direction of magnetic moments relative to the surface, we must use the non-collinear DFT formulas. These results for single absorbed atom will be compared with the results of one-dimensional atomic chains. At first step, we calculate the magnetic moments of the absorbed 3d atoms on the Au(110)-(1$\times$2) and Au(111) surfaces including the spin-orbit coupling interactions and non-collinear calculations. From Fig. \[fig2\], we can see that the spin moments reach the maximum in the middle of the group. The large spin moment of the absorbed Mn atom is about 4.163$\mu_{_{B}}$ on the Au(110)-(1$\times$2) surface. We can see from the left panel of the figure that the spin moment of the absorbed Cr atom is the second largest when including the spin-orbit coupling interactions and non-collinear calculations. The change of magnetic moments per absorbed magnetic atom across the 3d row has been found in many other [*ab initio*]{} calculations such as 3d atoms on Au(001), Ag(001) [@Cabria1] and Cu(001) [@Stepanyuk1] surfaces. Our results are consistent very well with these results although the energy cutoffs of plane-waves are not too large in our calculations.

Both the electronic correlations and the crystal field have significant influence on the orbital moments of the absorbed 3d 