  We investigate the interplay between the structural reconstruction and the
magnetic properties of Fe doublelayers on Ir (111)-substrate using
first-principles calculations based on density functional theory and mapping of
the total energies on an atomistic spin model. We show that, if a second Fe
monolayer is deposited on Fe/Ir (111), the stacking may change from hexagonal
close-packed to bcc (110)-like accompanied by a reduction of symmetry from
trigonal to centered rectangular. Although the bcc-like surface has a lower
coordination, we find that this is the structural ground state. This
reconstruction has a major impact on the magnetic structure. We investigate in
detail the changes in the magnetic exchange interaction, the magnetocrystalline
anisotropy, and the Dzyaloshinskii Moriya interaction depending on the stacking
sequence of the Fe double-layer. Based on our findings, we suggest a new
technique to engineer Dzyaloshinskii Moriya interactions in multilayer systems
employing symmetry considerations. The resulting anisotropic
Dzyaloshinskii-Moriya interactions may stabilize higher-order skyrmions or
antiskyrmions.
