The Analysis of EPR Spectra Using Tesseral Tensor Angular Momentum Operators

The advantages of using a tesseral rather than one of the conventional tensor angular momentum operator formulations for the zero field splitting terms in a phenomenological spin Hamiltonian are discussed in detail. The EPR spectral data for Gd3‡ impurity ions in the NH4Ln…SO4†2 4 H2O lattice where Ln = La, Ce, Pr, Nd, Sm, Eu are used to demonstrate these advantages. The tesseral zero field splitting parameters have been calculated from the conventional zero field splitting parameters reported in the literature. It is demonstrated that the values of these parameters are more consistent with C2h rather than D2h symmetry and may not be consistent with a C2 monoclinic symmetry crystalline electric field. It is also shown that there exist definitions of both the Hermitian adjoint and time reversal operations for these tensor angular momentum operators, which are independent of their representation. These definitions are consistent with the well known conclusion that only even rank zero field splitting terms can be used in the parameterization of the EPR spectra for systems with an odd number of electrons.