  It is found that all the zigzag chains except the nonmagnetic (NM) Ni and
antiferromagnetic (AF) Fe chains which form a twisted two-legger ladder, look
like a corner-sharing triangle ribbon, and have a lower total energy than the
corresponding linear chains. All the 3d transition metals in both linear and
zigzag structures have a stable or metastable ferromagnetic (FM) state. The
electronic spin-polarization at the Fermi level in the FM Sc, V, Mn, Fe, Co and
Ni linear chains is close to 90% or above. In the zigzag structure, the AF
state is more stable than the FM state only in the Cr chain. It is found that
the shape anisotropy energy may be comparable to the electronic one and always
prefers the axial magnetization in both the linear and zigzag structures. In
the zigzag chains, there is also a pronounced shape anisotropy in the plane
perpendicular to the chain axis. Remarkably, the axial magnetic anisotropy in
the FM Ni linear chain is gigantic, being ~12 meV/atom. Interestingly, there is
a spin-reorientation transition in the FM Fe and Co linear chains when the
chains are compressed or elongated. Large orbital magnetic moment is found in
the FM Fe, Co and Ni linear chains.
