  The Dzyaloshinskii-Moriya interaction (DMI) is an antisymmetric exchange
interaction, which is responsible for the formation of topologically protected
spin textures in chiral magnets. Here, by measuring the dispersion relation of
the DM energy, we quantify the atomistic DMI in a model system, i.e., a Co
double layer on Ir(001). We unambiguously demonstrate the presence of a
chirality-inverted DMI, i.e., a sign change in the chirality index of DMI from
negative to positive, when comparing the interaction between nearest neighbors
to that between neighbors located at longer distances. The effect is in analogy
to the change in the character of the Heisenberg exchange interaction from,
e.g., ferromagnetic to antiferromagnetic. We show that the pattern of the
atomistic DMI in epitaxial magnetic structures can be very complex and provide
critical insights into the nature of DMI. We anticipate that the observed
effect is general and occurs in many magnetic nanostructures grown on
heavy-element metallic substrates.
