168 V.S.Stepanyuk and W.Hergert Table 8.3.Magnetic orbital moments and magnetic anisotropy energy of a single Co adatom on the Cu(100)surface:L2 and L are the orbital moments for mag- netization along the normal Z and in-plane X direction;the electronic part of the mangetic anisotropy energy AE(meV)is presented. Unrelaxed geometry Relaxed geometry L四 1.06 0.77 1.04 0.80 AE 1.70 -0.37 the MAE reveal that for the unrelaxed position above thethe surface,out-of plane magnetization for the Co adatom is more stable.The relaxation of the vertical position of the adatom by 14%shortens the first nearest neighbour Co-Cu separation from 2.56 to 2.39 A and has a drastic effect on MAE.We find that the relaxation of the Co adatom leads to in-plane magnetization. Ideal geometry Relaxed geometry 1.757 Y -1.708 1.757 1.699 -1.829 1,783 X Atom 兕 叹 △E(X,Z) 以 以 △EX,Z) 1 0.11 0.25 -1.48 0.09 0.18 -1.13 2 0.17 0.24 -1.35 0.13 0.19 -1.05 2* 0.17 0.27 -0.87 0.13 0.25 -1.26 3 0.21 0.43 -2.44 0.18 0.39 -2.60 Atom 吗 LXY △EX+Y,Z) 喝 L △E(X+Y,Z 1 0.11 0.25 -1.47 0.09 0.21 -1.06 2 0.17 0.25 -1.20 0.13 0.20 -1.15 3 0.21 0.40 -2.17 0.18 0.37 -2.38 3* 0.21 0.40 -2.30 0.18 0.35 -2.71 Fig.8.5.Magnetic properties of Cog cluster on the Cu(100)surface in unrelaxed and relaxed geometries;spin magnetic moments in Bohr magnetons are shown for each atom in the cluster;orbital magnetic moments and electronic part of the MAE are presented in the table for the normal 2,in-plane X and X+Y directions of the magnetization.For the unrelaxed cluster the the average MAE is-1.74 meV/Co atom for X-direction;for X+Y direction these values are-1.69 meV/Co atom. For the relaxed cluster,the above energies are-1.79 meV/Co atom for X direction and -1.76 meV/Co atom for X+Y direction.168 V.S. Stepanyuk and W. Hergert Table 8.3. Magnetic orbital moments and magnetic anisotropy energy of a single Co adatom on the Cu(100) surface:Lm Z and Lm X are the orbital moments for mag￾netization along the normal Z and in-plane X direction; the electronic part of the mangetic anisotropy energy ∆E (meV) is presented. Unrelaxed geometry Relaxed geometry Lm Z 1.06 0.77 Lm X 1.04 0.80 ∆E 1.70 -0.37 the MAE reveal that for the unrelaxed position above the the surface, out-of plane magnetization for the Co adatom is more stable. The relaxation of the vertical position of the adatom by 14% shortens the first nearest neighbour Co-Cu separation from 2.56 to 2.39 ˚A and has a drastic effect on MAE. We find that the relaxation of the Co adatom leads to in-plane magnetization. Fig. 8.5. Magnetic properties of Co9 cluster on the Cu(100) surface in unrelaxed and relaxed geometries; spin magnetic moments in Bohr magnetons are shown for each atom in the cluster; orbital magnetic moments and electronic part of the MAE are presented in the table for the normal Z, in-plane X and X +Y directions of the magnetization. For the unrelaxed cluster the the average MAE is −1.74 meV/Co atom for X-direction; for X + Y direction these values are −1.69 meV/Co atom. For the relaxed cluster, the above energies are −1.79 meV/Co atom for X direction and −1.76 meV/Co atom for X + Y direction