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Title: Low symmetry effects in the crystal (ligand) field theory and related spectroscopic studies
Other Titles: Jing ti (pei wei) chang li lun zhong de di dui cheng xiao ying ji xiang guan guang pu xue yan jiu
Authors: Qin, Jian (秦健)
Department: Dept. of Physics and Materials Science
Degree: Doctor of Philosophy
Issue Date: 2005
Publisher: City University of Hong Kong
Subjects: Crystal field theory
Ligand field theory
Symmetry (Physics)
Notes: CityU Call Number: QD475.Q25 2005
Includes bibliographical references (leaves 184-202)
Thesis (Ph.D.)--City University of Hong Kong, 2005
vii, 202 leaves : ill. ; 30 cm.
Type: Thesis
Abstract: This thesis deals with low symmetry effects in the crystal (ligand) field theory and related spectroscopic studies. Firstly, the background theory underlying the low symmetry effects in crystal field theory and spectroscopic studies is reviewed. This includes crystal field Hamiltonian, spin Hamiltonian, zero-field splitting Hamiltonian, various operator and parameter notations, the experimental and theoretical determination of the crystal field parameters, the standardization idea, as well as the rotational invariants. Secondly, the extended version of the CST package for Conversions, Standardization and Transformations developed with some improved features is described. The new features and data input/output samples are presented. The CST package can facilitate general manipulations of the CF and ZFS parameters for various systems. Thirdly, applications of the Noether’s theorem to the crystal-field and ligand-field Hamiltonians invariant under continuous rotational symmetry are discussed. Deeper meaning of the seemingly unrelated concepts: (i) the Noether’s theorems, (ii) the algebraic symmetry of Hamiltonians, and (iii) the rotational invariants and moments of CF Hamiltonians, is considered. The conserved quantities stipulated by the Noether’s theorem for the CF Hamiltonians, which have profound implications for interpretation of experimental CF parameter datasets, and geometrical meaning of the second-order conserved quantities are investigated. Hence, two subtle aspects are considered, namely, (i) the feasibility of determination of CF parameters from fitting experimental spectra and (ii) the reduction of the existing higher-order rotational invariants to combinations of primary lower-order invariants. The conserved quantities stipulated by the Noether’s theorem for the trivalent rare earth (4fN) ions at S4 symmetry sites in LiYF4, for which sufficient amount of data is available to warrant a comparative analysis of the CFP datasets, are discussed as a case study. The aim of such systematics is to reveal any specific trends existing among the CF parameters and propose predictions for the ions for which no or little data are available. Various aspects bearing on the erratic behaviour of the CF parameters revealed by this systematics are discussed. Fourthly, the following fundamental intricate aspects for low symmetry cases are considered: (i) selection of the axis systems, (ii) types of CF parameters and their properties, (iii) introduction of a new notion of a nominal axis system for the fitted CFP datasets, (iv) implications of the Noether’s theorem and the algebraic symmetry of CF Hamiltonians, (v) correlation properties among CFP datasets, (vi) the rotational degrees of freedom and the reduction of the number of independent CFP’s, which are of special importance for triclinic symmetry cases, and (vii) extension of the multiple correlated fitting technique, including a quantitative method for CFP datasets comparison. As the cases study, a detailed reanalysis of the CFPs for Nd³+ in NdGaO3 and Pr³+ in PrGaO3 as well as trivalent rare-earth (R³+) ions in nickelates RNiO3 (R = Pr, Nd, Sm, Eu, and Pr1-xLax 0≤ x ≤0.7 ) is carried out. The CFPs for rare-earth ions in high temperature superconductors also are considered utilizing the general framework presented earlier. Fifthly, other works in the EMR spectroscopy area are briefly described. The considerations presented and the arising clarifications of the intricate aspects dealt with in this thesis enable to provide a set of guidelines aimed at achieving an increased compatibility and reliability of the CFP datasets for transition ions at low symmetry sites in crystals.
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