Results

The calculated hysteresis loop for a two-dimensional permalloy hexagonal antidot sample is shown in figure 6.7, showing a relatively large coercive field of around 25mT. The dot spacing in this sample is 100nm between centres, with the dot diameter being 40% of the dot spacing.

Figure 6.12: Coercivity of a 6x6 permalloy hexagonal antidot array with applied fields 10, 15, and 30 degrees from the $x$ direction ($d$ = 100nm).

Figure 6.12 shows the effect the radius ratio $r/R$ of the hole to spacing has on the coercivity of the sample. Simulations were performed on permalloy antidots $d$ = 100nm with applied fields offset by 10, 15 and 30 degrees from the $x$ direction. When $r/R$ is below 0.1, the antidots have little effect on the overall coercive field of the sample in all three cases. However, when $r/R$ increases above 0.1, the coercivity doubles sharply for offsets of 10 and 15 degrees; the 30 degree coercivity measurement also increases, but more gradually.

A more drastic change in behaviour is observed when $r/R$ increases to 0.8 and above; the coercivity rapidly increases as a result of the reduction in material between the antidots; this makes it more difficult for the system to reverse the magnetisation between these thin `walls' of material. In the most extreme case, the coercivity of the 30 degree sample when $r/R$ is 0.9 is approximately ten times greater than that when $r/R$ is 0.1 and below.

Any simulation performed in the situation where $r/R$ is 1.0 is likely to be inaccurate as the finite resolution of the simulation will not allow the extremely fine walls around the point where the antidots touch to be precisely resolved.

Figure 6.13 shows a coercive field graph of a 30$^{o}$ offset permalloy antidot system, similar to that shown in figure 6.12 only with $d$ = 200nm. In this larger system, the jump in the system at $r/R=0.1$ is less pronounced and the coercivity increases in a less abrupt fashion.

Figure 6.13: Coercivity of a larger 6x6 permalloy hexagonal antidot array with the applied field offset 30 degrees from the $x$ axis ($d$ = 200nm).

Figure 6.14 shows the results of the Monte Carlo simulation using values of $B_{c_{(r)}}$ from the $d$ = 200nm permalloy dataset demonstrated in figure 6.13, comparable to the experimental results shown in figure 6.3.

Figure 6.14: Monte Carlo simulation results with $B_{c_{(r/R)}}$ values from figure 6.13

Figure 6.15 shows on the left an experimental magnetic force microscope image of a cobalt antidot film ($d=700$nm, $h=100$nm) in zero applied field. The holes at the surface of the antidot film are indicated by the blue circles. The image on the right-hand side shows the remanent magnetisation pattern from the two-dimensional micromagnetic modelling case when $r/R=0.5$. In both cases the applied field was 30 degrees from the indicated $x$ axis.

The numerical results show that the magnetisation follows around the holes, forming a consistent periodic microstructure. The magnetisation between neighbours in $\ensuremath{\mathbf{a}}_1$ (see equation 6.1) is 90 degrees from $x$ (60 degrees from the applied field), but between neighbours in $\ensuremath{\mathbf{a}}_2$ the magnetisation is 60 degrees from $x$ (30 degrees from the applied field). The magnetisation between neighbours in
$(-\ensuremath{\mathbf{a}}_{2(x)}, \ensuremath{\mathbf{a}}_{2(y)})$ is 30 degrees from $x$ (aligned with the applied field).

Figure 6.15: Experimental and numerical images for a cobalt antidot film (left) MFM image of film prepared with spheres of diameter 700nm with thickness 100nm; blue circles indicate the position of the holes in the film and (right) magnetisation direction from numerical modelling with $r/R=0.5$; the colour scale represents the magnetisation angle in the $xy$ plane in radians