4 Magneto-crystalline anisotropy energy as a function of the lattice relaxation.

At this point we would like to address the question on how the MCA energy is affected by the relaxation of the lattice. For this purpose, we have calculated the MCA energy of $Co\setminus Ag$ system at the interfaces (100) and (111) as a function of the rigid relaxation of the lattice. The results are plotted in Fig. 6.12.

The relaxation of the lattice is ranged from $0\%$ to $12\%$. We observe that in all cases the MCA energy at the interface $Co\setminus Ag$ (111) is almost an order of magnitude higher than in the case of (100) interface.

Figure 6.12: The MCA energy, $\Delta E_{B}$, calculated for a $Co(100)\setminus Ag_{1}$ and $Co(111)\setminus Ag_{1}$ as a function of the rigid relaxation parameter $r$.

The value of the MCA energy is affected by the relaxation of the lattice. For all studied cases, for the $(100)$ interface the MCA suffers an increment when the relaxation of the system is increased. In the systems with $(111)$ interface the behavior is slightly different. Initially when the relaxation is changed from $6\%$ to $11\%$, the MCA is increased, starting from this point if the relaxation increases, the MCA energy manifests a slight decrease.