Reversal mechanism

A strong magnetic field applied across a nickel sphere of diameter 200nm gives a homogeneous magnetisation. As this field is reduced the magnetisation at the surface of the sphere diverges as a consequence of the dipolar interactions (figure 3.12 corresponding to point $a$ in figure 3.11; also shown in figure 3.13); this behaviour is similar to that in small cylinders.

Figure 3.12: Nickel sphere in high applied field showing spin tapering owing to demagnetising energy; the left image shows a cut-plane through $x$ and $y$, the right image shows a cut-plane through $x$ and $z$. This corresponds to point $a$ in figure 3.11

As the field is reduced, the sphere falls into the vortex state a little above 100mT (see figure 3.14, corresponding to point $b$ in figure 3.11), but, contrary to the cylinder, this vortex forms around the axis of the applied field. The majority of the magnetisation at this stage is pointing in the direction of the applied field rather than against it, as the core of the vortex is aligned with the direction of the initial magnetisation. The magnetisation around the core of the vortex is able to maintain its circular vortex pattern and adjust its alignment with the present applied field.

At zero field, the magnetisation in the vortex core remains pointing in the direction of the applied field (figure 3.15, corresponding to point $c$ in figure 3.11), however if the field is increased in the $-x$ direction then the magnetisation in the core is reversed (figure 3.16, point $d$ in figure 3.11).

Further increasing the field eventually results in the vortex dissipating at around 180mT. This results in the magnetisation of the sample pointing entirely in the direction of the applied field as in figure 3.13, only in the opposite direction.

Figure 3.13: Sphere at high applied field (point $a$ in figure 3.11); see also figure 3.12.

Figure 3.14: Sphere immediately after entering the vortex state (point $b$ in figure 3.11).

Figure 3.15: Sphere in vortex state (point $c$ in figure 3.11).

Figure 3.16: Sphere in vortex state at a further reduced field (point $d$ in figure 3.11).