Manual Calculations of Spin Hamiltonian Parameters

The apparatus developed above is rigorous with respect to the calculation of the ZFS but suffers from transparency. On its output we get the numbers, but it might be difficult to control and tune them. It would be helpful to have a set of formulae as simple as possible that, even with a limited applicability, could provide a better understanding of the crucial factors that determine the ZFS and other MPs. Considerable work has been done so far in this respect however, no comprehensive review of this approach exists. 

Angular Momentum Among Crystal-Field Terms 

The transformation of the angular momentum operator from the basis set of the AT kets to the CF kets can be done using the symmetry-adapted coefficients = LMl LPya) in the equation 

The CFTs can be hand-evaluated if one knows the symmetry adaptation coefficients s[ aL = LMi ILPya) that transform the basis set of AT functions. In some cases these appear in tabulated form (Table 7). 

Since the matrix elements of the angular momentum operator have already been determined in a simple form, and the symmetry adaptation coefficients are also known, we can proceed in the transformation to the basis set of CFTs. This work is presented in Table 8. 

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