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

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.