9.3.1 Magnetization Distribution

In order to speed up the calculation of equilibrium magnetization distributions of magnetic vortices the rigid vortex model has been implemented in the FE code and it has been used to initialize the magnetization distribution with the vortex at the beginning of the simulation. The plots of $M_z$ in Fig. 9.8 show a comparison of the rigid vortex model with the finite element approximation (due to the finite resolution of the mesh, there is a small difference in the core diameter) and the equilibrium magnetization distribution, which has been found by integrating the Landau-Lifshitz equation of motion with the damping constant $\alpha =1$ until equilibrium has been reached.

Figure 9.8: Profiles of $M_z$ along the $x$-axis through the center of the nanodot for the analytical model, its finite element approximation, and the relaxed magnetization in equilibrium.

The results show, that the vortex core is approximately 54 % larger (18.5 nm) than assumed by the rigid vortex model (12 nm) due to a ``broadening'' of the $M_z$ distribution (if the core radius is defined by $M_z = 0$). Furthermore it is interesting to note that the finite element simulation shows that there is a region with $M_z > 0$ outside the core. Thus, we find positive surface charges in the core of the vortex, which are surrounded by negative surface charges. Only outside of approximately half the radius (50 nm) almost all surface charges disappear. It has been verified, that there is very little variation of the magnetization distribution across the thickness of the nanodot.