on the two-mechanism(including bonding and antibonding molecular orbitals) are constructed.The perturbation formula for g-factor in CT mechanism is deduced from the Macfarlane's perturbation loop method, and the relations among the related parameters are established. So, for the cubic 3d³ ion clusters, the calculated method of g factor and the corresponding programs in the two-mechanism models are established.2. The above models are applied to investigate the g-factor for the isoelectronic 3d3 ion series Cr³⁺,Mn⁴⁺and Fe⁵⁺ at octahedral sites in SrTiO₃ crystals. The results show that the contributionâ–³g_CT from CT mechanism in sign is contrary to the correspondingâ–³g_CF from CF mechanism and the relative importance of CT mechanism(characterized by|â–³g_CT/â–³g_CF|) is about 14%, 60% and 155% for Cr³⁺, Mn⁴⁺ and Fe⁵⁺, respectively. Obviously, for the above 3d³ series in SrTiO₃, the relative importance of CT mechanism increases with the increasing valence state(and hence atomic number) of 3d³ ion. Then, the facts that the g-factor increases with increasing valence state of transition-metal ion and that for central Fe⁵⁺ ion, the experimental g-factor is larger than g_e are explained reasonably. Moreover, the two-mechanism model for cubic symmetry is also successfully applied to Cr(CN)₆^3- which has lower valence state of central metal ions and smaller spin-orbit coupling parameter of ligand ions, however, the strong covalence of cluster results in the lower charge-transfer(CT) energy level. The studies show that if the contributionâ–³g_CT of CT mechanism is added, the calculatedâ–³g(tot) is consistent with the observed value. The contributionâ–³g_CT due to CT mechanism is opposite in sign and about 34% in magnitude compared with the contributionâ–³g_CT due to the CF mechanism. So, the reasonable theoretical explanation of g-shiftâ–³g should take the CT mechanisms into account.3. Considering the low symmetry positions of transition-metal ions in crystals, we make use of the wave-functions including CT mechanism for tetragonal symmetry, reconstruct perturbation Hamiltonian operator and deduce high-order perturbation formulae of g-factors and zero-field splitting D for tetragonal 3d³ clusters. Then, the two-mechanism model for EPR parameters of 3dⁿ clusters with tetragonal symmetry is established.4. By applying the above perturbation formulae to some tetragonal systems including 3d³ ions, we properly account for the EPR parameters g_∥, g_⊥, D of Cr³⁺ and Mn⁴⁺ ions in lead titanate(PbTiO₃) and anatase(TiO₂). The results show that for the isoelectronic 3dⁿ ions in tetragonal-symmetry crystal field, the relative importance of CT mechanism to EPR parameters increases with the increasing valence state of 3d³ ion. Since the values ofâ–³g_i(i=∥or⊥) in CF and CT mechanisms come mainly from the second-order perturbation terms, but those of D from the third-order terms. Thus, the value of|â–³g_i^CT/â–³g_i^CF| is sketchily related to|E_l/E_n|(where E_l=10Dq and E_n is the CT energy level), but that of|D_CT/D_CF|to|E_l/E_n|². In view of|E_l/E_n|<1, the value of |â–³g_i^CT/â–³g_i^CF|is greater than that of|D_CT/D_CF|.In addition, since the D_CF is related to the tetragonal field parameter Dt, but D_CT is related to both the tetragonal field parameters Dt and Ds, the relative importance|D_CT/D_CF|depends upon the tetragonal distortion of 3d³ octahedral clusters.5. Because in some important and promising functional materials, the 3d³ octahedral clusters have trigonal symmetry, we construct wave-functions(where both anti-bonding and bonding molecular orbitals are taken into account) in trigonal symmetry. According to the Macfarlane's perturbation loop method, we establish the complete high-order perturbation formulas based on the two-mechanism model for the EPR parameters g_∥, g_⊥, D of 3d³ ions in trigonal MX₆ clusters and the corresponding programs.6. By using the above formulas, we study the EPR parameters of the isoelectronic 3d³ ions Cr³⁺, Mn⁴⁺, and Fe⁵⁺ in nonlinear optical material BaTiO₃ crystal and Mn⁴⁺ in Al₂O₃ crystal. It is found that when the CT mechanism is considered, the calculated values are consistent with the experimental data. The results suggest that for the isoelectronic 3d³ ions in crystals, the relative importance of CT mechanism to EPR parameters also increases with the increasing valence state of 3d³ ion, and the relative contribution to g-factor by CT mechanism is larger than that to zero-splitting D. In addition, since the EPR parameters(in particular, the zero-field splitting D) in CF mechanism is related to the trigonal field parameter v and v', but that in CT mechanism to v, the relative importance|D_CT/D_CF|is also relative to the trigonal distortion of 3d³ octahedral clusters.In conclusion, in the cases that the 3d³ ions have high valence state and that the 3d³ octahedral clusters have strong covalence, the contributions to EPR parameters form CT mechanism can not be neglected and the reasonable explanation of EPR parameters of 3d³ ions in various symmetries should take both CF and CT mechanisms into account.