  The magnetic force theorem provides convenient ways to study exchange
interactions in magnetic systems. However, it is well known that short range
interactions in itinerant magnetic systems are poorly described with the
conventional use of the theorem and numerous strategies have been developed
over the years to overcome this deficiency. In this study, we discuss this
issue in the context of the frozen magnon method and find that a
self-consistent approach is in general preferable. Moreover, an extended
Heisenberg model is suggested in order to better describe finite deviations
from the magnetic ground state and is shown through cross-validation to give a
superior description of the interactions in non-collinear magnetic
configurations compared to the regular Heisenberg model. The present study thus
supplies a fully self-consistent method for systematic investigations of
exchange interactions beyond the standard Heisenberg model. This may prove
relevant to high-throughput computational materials science, e.g., in
developing high moment materials for the magnetic storage industry.
