  Chirality is an inherent characteristics of some objects in nature. In
magnetism chiral magnetic textures can be formed in systems with broken
inversion symmetry and due to an antisymmetric magnetic interaction, known as
Dzyaloshinskii--Moriya interaction (DMI). Here, aiming on a fundamental
understanding of this chiral interaction on the atomic scale, we design several
synthetic layered structures composed of alternating atomic layers of 3d
ferromagnetic metals epitaxially grown on Ir(001). We demonstrate both
experimentally and theoretically that the atomistic DMI depends critically not
only on the orbital occupancy of the interface magnetic layer but also on the
sequence of the atomic layers. The effect is attributed to the complexity of
the electronic structure and the contribution of different orbitals to the
hybridization and DMI. We anticipate that our results provide guidelines for
controlling both the chirality and the magnitude of the atomistic DMI.
