Recent ab intio studies of the magnetic properties of all 3d transition metal (TM) freestanding atomic chains have predicted that these nanowires could have a giant magnetic anisotropy energy (MAE) and might support a spin-spiral structure, thereby suggesting that these nanowires would have technological applications in, e.g. high-density magnetic data storage. In order to investigate how the substrates may affect the magnetic properties of the nanowires, here we systematically study V, Cr and Mn linear atomic chains on a Cu(0 0 1) surface based on the density functional theory with the generalized gradient approximation. We find that V, Cr and Mn linear chains on the Cu(0 0 1) surface still have a stable or metastable ferromagnetic state. However, the ferromagnetic state is unstable against the formation of a noncollinear spin-spiral structure in the Mn linear chains and also the V linear chain on the atop sites on the Cu(0 0 1) surface, due to the frustrated magnetic interactions in these systems. Nonetheless, the presence of the Cu(0 0 1) substrate does destabilize the spin-spiral state already present in the freestanding V linear chain and stabilizes the ferromagnetic state in the V linear chain on the hollow sites on Cu(0 0 1). When spin-orbit coupling (SOC) is included, the spin magnetic moments remain almost unchanged due to the weakness of SOC in 3d TM chains. Furthermore, both the orbital magnetic moments and MAEs for V, Cr and Mn are small, in comparison with both the corresponding freestanding nanowires and also the Fe, Co and Ni linear chains on the Cu(0 0 1) surface.
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