  Atomistic spin models are of great value for predicting and understanding the
magnetic properties of real materials, and extensions of the existing models
open routes to new physics and potential applications. The
Dzyaloshinskii-Moriya interaction is the prototype for chiral magnetic
interactions, and several recent works have uncovered or proposed various types
of generalized chiral interactions. However, in some cases the proposed
interactions or their interpretation do not comply with basic principles such
as being independent of the magnetic configuration from which they are
evaluated, or even obeying time-reversal invariance. In this letter, we present
a simple explanation for the origin of these puzzling findings, and point out
how to resolve them.
