3 Layer-resolved magneto-crystalline anisotropy energy

The Budapest-Vienna Code allows us to obtain the layer resolved MCA energy values. This tool gives us the opportunity to analyze the spacial distribution of the magneto-crystalline anisotropy energy.

Figure 6.11: The layered resolved $\Delta E_{B}$ calculated for: semi-infinite Co, $Co\setminus Ag_{1}$ and $Co\setminus Ag_{2}$ systems with surface or interface (100) and (111) in the left and right graphs respectively. We have to note that for the system with Ag capping we have supposed a rigid relaxation of the lattice $r=10\%$. Here $n_{S}$ indicates the index of the atomic layer of the surface or the interface of the system and $n_{i}$ is the label of the atomic layer, in this way $n_{i}-n_{s}=0$ corresponds to the surface or the interface.

In Fig. 6.11 we present the layered resolved $\Delta E_{B}$ calculated for: semi-infinite Co, $Co\setminus Ag_{1}$ and $Co\setminus Ag_{2}$ systems with surface or interface (100) and (111) in the left and right graphs respectively.

In first place, we would like to point out that the layer resolved MCA energy shows an oscillating behavior due to the existence of the surface. The principal contribution to the crystalline anisotropy energy comes from the subsurface layer. We can also conclude that approximately $3-4$ layers have their local anisotropy different from that of the bulk. For example in the case of the $Co(111)$ surface the contribution to MCA energy of the surface layer is approximately two orders of magnitude larger that the MCA energy for a bulk Co (fcc).