the other 3d atoms except for the absorbed Ti atom. This is due to the weaker crystal field above the surface than that in the trough. The absorbed Ti atom has almost the same height as the top row after the relaxations and its orbital moment slightly increases. Thus our results indicate that the surface relaxation decreases the orbital moments of the absorbed 3d atoms with the excess half-filled 3d states and increases the orbital moments of the absorbed atoms with less half-filled 3d states on Au(110)-(1$\times$2) surface.

The 3d density of states of the absorbed 3d atoms on the two surfaces are shown in Fig. \[fig4\]. The absorbed Ti, V, Co atoms on the Au(110)-(1$\times$2) surface and V, Co atoms on the Au(111) surface have large 3d densities of states at the Fermi energies and large orbital moments too. We get the same arguments on the magnetism of Ni$_{n}$ (n=1-5) chains. Large density of state $N(E_{f})$ at Fermi energy is advantaged to the formation of the orbital moments. The single Ni atom has small magnetic moment, however we can see in section \[Ni\_Chain\] the Ni clusters such as one-dimensional Ni chains have significant magnetic moments on the Au surface. 