Magnetization curves of small isotropic spheres

Magnetization curves of small isotropic spheres have been calculated numerically, and compared with previous Ritz method calculations. Apart from imposing cylindrical symmetry (curling mode), no prior assumptions have been made about the magnetization distribution. The energy was calculated by subdividing the sphere into quasi‐toroids within which the magnetization is independent of r and θ, a method that has already been used for the exchange energy. The calculation of the magnetostatic energy was based on another recently developed theory. Figure 1 shows 〈mz〉 plotted against h=3H/2Ms The arrows indicate the theoretical nucleation fields for the four largest radii, and the line shows the results from the Ritz model for 20‐nm radius. Magnetization reversal is seen to nucleate more gradually than in the Ritz model. The contribution of the surface charges to the magnetostatic energy was also calculated, and found to be similar to, and in some cases slightly higher than the total magnetostatic energy, showing that the contribution of volume charges is relatively small. This may enable first approximations to magnetization configurations to be obtained more rapidly.