Alternative zero-field splitting (ZFS) parameter sets and standardization for Mn ions in various hosts exhibiting orthorhombic site symmetry

The intrinsic properties of orthorhombic Hamiltonians, e.g. zero-field splitting (ZFS) ones or crystal-field (CF) ones, embodied in the standardization idea may be utilized to improve reliability and comparability of experimentally determined ZFS (or CF) parameters. These properties have enabled derivation of transformation relations for Hamiltonian parameters expressed in several related axis systems defined earlier by one of us. In this paper the standardization transformations are used to generate alternative physically equivalent yet numerically distinct parameter sets for Mn²⁺ ions in various hosts exhibiting orthorhombic or lower site symmetry. One parameter set out of six alternative sets satisfies the standardization criteria. Importantly, the standardized sets should be used for direct comparisons. Several non-standard ZFS parameter (ZFSP) sets for Mn²⁺ ions in crystals, identified in our literature survey of EMR studies, are here standardized. Thus the ratio of λ=E/D or λ′=B₂²/B₂⁰ is limited to the standard range (0, ±1/3) or (0, ±1), respectively. Our considerations provide useful correlations between the distinct and non-compatible yet physically equivalent ZFS parameter sets reported in literature. All calculated alternative sets are tabularized for ten Mn²⁺ complexes considered. These ZFSP sets may serve for application of the multiple correlated fitting techniques in follow-up EMR studies. Some misinterpretations yielding ambiguous and unreliable results are clarified. The intricate low symmetry aspects are also discussed, whenever applicable. The results of this paper enable more reliable analysis, comparison, and fitting of ZFSP sets from EMR spectra for Mn²⁺ ions in various crystals.