  Based on Density Functional Theory with no-collinear-magnetism formulations,
we have calculated magnetic anisotropy of supported Ni chains. Our results
indicate that the magnetic anisotropy is closely related to orbital quenching.
The easiest magnetized axis changes from parallel to perpendicular to the Ni
chains once they absorb on the surface. Our results for single absorbed 3d
transition metal atom show that the surface relaxation enhances the orbital
moments of left-end elements (Ti,V) and quenches the orbital moments of
right-end elements (Fe,Co,Ni) on the Au(110)-(1$\times$2) surface. This is
because Ti and V atom raise their position above the trough and Fe, Co, Ni atom
trap more deeply in the trough after the surface relaxation.
