Low symmetry aspects inherent in electron magnetic resonance (EMR) data for transition ions at triclinic and monoclinic symmetry sites: EMR of Fe3+ and Gd3+ in monoclinic zirconia revisited

Our recent survey of the EMR literature has revealed a number of experimental zero-field splitting (ZFS) parameter datasets for transition ions at triclinic symmetry sites in various compounds, which include for a given rank (k=2, 4, 6) all components −k⩽q⩽+k. Model calculations of ZFS parameters, which usually employ the crystallographic axis system centered at the transition ion, may also yield triclinic-like ZFS parameter datasets. Closer analysis is required in order to distinguish the actual low symmetry aspects from the apparent ones. A comprehensive approach is proposed to analyze the low symmetry aspects involved in the monoclinic- or triclinic-like spin Hamiltonian (SH) terms, especially the ZFS ones. The approach comprises three methods: (i) finding the principal values of the various 2nd-rank SH terms and the orientation of the respective principal axis systems w.r.t. the laboratory or crystallographic axis system, (ii) extending the cubic/axial pseudosymmetry axes method (PAM) to lower symmetry cases and finding the pseudosymmetry axis system for the 4th-rank ZFS parameters, and (iii) employing the closeness factors C and the norms ratios R=NA/NB for quantitative comparison of several ZFS parameter datasets. Each method is facilitated by recently developed computer programs. Application of this approach, with focus on the PAM, for the ZFS parameter datasets for Fe3+ and Gd3+ in monoclinic zirconia (m-ZrO2) is presented. Our considerations enable better understanding of the low symmetry aspects as well as correlation of the principal axis systems and/or pseudosymmetry axis systems with the symmetry-adapted axis systems, which may be approximately related to the respective metal ion-ligands bonds. The equivalence between various physically equivalent ZFS parameter datasets generated by the first and second method, especially those transformed to the standard range by proper rotations of the axis systems, is also studied. This equivalence may be utilized in the multiple correlated fitting technique to improve the reliability of the fitted results. The final standardized ZFS parameters are best to be used as the starting parameters for simulations and fittings of the EMR spectra for transition ions in structurally similar hosts. Importantly, the three methods proposed here may be also applied to the crystal field parameters studied by optical spectroscopy.