interaction but without orbital polarization interaction. We have calculated the magnetic anisotropy energies of the supported Ni chains and found an off-plane easy magnetization axis perpendicular to the chains and the surface. On the contrary, the easy magnetization axes of the free-standing Ni chains are parallel to these chains. The change of the easy magnetization axes of the surface-supported chains are also found in the others systems [@Dovila1]. Our results also indicate the closed relationship between the magnetic anisotropy and the orbital magnetism.

The paper is arranged as follow. In the next section, we introduce the theoretical methods used in this paper. The third section will present the results for single 3d transition metal atoms absorbed on Au(110)-(1$\times$2) and Au(111) surface. The magnetism of a single magnetic atom on a surface is important to understand the magnetism of materials with more complex structures such as the one-dimensional nano-structure. The reduced dimensionality and coordination number for surface still enhance the magnetism of single absorbed atoms [@Gross1; @Gross2; @Hanf1; @Riegel1; @Ortega1]. The results of short one-dimensional mono-atomic Ni chains are included in the forth section. Our studies focus on the magnetic anisotropy of Ni mono-atomic chains. Finally, we conclude our results.

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