Numerical micromagnetic modeling is a vital tool to predict and understand the various magnetic configurations, which are strongly dependent on the material parameters but more importantly on the shape of the nanostructures. These calculations will then have to be compared to the results obtained from direct imaging. For this purpose we have developed a 3D micromagnetic code which has been used to obtain a magnetization vector plots. The confidence of this code has been checked by treating several benchmark problems such as the magnetization configuration in small cubic particles (Problem 3) as well as the reversal dynamics of a thin permalloy platelet (problem 4).

The magnetization configurations are obtained by minimizing the total free energy of the system, which includes contributions from the magnetocrystalline anisotropy, the demagnetization, the exchange and the Zeeman energy. The minimization is carried out with respect to

under the constraint

Starting from a given configuration, the system proceeds towards a local minimum by following the states according to the Landau-Lifshitz-Gilbert equation (LLG). The real system is discretized into cubic cells of constant magnetization. The cell size is chosen to be smaller than the characteristic magnetic lengths. The magnetostatic energy is evaluated in the approximation of uniformmagnetized cubic cells and the demagnetization field is substituted by its value averaged over the cell. The fast Fourier method is implemented for the stray field evaluation. The numerical stability of the time integration of the LLG equation is assured by the use of an implicit forward difference method for the time discretization. A constant time step of dt = 0.1 ps has been used and the damping parameter was set to alpha = 1.0 since we are only interested in the static stable state.