Crystal field analysis of the energy level structure of Cs₂NaAlF₆:Cr³⁺

Abstract

An analysis of the energy level structure of Cr 3+ ions in Cs 2 NaAlF 6 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 Cr 3+ ions at the two crystallographically inequivalent sites in Cs 2 NaAlF 6 . Using the ECM initial adjustment procedure, the CFPs are calculated in the crystallographic axis system centred at the Cr 3+ 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 soobtained CFP datasets reveals that the latter axis system matches the symmetryadapted 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 Cr 3+ 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 Cs 2 NaAlF 6 :Cr 3+ 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 Cr 3+ ions in structurally similar hosts.

Semi-ab initio calculations of superposition model and crystal field parameters for Co2+ ions using the exchange charge model

“…Previously, the ECM has been successfully applied for calculations of the energy levels of both rare earth 8,[28][29][30][31][32] and transition metal ions [33][34][35][36] in different hosts, and in analysis of the electron-phonon coupling. [37][38][39][40] 3.…”

Comparative Study between Energy Levels of Cr3+and Co2+Ions Doped in MgF2Crystal

“…In order to analyse the crystal field of Cr 3+ doped in MgF 2 crystal we follow papers [8,9]. In the framework of the ECM of crystal field the energy levels of an impurity ion are considered as the eigenvalues of the following Hamiltonian:…”

A Unified Calculation of the Optical and EPR Spectral Data for the Trigonal Cr3+Center in Cr3+-Doped α-RbAl(SO4)2·12H2O Alum Crystal

“…The effectiveness of this model in predicting CF parameters gains the support of angular overlap model [21] and the exchange charge model [33,34]. For d n ions in trigonal (approximately D 3d ) octahedral cluster, the SPM expressions of B kl are [19,20]: …”

“…Since the ratioĀ 2 (R)/Ā 4 (R) ≈ 8−12 was found for 3d n ions in many crystals by studying the optical and EPR spectra [20,23,[33][34][35][36][37][38][39], we take the valueĀ 2 (R)/Ā 4 (R) ≈ 10 here. The parameterĀ 4 (R) and angle β are also treated as adjustable parameters.…”