We have studied the magnetisation reversal in nickel cylinders and spheres of the size order 200nm. Around this size, in nickel the samples will not tend to form domain walls as the samples are physically too small -- the energy from dipolar interaction is not great enough to counteract the domain wall energy -- and neither will the shapes behave as single-domain states as the dipolar energy is then too great (Wachowiak et al., 2002).
Below a certain critical diameter, cylinders exhibit single-domain
behaviour. Above this critical diameter, the cylinders enter the
vortex state. In this regime, the vortex penetrates and moves to
adapt 
to 
after the field is reversed. In all cases, nickel
cylinders cannot maintain a single-domain reversal method once their
height is above a critical value; we find that the vortex reversal
method is present in all cylinders with a height greater than 60nm.
The results for the simulated cylinders are qualitatively in agreement
with work by Cowburn et al. (1999b), however these cannot be compared
directly because different materials have been investigated.
With the simulated spheres, vortex behaviour exists for a sufficiently large system, however the vortex penetrates at a greater applied field than that in a cylinder of comparable size. The vortex in spheres is also static with the core of the vortex pointing in the original direction of the applied field, as opposed to the vortex appearing in cylindrical samples, where the core of the vortex is able to move through the system to compensate for a change in applied field. In cylindrical samples, the core of the vortex is perpendicular to the direction of the applied field, i.e. it points out of the circular plane.
We have shown that for non-cuboidal structures, great care has be taken to ensure that the finite difference simulation technique does not introduce artefacts that do not reflect the behaviour of the physical system. In subsequent chapters we have used finite element simulations to corroborate finite difference simulation results, and varied the directions of applied field to ensure to exclude such artefacts from our observations.