  Using first-principles calculations, we study the occurrence of non-collinear
magnetic order in monatomic Mn chains. First, we focus on freestanding Mn
chains and demonstrate that they exhibit a pronounced non-collinear ground
state in a large range of interatomic distances between atoms in the chain. By
artificially varying the atomic number of Mn we investigate how the magnetic
ground state is influenced by alloying the Mn chains with Fe and Cr. With
increasing number of 3d-electrons we find a smooth transition in the magnetic
phase space starting from an antiferromagnetic state for pure Cr chains through
a regime of non-collinear ground states for Mn-rich chains to a ferromagnetic
solution approaching the limit of pure Fe chains. Second, we investigate the
magnetism in supported Mn chains on the (110)-surfaces of Cu, Pd, and Ag. We
show that even a weak chain-surface hybridization is sufficient to dramatically
change the magnetic coupling in the chain. Nevertheless, while we observe that
Mn chains are antiferromagnetic on Pd(110), a weak non-collinear magnetic order
survives for Mn chains on Cu(110) and Ag(110) a few meV in energy below the
antiferromagnetic solution. We explain the sensitive dependence of the exchange
interaction in Mn chains on the interatomic distance, chemical composition, and
their environment based on the competition between the ferromagnetic double
exchange and the antiferromagnetic kinetic exchange mechanism. Finally, we
perform simulations which predict that the non-collinear magnetic order of Mn
chains on Cu(110) and Ag(110) could be experimentally verified by
spin-polarized scanning tunneling microscopy.
