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.
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