In addition to the common zero-field splitting parameters D and E,
the most common set of high-order operators used in spin Hamiltonians
for high-spin systems are the so-called extended Stevens operators
for
.
The associated coefficients
are always real.
In Easyspin, matrix representations of the extended Stevens operators are provided by the function stev and are used by the simulation functions eigfields, resfields and pepper.
The common zero-field splitting parameters D, E and
the conventional high-spin operator parameters F and a
are related to the coefficients.
The terms in the Hamiltonian containing a and F have the forms
The following table lists the most common Stevens operators in terms of polynomials in S+, S- and Sz. A more general list of extended Stevens operators (including odd k) can be found in Al'tshuler/Kozyrev. Abragram/Bleaney contains only a partial, but compatible list. Ryabov has devised a formula for computing Stevens operator polynomials for arbitrary 0<=k and -k<=q<=k.
Here are the most important references for the operators
Note that there are misprints in both Al'tshuler/Kozyrev and Abragam/Bleaney, as discussed by Rudowicz (2004).