Reversal mechanism

Figure 5.17: The hysteresis loop for the 140nm droplet with inset $x$-$y$ cut-planes showing vortex propagation

Figure 5.18: Hysteresis loops for droplets of bounding sphere diameter 140nm, 350nm and 500nm; note that the loops are offset in the $y$ direction for clarity. Inset is the hysteresis loop for a droplet of bounding sphere diameter 50nm.

Figure 5.17 shows the hysteresis loop for a droplet with bounding sphere diameter $d$ = 140nm. From an initially homogeneous magnetisation brought about through the application of a saturating magnetic field in the $x$ direction, a slight tapering effect appears at the surface as this field is reduced owing to long-range dipolar interactions (see figure 5.17, point $A$).

Further reduction of the applied field causes the dipolar energy to become more dominant. At slightly above zero field this causes the formation of a vortex slightly away from the sample centre (see figure 5.17, point $B$), the direction of which allows the overall magnetisation direction to remain in that of the applied field. The vortex moves closer to the centre of the sample as the field tends towards zero, and when there is no applied field, the Zeeman energy term is also zero and the vortex moves to the centre.

The net magnetisation $M_x$ of the sample at this point is now zero (see figure 5.17, point $C$). Reducing the field further (i.e. increased in the opposite direction) shifts the vortex further across the sample (see figure 5.17, point $D$), until the Zeeman energy term influences the magnetisation more than the other energy terms and the magnetisation of the sample becomes homogeneous in the direction of the applied field.

It is interesting to note that if the height $l_{z(s)}$ from equation 5.1 is increased to around $0.5d$, the reversal mechanism is slightly different. Although the magnetisation falls into the vortex state, only the lower half of the vortex moves through the system; the upper half is `pinned' to the centre of the ellipsoidal part during the entire reversal in a similar fashion to the three-quarter sphere in figure 5.16. This gives the vortex a pendulum-like movement throughout the system. Indeed, immediately after nucleation, the vortex is almost flat across the droplet in the plane of the applied field in a similar way to the sphere in section 3.5.