The superposition model of crystal fields

Abstract

The superposition model was originally developed to separate the geometrical and physical information in crystal field parameters. Its success in the analysis of lanthanide spectra has been paralleled by the success of the related angular overlap model in the analysis of d-electron spectra. The basic ideas, method of application and reliability of the superposition model are discussed and its relationship with the angular overlap model is clarified.Recent developments, described in this review, are the application of the superposition model to the ground ( L = 0) multiplet splittings of d5 and f 7 ions, orbit-lattice interactions, transition intensities and correlation crystal fields. Special attention is paid to work which has been claimed to support or disprove the postulates of the model.

Alternative zero-field splitting (ZFS) parameter sets and standardization for Mn2+ ions in various hosts exhibiting orthorhombic site symmetry

“…The usual Stevens operators [1,2] in EMR studies [27,28] and to a lesser extend in the crystal field theory and superposition model analysis [29,30,31]. Group theory predicts that for lower symmetry cases the negative q components are required [2,3,4].…”

“…Correlation of the axis systems assigned to experimentally determined ZFSP sets may be possible by comparison with model calculations using, e.g. superposition model analysis [29][30][31], which must be carried out in a well-defined axis system, usually the crystallographic one.…”

Semi-ab initio calculations of superposition model and crystal field parameters for Co2+ ions using the exchange charge model

“…Since the SM was introduced by Newman and his co-workers 7,9 to successfully analyse the CFP of lanthanide ions in various garnets and other crystal systems 10 , its equation and formalism had been widely extended to model the spin-Hamiltonian parameters (SHP) for the zero-field splittings of the ground 8 S 7/2 state of the 4f 7 (Gd 3+ and Eu 2+ ) ions or ground 6 S 5/2 state of 3d 5 (Fe 3+ and Mn 2+ ) ions [11][12][13] , even though the contributing mechanisms to SHP are substantially different from those of CFP. For analyzing the crystal field splittings of the 3d transition-metal ions, the examples of SM application were relatively fewer [14][15][16] because of the rather limited number or incomplete set of CFP derived from some experimental energy levels of which their states are often poorly determined or identified.…”

“…Since the pioneering paper by Bethe 1 However, there are several models of crystal field which allows for direct calculation or estimation of the numerical values of CFP's. In the next section two such models used in the present paper -superposition model (SM) 7 and exchange charge model (ECM) 8 will be described briefly. The main goal of the present study is to establish a feasible way to extract the values of the SM intrinsic parameters for Co 2+ using the values of CFP obtained within the framework of ECM and to re-examine the plausible form of the distance dependence of the SM intrinsic parameters.…”

Crystal field analysis of Dy and Tm implanted silicon for photonic and quantum technologies

“…However, these parameters do not in themselves give a direct insight into the mechanisms of the crystal field splitting [36]. The rank 4 CFPs are dominated by covalency and closely related overlap contributions [31].…”