On standardization and algebraic symmetry of the ligand field Hamiltonian for rare earth ions at monoclinic symmetry sites

Publisher Website
Google Scholar
Abstract
The standardization idea previously applied for an orthorhombic Hamiltonian is now extended to the monoclinic crystal‐field Hamiltonian (HCF). Relations are given which allow for transformations of the three admissible forms of monoclinic HCF between themselves to achieve the ratio of B22/B02 confined to the standard range (0,±1). Thereby correlations between the apparently different crystal‐field parameter (CFP) sets of various authors can be established. Algebraic symmetry of the characteristic equation of HCF for monoclinic C2, C1h(Cs), and C2h symmetry is considered by the method proposed earlier using altran. Magnitudes, signs, and/or relative signs of the CF parameters which can be determined from fitting the optical spectra of fn ions at sites of the above symmetry are established for the reduced approach (with one [B−qk]=0). Some misinterpretations on the complete approach, which yields ambiguous and unreliable results in general, as well as on the approximated approach are clarified. An extensive survey has revealed several cases of usage of the inappropriate complete approach. Based on the theoretical considerations a multipole correlated fitting technique has been proposed. The results of this paper are expected to greatly facilitate fitting of the optical spectra of fn ions as well as dn ions at sites of low symmetry.