The Origin of the Crystal Field for 4fn Ions in Insulators
The 4f-ligand overlap for the rare earth ions in crystals is considerably smaller than the 3d-ligand one for transition metal ions. Therefore the theory of low-lying electronic levels of these ions is often based on the hypothesis that major forces acting upon 4f electrons are of a classical electrostatic nature. However, as it follows from simple calculations for the divalent ions, the ratio of the square of the 4f-ligand overlap integral to the 3d-ligand one is proportional to the ratio of the energy level splittings of the 4f and 3d electrons in the crystal field. This means that, as in the case of 3d electrons, the overlap effects must play an important role in determining both the energy level splittings of the 4f electrons and the corresponding crystal field parameters. To illustrate this, calculations of the crystal field splittings were performed for the simple systems CaF2:Tm2+ and SrF2:Tm2+, where Tm2+ is at a cubic site and has one 4f hole in the 4f electronic shell. The 2F7/2 and 2F5/2 levels of free Tm2+ split in the cubic field into levels Γ7, Γ8, Γ6 and Γ 7 ’ , Γ 8 ’ . Using only one spin-orbit coupling parameter ζ4f for all 4f electrons in the crystal field, one can determine from the experimental data the values of ζ4f and two crystal field parameters B4 and B6 (the experimental position of the Γ6 level is unknown). Theoretical investigations were performed for the crystal field splittings ΔE12=Etl-Et2 and ΔE13= Etl-Eα2 (Eγ is the energy of the crystal field configuration with a hole in the γ shell). These are connected with B4 and B6 by simple relations. However, as the experimental value of ΔE12 is determined less accurately than ΔE13 (due to the use of a single value of the spin-orbit coupling constant instead of four values) only the results for the AE13 splitting will be presented.
KeywordsCrystal Field Crystal Field Parameter Crystal Field Splitting Energy Level Splitting Wave Funetions
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