  Recent ab intio studies of the magnetic properties of all 3d transition
metal(TM) freestanding atomic chains 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
applicationsin, e.g., high density magnetic data storages. In order to
investigate how the substrates may affect the magnetic properties of the
nanowires, here we systematically study the V, Cr and Mn linear atomic chains
on the Cu(001) surface based on the density functional theory with the
generalized gradient approximation. We find that V, Cr, and Mn linear chains on
the Cu(001) surface still have a stable or metastable ferromagnetic state.
However, the ferromagnetic state is unstable against 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(001) surface, due to the frustrated
magnetic interactions in these systems. Nonetheless, the presence of the
Cu(001) 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(001). 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 the 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 (001) surface.
