Size dependence

Figure 5.19: Size dependence of coercive field in droplet nanodots. An error of $\pm1$mT is present as this is the applied field step size. Where $B_c>0$mT, the remanent state is single domain, where $B_c=0$mT there is a vortex remanent state.

We have varied the diameter $d$ of the droplet from 50nm to 500nm and computed a hysteresis loop for every $d$ in steps of 10nm. We find two different régimes. Figure 5.19 reflects the size dependence of the coercive field for these droplets.

When $d <$ 140nm, the magnetisation reversal mechanism is single-domain (see figure 5.21, left and centre). When $d \geq$ 140nm, the magnetisation reverses through the vortex state (see figure 5.17 and figure 5.21, right).

The relatively consistent coercivity of 5mT between 60nm and 130nm in figure 5.19 is a result of a coherent rotation reversal process, unlike that shown by dots smaller than 60nm. The hysteresis loops at 60nm  $\leq d \leq$ 130nm are substantially less ``square'' than those shown with sub-60nm bounding sphere sizes and bear a resemblance to the loops from 140nm and greater droplets, as indicated by the centre loop ($d$=90nm)in figure 5.21.

Above 140nm the coercivity of the droplets is zero. For droplets of greater size the hysteresis characteristics are similar, although as the size is increased the reversal takes place over an increasingly large applied field, and the smaller loops at the top and bottom of the hysteresis graph become more rounded (see figure 5.18).

Figure 5.20: Two hysteresis curves for nickel nanodots with bounding sphere diameter of 500nm. The hysteresis loop on the left shows results obtained from experiment. The right-hand loop shows the results of the numerical modelling.

There is a good agreement between the experimental hysteresis curve measured across a nickel nanodot of bounding sphere diameter 500nm (figure 5.20, left) and the results of the numerical simulation for the droplet of the same bounding sphere diameter (figure 5.20, right).

Figure 5.21: Hysteresis loops for droplet nanodots of (from left to right) bounding sphere diameter $d$ of 30nm, 90nm and 140nm