planes are all along C-\[110\] direction ($\theta = 90^{\circ}$ and $\phi = 0^{\circ}$), which is perpendicular to the chain and the surface. The magnetic anisotropy energies can be represented as $K_{0}+K_{1}sin^2(\theta)$ in S$_{1}$ plane and $K'_{0}+K'_{1}sin^2(\phi)$ in S$_{2}$ plane [@Autes1; @Brooks2]. The parameters $K_{0}$=0.158 (meV), $K_{1}$=-0.158 (meV) in S$_{1}$ and $K'_{0}$=0.0 (meV), $K'_{1}$=0.62 (meV) in S$_{2}$ are obtained by fitting the magnetic anisotropy curves using above two functions. The magnetic anisotropy isn’t good fit with $K_{0}+K_{1}sin^2(\theta)$ in S$_{1}$. The underlaying reasons are (1) there isn’t simple cubic symmetry in the region where the one-dimensional atomic chain absorbed; (2) the heterogeneously distributed the nearest nearby distances along the chain induced by the lattice misfit between the chain and the substrate. On the other hand, the value of $K_{1}$ is close to the lowest limit of allowed error in total energy about $\pm$0.1meV, thus more accurate calculations are required. Our results also show that $K_{1}$ (or $K'_{1}$) isn’t equal to the simple $\delta E_{1}=E^{C}-E^{A}$ (or $\delta E_{2}=E^{C}-E^{B}$).

Experimentally, the values of magnetic anisotropy energy are from 1 meV to 10 meV for magnetic clusters on metal surface and from 0.1 mV to 1.0 meV for magnetic film. Based on our calculations, the 