Applying an out-of-plane external field

By adjusting the direction of the applied field such that it is now along the short axis of the droplet, or out-of-plane, rather than across the symmetry plane we can perform further studies on the droplet nanodot.

Figure 5.22 demonstrates a typical hysteresis loop obtained from these simulations and also the associated reversal mechanism. The vignette images along the hysteresis loop show a cut-plane of the magnetisation in the $xz$ plane, $z$ being the short axis and that of the applied field. Initially, a high external magnetic field is applied such that the magnetisation becomes homogeneous in $+z$ (point A), then this field is gradually lowered until it is sufficiently high in the opposite direction ($-z$) to maintain a homogeneous magnetisation in this direction.

As the field is reduced, the system falls into the out-of-plane vortex state with no apparent energy barrier to overcome (point B), with the core pointing in the direction of the initial applied field (point C). Further reduction of the applied field results in the magnetisation surrounding the core pointing more towards the direction of the applied field, so that when the applied field is $<0$mT the overall magnetisation is in $-z$ (point D). The core, however, remains pointing in $+z$ until around $-50$mT, at which point the core flips causing the small jump in magnetisation around this point (point E).

Finally, once the magnetisation is sufficiently large in $-z$, the vortex disappears completely and the magnetisation is homogeneous in $-z$ (point F).

Figure 5.22: Reversal mechanism of a nickel droplet of bounding sphere diameter 200nm in a perpendicular applied field

Figure 5.23 shows the size dependence of the droplets when the applied field is out of the plane. The coercive field of the droplets decreases as the bounding sphere radius is increased, with the rate of coercivity reduction decreasing as the radius is further increased.

Figure 5.23: Size dependence of the out-of-plane coercive field in droplet nanodots.

Figure 5.24 places the coercive field size dependence of the droplets where the initial applied field is out of the plane into context by comparing this to the coercivity of the same droplets when the original applied field is in the plane. It is clear from these results that applying the field across the short out-of-plane axis of the droplets increases the coercivity significantly; for a coercive field of 20mT a droplet of bounding sphere diameter of around 25nm is sufficient with an in-plane applied field, however with an out-of-plane field a bounding sphere diameter of $\approx$160nm is required.

Figure 5.24: Size dependence of the out-of-plane (see figure 5.19) and in-plane coercive field (see figure 5.23 in droplet nanodots. $M_x$ is the in-plane magnetisation, $B_x$ the in-plane applied field, $M_z$ the out-of-plane magnetisation and $B_z$ the out-of-plane applied field