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The g ‐Tensor Theory Based on the Single‐Determinant‐Basis Crystal‐Field Method
Author(s) -
Zhou KangWei,
Yang JianHua
Publication year - 1995
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221890213
Subject(s) - field (mathematics) , tensor (intrinsic definition) , crystal (programming language) , isotropy , basis (linear algebra) , electron paramagnetic resonance , coupling (piping) , series (stratigraphy) , spectral line , physics , g factor , mathematics , mathematical analysis , atomic physics , chemistry , quantum mechanics , magnetic field , geometry , materials science , pure mathematics , paleontology , computer science , metallurgy , biology , programming language
The g ‐tensor theory of the single‐determinant‐basis (SDB) crystal‐field method which has been published recently is developed. With such an SDB method a unified calculation of both the optical spectrum and EPR parameters of any d 5 complex can be carried out in general. It is shown that the g ‐value (being isotropic) of a cubic d 5 complex decreases with decreasing average orbital reduction factor N for given Dq but increases with decreasing | Dq | for given N and that g is exactly a function of ( Dq ) 2 for | Dq | < 1000 cm −1 and that g also decreases with increasing |ζ| for given B, C , and Dq . The application of the SDB method to Mn 2+ ions in CaF 2 and KZnF 3 shows that not only the calculated optical spectra and the zero‐field splittings but also the g ‐values are in good agreement with the findings. The calculated g ‐values are, respectively, 2.00203 and 2.00194, while the findings are 2.0010 ± 0.0005 and 2.0021. Since it diagonalizes the electrostatic interaction, the crystal‐field, and the spin‐orbit coupling energies simultaneously, the SDB method can be extended to cases of arbitrary crystal‐field intensity, i.e., to arbitrary transition series.