Theoretical Study On The Spin Hamiltonian Parameters For 3d~9 Ions In Crystals

Properties of various functional materials largely depend on the electronic structures and impurity (or defect) behaviours of the doped transition-metal ions in the hosts. Electron paramagnetic resonance (EPR) is a powerful tool to investigate optical, magnetic and local structure properties of crystals and complexes containing transition-metal ions. 3d⁹ ions belong to the typical and important systems of the transition-metal groups and attract extensive interests of researchers due to the relatively simpler energy structure with only one ground state and one excited state under ideal cubic symmetry. Abundant EPR experimental data have been reported for many materials doped with 3d⁹ ions, which were usually described as the spin Hamiltonian parameters (anisotropic g factors and the hyperfine structure constants). Up to now, however, theoretical explanations to these experimental results seem not satisfactory yet. i) The previous studies were often based on the simple second-order g formulas by considering only the central ion orbital and spin-orbit coupling contributions, while the influences of the ligand orbital and spin-orbit coupling interactions were not taken into account. ii) The previous treatments did not establish the theoretical relationships between EPR spectra and local structures of the systems but introduced various adjustable parameters to describe the low symmetrical distortions. iii) In the previous studies of the superhyperfine parameters, the unpaired spin densities were normally estimated by fitting the two experimental superhyperfine parameters, failing to connect the unpaired spin densities with the orbital admixture coefficients or covalency of the systems.In order to overcome the above shortcomings, the high order perturbation formulas of the spin Hamiltonian parameters based on the ligand-field theory for 3d⁹ ions in tetragonally elongated and rhombically (or orthorhombically) elongated (or compressed) octahedra and tetragonally distorted tetrahedra are adopted to the studies of some 3d⁹ (e.g., Cu²⁺, Ni⁺) centers, which have not been theoretically treated or unsatisfactorily investigated. These EPR experimental results are reasonably interpreted, and information of the local structures of the impurity centers are also acquired.1) The EPR spectra and the local structures are theoretically investigated for the Cu²⁺ centers in PrBa₂Cu₃O_6+x and Pr_0.5Er_0.5Ba₂Cu₃O_6+x as well as the uncompensated Ni⁺ center I and centers II and III with one and two nearest neighbour F– vacancy in RbCaF3. As for PrBa₂Cu₃O_6+x and Pr_0.5Er_0.5Ba₂Cu₃O_6+x, the Cu-O bonds suffer elongations of 0.05 and 0.01(A|°), respectively, along the C₄ axis due to the Jahn-Teller effect. As regards the three Ni⁺ centers in RbCaF₃, the quantitative relationships of the tetragonal field parameters, the molecular orbital coefficients and the unpaired spin densities with the impurity local structures or experimental optical spectral data are established on the basis of the cluster approach including ligand orbital and spin-orbit coupling contributions. It is found that the impurity-ligand bonds in center I experience the relative elongation of 5% along the C₄ axis due to the Jahn-Teller effect. The calculations of the superhyperfine parameters for the centers I, II and III reveal that the unpaired spin densities are f_s(?0.28, 0.30 and 0.31%) and f_?(?1.55, 2.39 and 2.68%), respectively.2) The high order perturbation formulas of the spin Hamiltonian parameters for a 3d⁹ ion under rhombically (or orthorhombically) elongated (or compressed) octahedra are applied to the studies of the EPR spectra and the local structure properties for the relevant systems. i) The anisotropic g factors gx, gy and gz are reasonably explained for the orthorhombic Cu²⁺ center in Y₂BaCuO₅, and the oxygen octahedron is found to undergo the elongation of about 0.05(A|°) along c axis and the relative planar bond length variation of about 0.1(A|°) along a and b axes due to the Jahn-Teller effect. ii) The g factors and the hyperfine structure constants are satisfactorily interpreted for the rhombic Cu²⁺ center in TiO₂. The planar impurity-ligand bond angle is found to be about 5.8°larger than the host value due to the Jahn-Teller effect via bending the planar bonds, which considerably reduces the rhombic distortion of the system. In addition, the experimental optical spectral data are also uniformly interpreted. iii) The high order perturbation formulas of the spin Hamiltonian parameters for a 3d⁹ ion under orthorhombically compressed octahedra are established and applied to the Cu²⁺ centers in AWO₄(A= Zn, Cd and Mg). The planar impurity-ligand bond lengths are found slightly different from those in the hosts, i.e., the orthorhombic distortions can be described by the relative planar bond length variations 0.096?0.021 and 0.028 (A|°) along X and Y axes for CdWO₄, ZnWO₄ and MgWO₄, respectively.3) Based on the cluster approach, the perturbation formulas of the spin Hamiltonian parameters for a 3d⁹ ion under tetragonally distorted tetrahedra are established, and the related parameters (e.g., the tetragonal field parameters and the molecular orbital coefficients) are correlated with the local structures and the optical spectral data of the systems. These formulas are applied to the tetrahedral tetragonal Ni⁺ centers in ABS₂ (A = Cu, Ag; B = Al, Ga), and the EPR and optical spectral data are satisfactorily interpreted. Around the impurity Ni⁺ replacing the host A⁺, the local impurity-ligand bond angle may be different from the host value due to the size mismatching substitution. It is found that the local bond angles are about 1.73, 1.44 and 4.54°smaller than the host values for CuAlS₂, CuGaS₂ and AgGaS₂, respectively. In addition, the ligand orbital and spin-orbital coupling contributions should be considered in view of the significant covalency of the systems.4) The perturbation formulas of the anisotropic g factors and the superhyperfine parameters for a 4d7 ion under tetragonally elongated octahedra are established, and the related molecular orbital coefficients and the unpaired spin densities are determined from the cluster approach in a uniform way. These formulas are applied to the tetragonal Pd³⁺ centers in AgX (X=Cl, Br). From the calculations, the [PdX₆]^3- clusters are found to suffer the elongations of about 0.01 and 0.06 (A|°) along the C4 axis for AgX and AgBr, respectively, due to the Jahn-Teller effect. Interestingly, the EPR behaviours for a 4d⁷ ion under tetragonally elongated octahedra are quite similar to those for a 3d⁹ ion under tetragonally compressed octahedra, e.g., both exhibiting the same ²A_1g ground state and anisotropy of g_s(?2.0023)?g//?g?. As compared with the previous works, the calculated superhyperfine parameters based on the uniform formulas and the fewer adjustable parameters in this work show good agreement with the experimental data, and the shortcoming of the unpaired spin densities obtained by fitting the two experimental superhyperfine parameters in the previous treatments is thus overcome.