  The spectrum of magnon excitations in magnetic materials can be obtained
exactly from the transverse dynamic magnetic susceptibility, which is however
in practice numerically expensive. Many ab initio approaches therefore consider
instead the adiabatic magnon spectrum, which assumes a separation of time
scales of magnons and electronic excitations. There exist two alternative
implementations for adiabatic magnon spectra: one based on the magnetic force
theorem (MFT) and the other with a constraining field that enforces static
non-collinear spin configurations. We benchmark both implementations against
the exact magnon spectrum of an exactly solvable mean-field model. While both
adiabatic methods are equally valid in the low magnon energy and strong Stoner
coupling limits, we find that the constraining field method performs better
than the MFT in both the cases of strong Stoner coupling and high magnon
energies,while the MFT performs better for combined weak coupling and low
magnon energies.
