Discussion

Although hysteretically this exhibits a qualitative similarity with the sphere (figure 3.11) insofar as their possession of two minor loops, the magnetic microstructure is more reminiscent of the flat cylinder in that the vortex nucleates out of the plane and moves through the geometry in the same fashion as the flat cylinder (figures 3.3 to 3.8), however the vortex appears prior to the applied field being reduced below zero.

Figure 5.7 illustrates that at zero field the direction of the vortex core is perpendicular to and in the centre of the $xy$ plane; see point $b$ in figure 5.5. For isolated half-spheres we always find the magnetisation in the core of the vortex to point ``down'' (i.e. towards the spherical surface). We attribute this to the asymmetry of the half-sphere in the $z$ direction.

Figure 5.5: Hysteresis loop for a nickel half-sphere of diameter 200nm

Figure: Half-sphere at high applied field (point $a$ in figure 5.5)

Figure 5.7: Half-sphere in vortex state in zero applied field (point $b$ in figure 5.5). Axes are the same as those in figure 5.6

Figure 5.8: Half-sphere in late vortex state (point $c$ in figure 5.5). Axes are the same as those in figure 5.6