3.3.3 Micromagnetic simulations of Fast switching process

The final steps in our analysis is to verify whether the indication of the theory above are still reasonable when we take into account the weak interactions among the grains. To this end we have performed finite element [78] calculations (FEM) for weakly exchange and magnetostatically coupled granular media. The applied field is chosen within the range estimated with the uniform mode theory. Both perpendicular and tilted recording media with a weak exchange coupling between the grains ( $A_$inter$=3 \times 10^{-14}$ J/m) are investigated. The material parameters within the grains are: $J_s=\mu_0 M_s$ = 0.5 T, $A=10^{-11}$ J/m and $K_1=3.5 \times 10^{5}$ J/m$^3$. The thickness of the perpendicular media and the tilted media is $12$ nm and $8.5$ nm, respectively. The average grain diameter is 10 nm for both media. More than 45000 finite elements are used to provide an edge length smaller than the exchange length. A normal distribution of the easy axes directions with a maximum opening angle of 5$^\circ$ is assumed for both media. For the perpendicular media the average easy axis direction is parallel to the film normal. For the tilted media the angle between the average easy axis direction and the film normal is 45$^\circ$. Thus, for both samples the average easy axis direction points parallel to the edges between the grains. The external field is applied 45$^\circ$ off the film normal and parallel to the film normal for the perpendicular media and the tilted media, respectively. The field rise time is 10 ps. The FEM simulations for granular structures verify that switching is possible for fields smaller than the SW switching field and within the range predicted by the uniform mode theory. The switching time is defined as the time until the average magnetization component parallel to the easy axis crosses zero the last time. Figure 3.18 compares the switching time as a function of the external field strength, for the perpendicular media and the tilted media, significantly different due to the different demagnetizing field. The jumps that can be observed in Fig. (3.18) are due to ringing of the magnetization. For tilted media, the FEM simulations also show that a change of the opening angle of the easy axes distribution from 5$^\circ$to 1$^\circ$ changes the switching time by less than 0.1 %. Small switching field distributions lead to a high signal to noise ratio.