On the relations between the zero-field splitting parameters in the extended Stevens operator notation and the conventional ones used in EMR for orthorhombic and lower symmetry

Abstract

Electron magnetic resonance (EMR) studies of paramagnetic species with the spin S ≥ 1 at orthorhombic symmetry sites require an axial zero-field splitting (ZFS) parameter and a rhombic one of the second order (k = 2), whereas at triclinic sites all five ZFS (k = 2) parameters are expressed in the crystallographic axis system. For the spin S ≥ 2 also the higher-order ZFS terms must be considered. In the principal axis system, instead of the five ZFS (k = 2) parameters, the two principal ZFS values can be used, as for orthorhombic symmetry; however, then the orientation of the principal axes with respect to the crystallographic axis system must be provided. Recently three serious cases of incorrect relations between the extended Stevens ZFS parameters and the conventional ones have been identified in the literature. The first case concerns a controversy concerning the second-order rhombic ZFS parameters and was found to have lead to misinterpretation, in a review article, of several values of either E or b₂² published earlier. The second case concerns the set of five relations between the extended Stevens ZFS parameters b_k^q and the conventional ones D_ij for triclinic symmetry, four of which turn out to be incorrect. The third case concerns the omission of the scaling factors f_k for the extended Stevens ZFS parameters b_k^q. In all cases the incorrect relations in question have been published in spite of the earlier existence of the correct relations in the literature. The incorrect relations are likely to lead to further misinterpretation of the published values of the ZFS parameters for orthorhombic and lower symmetry. The purpose of this paper is to make the spectroscopists working in the area of EMR (including EPR and ESR) and related spectroscopies aware of the problem and to reduce proliferation of the incorrect relations.