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 ofparamagnetic species with the spin S ⩾ 1 at orthorhombicsymmetry sites require an axial zero-field splitting (ZFS)parameter and a rhombic one of the second order (k = 2), whereasat triclinic sites all five ZFS (k = 2) parameters are expressed inthe crystallographic axis system. For the spin S ⩾ 2 also thehigher-order ZFS terms must be considered. In the principalaxis system, instead of the five ZFS (k = 2) parameters, the twoprincipal ZFS values can be used, as for orthorhombic symmetry;however, then the orientation of the principal axes with respectto the crystallographic axis system must be provided. Recentlythree serious cases of incorrect relations between the extendedStevens ZFS parameters and the conventional ones have beenidentified in the literature. The first case concerns a controversyconcerning the second-order rhombic ZFS parameters and was foundto have lead to misinterpretation, in a review article, ofseveral values of either E or b22 published earlier.The second case concerns the set of five relations between theextended Stevens ZFS parameters bkq and theconventional ones Dij for triclinic symmetry, four of whichturn out to be incorrect. The third case concerns the omission ofthe scaling factors fk for the extended Stevens ZFS parameters bkq. In all cases the incorrect relations inquestion have been published in spite of the earlier existenceof the correct relations in the literature. The incorrectrelations are likely to lead to further misinterpretation of thepublished values of the ZFS parameters for orthorhombic andlower symmetry. The purpose of this paper is to make thespectroscopists working in the area of EMR (including EPR and ESR) and related spectroscopies aware of the problem and toreduce proliferation of the incorrect relations.