Superposition model and crystal-field analysis of the ⁴A₂ and ₐ²E states of Cr³⁺ ions at C₃ sites in LiNbO₃

Y. M. CHANG, T. H. YEOM, Yau Yuen YEUNG, C. RUDOWICZ

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Abstract

The energy levels and wavefunctions including the two lowest-lying levels, namely ⁴A₂ and ₐ²E, for which reliable experimental data exist for Cr³⁺ ions at C₃ symmetry sites in LiNbO₃, are calculated using the complete matrix diagonalization method within the 3d³ configuration. The Hamiltonian considered includes the electrostatic term, the Trees correction, the spin-orbit interaction and the crystal-field interaction. The role of the additional low-symmetry crystal-field term B₄⁻³O₄⁻³ (in the Stevens operator notation), neglected in the C₃ᵥ approximation used so far in the literature, is studied. The superposition model is developed for 3d³ ions at C₃ symmetry sites and applied to study the site occupancy of Cr³⁺ in LiNbO₃. Analysis of the optical data indicates that Cr³⁺ ions substitute at Nb sites and Li sites simultaneously. The present considerations offer an improvement over the earlier approximations using C₃ᵥ symmetry only. The zero-field splitting predicted by the crystal-field calculations for Cr³⁺ at the Nb site matches the experimental value from EPR studies very well. This is contrary to the earlier prediction by the superposition model analysis of the spin-Hamiltonian parameters indicating that the zero-field splitting for Cr³⁺ ions at Li sites matches the experimental zero-field splitting better than that for Cr³⁺ at Nb sites. Since the present calculations involve fitting not only the zero-field splitting but also the energies of the ₐ²E state, the present predictions may be more reliable than the previous predictions. Copyright © 1993 IOP Publishing Ltd.
Original languageEnglish
Pages (from-to)6221-6230
JournalJournal of Physics: Condensed Matter
Volume5
DOIs
Publication statusPublished - 1993

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crystal field theory
symmetry
ions
predictions
spin-orbit interactions
approximation
matrix methods
coding
energy levels
substitutes
electrostatics
operators
configurations
interactions
energy

Citation

Chang, Y. M., Yeom, T. H., Yeung, Y. Y., & Rudowicz, C. (1993). Superposition model and crystal-field analysis of the ⁴A₂ and ₐ²E states of Cr³⁺ ions at C₃ sites in LiNbO₃. Journal of Physics: Condensed Matter, 5, 6221-6230. doi: 10.1088/0953-8984/5/34/009