Higher-order Zeeman and spin terms in the electron paramagnetic resonance spinHamiltonian; their description in irreducible form using Cartesian, tesseral spherical tensorand Stevens’ operator expressions

Abstract

In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spinnuclear and/or electronic interactions in electron paramagnetic resonance (EPR)experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseralcombinations of spherical tensor operators is necessary. Then, the SH contains only thoseterms that are necessary and sufficient to describe the particular spin system.The paper proceeds then to obtain interrelationships between the parametersof the MRSH and those of alternative SHs expressed in Cartesian tensor andStevens operator-equivalent forms. The examples taken, initially, are those ofCartesian and Stevens’ expressions for high-spin Zeeman terms of dimensionBS3 andBS5. Starting from the well-known decomposition of the general Cartesian tensor of secondrank to three irreducible tensors of ranks 0, 1 and 2, the decomposition of Cartesian tensorsof ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseralspherical tensor equations, the interrelationships amongst the parameters of the three kindsof expressions, as derived from equivalent SHs, are determined and detailed tables,including all redundancy equations, set out. In each of these cases the lowest symmetry, Laue class, is assumed and then examples of relationships for specific higher symmetriesderived therefrom. The validity of a spin Hamiltonian containing mixtures ofterms from the three expressions is considered in some detail for several specificsymmetries, including again the lowest symmetry. Finally, we address the application ofsome of the relationships derived here to seldom-observed low-symmetry effects inEPR spectra, when high-spin electronic and nuclear interactions are present.