High-order operators

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 [eqn] for [eqn]. The associated coefficients [eqn] 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.

[eqn]

The common zero-field splitting parameters D, E and the conventional high-spin operator parameters F and a are related to the [eqn] coefficients.

[eqn]

The terms in the Hamiltonian containing a and F have the forms

[eqn]
[eqn]
(see e.g. Abragam/Bleaney, p.437).
Extended Stevens operators

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.

[eqn]
References

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).