Size dependence

A size dependence study was performed on the diameter of nickel spheres; the results of this can be seen in figure 3.17, showing a change in behaviour at a certain diameter.

There is a qualitative change in the magnetisation reversal when the diameter is reduced; the hysteresis loops for spheres of diameter 50nm and 80nm are shown in figure 3.18.

Figure 3.17: Size dependence of the domain state in nickel spheres. The vertical dotted line shows the critical radius for state transition computed with equation 3.1

Figure 3.18: Hysteresis loops for nickel spheres of (left) diameter 50nm and (right) diameter 80nm. The 50nm sphere reverses through the single-domain state; the 80nm sphere through the vortex state

The following equation (O'Handley, 1999) gives the critical radius (i.e. the radius above which a sphere changes from single domain behaviour to vortex behaviour) of a spherical sample of some material which has a low anisotropy value.

$$r_{n+1} = \sqrt{ {9A \over \mu_0 M_s^2} \left[\ln \left({2r_n \over a} \right) -1 \right]}$$ (3.1)

$r$In geometry, the radius of the circular or spherical part of a sample, usually measured across the $xy$ plane Using this equation, one can quickly converge on the critical radius for nickel by iterating equation 3.1 until $r_{n+1} - r_n = 0$. The calculated critical radius of 34nm agrees well with our simulations of nickel spheres; these studies show that the magnetisation pattern of a nickel sphere of diameter 60nm ($r=30$nm) reverses as a single-domain, and the magnetisation pattern when the diameter is 70nm is vortex-like.