Can the low symmetry crystal (ligand) field parameters be considered compatible and reliable?

Abstract

This paper stems from our recent efforts to clarify the inconsistencies between the crystal-field parameter (CFP) data sets reported in the literature for various low symmetry transition ion–host systems. Prompted by the results of these studies, in this paper we consider the intricate properties of CF Hamiltonians, hitherto not fully understood. The term ‘low symmetry’ here includes the continuous rotational symmetry cases, i.e. hexagonal II, tetragonal II, trigonal II, monoclinic, and triclinic ones, as well as orthorhombic ones. The following fundamental intricate aspects are considered: (1) selection of the axis systems, (2) types of CFPs and their properties, (3) introduction of a new notion of a nominal axis system for the fitted CFP data sets, (4) implications of the Noether's theorem and the algebraic symmetry of CF Hamiltonians, (5) correlation properties among CFP data sets, (6) the rotational degrees of freedom and the reduction of the number of independent CFPs, which are of special importance for triclinic symmetry cases, and (7) extension of the multiple correlated fitting technique, including a quantitative method for CFP data sets comparison. Clarification of these intricate aspects enables us to provide a general framework aimed at achieving an increased compatibility and reliability of CFP data sets for transition ions at low symmetry sites in crystals. This framework may be especially useful for trivalent lanthanides in technologically important low symmetry hosts for which only limited energy-level data are available.