Interpretation of multiple solutions and selection of the final crystal field parameter sets for orthorhombic and lower symmetry—Case study: Er 3+ ions at orthorhombic sites in ErNiAl 4

Abstract

Existence of multiple solutions for the crystal field (CF) parameter (CFP) sets obtainable from fitting or matching procedures for orthorhombic (as well as monoclinic and triclinic) site symmetry has recently been gaining wider recognition. However, the peculiarities encountered in interpretation of multiple solutions and subsequent selection of the final CFP sets appears not to be properly understood in many cases. In this paper pertinent explanations for the peculiarities in question are provided. As a case study, we carry out analysis of the CFP sets for Er 3+ ions at orthorhombic sites in ErNiAl 4 obtained using theoretical calculations as well as Mössbauer spectroscopy and inelastic neutron scattering data. It turns out that the original and revised CFP sets reported for Er 3+ in ErNiAl 4 require reconsideration in view of these explanations. Clarifications concerning the matching procedure used as well as interpretation of the CFP sets and the assigned axis systems are provided. It appears that the specific constraints involved in matching have generated some incorrect CFP solutions. The crux of the problem is in the intrinsic features of CFP sets for orthorhombic symmetry, which previously were not fully utilized. Consideration of these features enables proper interpretation of multiple solutions as well as discrimination between the physically valid alternative CFP sets, which must be internally correlated, and the additional incorrect solutions generated by inappropriate matching or fitting procedures. Five alternative and correlated CFP sets are calculated for each set obtained for Er 3+ in ErNiAl 4. These considerations provide guidance for reinterpretation of CFP sets reported in literature and may facilitate subsequent fittings. This would enable experimental identification of the alternative CFP sets.