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Zeeman splitting factor of the Er3+ ion in a crystal field

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Abstract

Numerical computations are presented on the energy levels of the Er3+ ion in crystalline fields of cubic, trigonal, tetragonal and orthorhombic symmetry. Zeeman splitting factors were obtained from the level splitting in an additional magnetic field. For the quartet Γ8 states in cubic symmetry the Zeeman effect is described by an effective Hamiltonian ℋ= gμBBJ+ uμBBJ3 with the parametersg andu calculated for mixed fourth- and sixth-order potentials. For the eight doublets in the lower symmetry of an axial trigonal or tetragonal crystal field the principalg tensor components g∥ and g⊥ were calculated. The results of such calculations for a ground-state doublet can exactly account for the experimental data obtained on around 70 erbium centers in various crystalline hosts. However, sometimes different sets of parameters give comparably good results. An empirical rule of constant trace g∥ + 2g⊥ is supported by the calculations. In contrast to analytical treatments the effect of the crystalline field can be followed over a continuous range of the crystal field parameters. This allows one to establish relations on the relative signs of tensor components. It is found that the measured trace of tensors |g∥| + 2|g⊥| is not always equal to their real trace g∥ + 2g⊥. In an exploratory calculation a nonaxial center was simulated in an orthorhombic field, with calculation of the three principal values gx, gy and gz. A good agreement is obtained for the recently reportedg values of an erbium center in silicon.

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  1. Van der Waals-Zeeman Institute, University of Amsterdam, Amsterdam, The Netherlands

    C. A. J. Ammerlaan & I. de Maat-Gersdorf

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  1. C. A. J. Ammerlaan
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  2. I. de Maat-Gersdorf
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Ammerlaan, C.A.J., de Maat-Gersdorf, I. Zeeman splitting factor of the Er3+ ion in a crystal field. Appl. Magn. Reson. 21, 13–33 (2001). https://doi.org/10.1007/BF03162436

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