Crystal field analysis of the energy level structure of Cs ₂NaAlF₆:Cr³⁺

An analysis of the energy level structure of Cr³⁺ ions in Cs₂NaAlF₆ crystal is performed using the exchange charge model (ECM) together with the crystal field analysis/microscopic spin Hamiltonian (CFA/MSH) computer package. Utilizing the crystal structure data, our approach enables modelling of the crystal field parameters (CFPs) and thus the energy level structure for Cr³⁺ ions at the two crystallographically inequivalent sites in Cs₂NaAlF₆. Using the ECM initial adjustment procedure, the CFPs are calculated in the crystallographic axis system centred at the Cr³⁺ ion at each site. Additionally the CFPs are also calculated using the superposition model (SPM). The ECM and SPM predicted CFP values match very well. Consideration of the symmetry aspects for the so-obtained CFP datasets reveals that the latter axis system matches the symmetry-adapted axis system related directly to the six Cr-F bonds well. Using the ECM predicted CFPs as an input for the CFA/MSH package, the complete energy level schemes are calculated for Cr³⁺ ions at the two sites. Comparison of the theoretical results with the experimental spectroscopic data yields satisfactory agreement. Our results confirm that the actual symmetry at both impurity sites I and II in the Cs₂NaAlF ₆:Cr³⁺ system is trigonal D_3d. The ECM predicted CFPs may be used as the initial (starting) parameters for simulations and fittings of the energy levels for Cr³⁺ ions in structurally similar hosts.