The maximal axial parameters in equivalent parametrizations of high symmetry crystal‐field Hamiltonians

The variation ranges of the axial B k 0 crystal‐field parameters (in Wybourne parametrization), for k = 2, 4, 6, of tetragonal (including cubic) and hexagonal crystal‐field Hamiltonians ℋ CF for all possible orientations of the relevant reference frame are studied. The distinguished z ‐axis directions fixed by the maximal absolute values of B k 0 are analyzed. The diagrams for any tetragonal and hexagonal ℋ CF parametrization depicting the maximal values of | B k 0 |/ M k , where M k is the 2 k ‐pole modulus, as a function of the x = B k 4 / B k 0 or B 66 / B 60 ratios, together with the distinguished directions are presented. The| B k 0 |/ M k magnitudes and the relevant distinguished directions are the discriminants of all the equivalent parametrizations. They vary within the intervals (0.7395,1], (0.6074,1] and (0.6717,1] for tetragonal k = 4, tetragonal k = 6 and hexagonal k = 6ℋ CF components, respectively. Such specified directions determine the mutual spatial orientation of the component 2 k ‐poles of the ℋ CF , and due to their rigid coupling in the ℋ CF , they also refer to the global ℋ CF parametrization. This approach demonstrates the difference in fitting capability between the real and complex isomodular ℋ CF parametrizations. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)