Prior work

Previous work with flat cylinders, i.e where the diameter of the circular plane is significantly larger than the height, has been done by Cowburn et al. (1999a), Cowburn et al. (1999b). These papers present hysteresis loops and SEM micrographs for supermalloy
single-domain circular nanomagnets (flat cylinders). The diameter $d$ of these cylinders is between 55nm and 500nm, and their height $h$ is between 6nm and 15nm. Cowburn concludes that there is a distinct behaviour switch between the vortex state and the single-domain state (see figure 3.1) dependent on the diameter of the nanomagnet, confirmed by micromagnetic simulation (Dao et al., 2001). Two-dimensional simulation studies by Gubbiotti et al. (2002) show the vortex behaviour in circular permalloy dots of diameter 200nm. Other single-domain to vortex state transitions and phase studies have been performed by Scholz et al. (2003b).

Figure 3.1: Two states: the single domain state (left) and the vortex state (right)

Ha et al. (2003) suggest that many interesting states are formed in permalloy cylinders, which are dependent on height, radius and applied field. In flat cylinders at zero field with a diameter of 200nm, they observe the onion state; when the diameter is doubled, the vortex state is apparent at zero field.

Initial micromagnetic studies of spheres have been previously performed (Aharoni, 1980, C. H. Stapper, 1969, Eisenstein and Aharoni, 1975) and the results of these studies indicate that there is a smooth, gradual reduction in the overall magnetisation of a sphere as the applied field is reduced. Later work (Aharoni, 1983) notes there is a form to the magnetisation transition which is not certain.

Mayes et al. (2003) and Hoinville et al. (2003) discuss the practicality of storing data on spherical cobalt-platinum nanoparticles, created using a biological process and provide experimental results when used directly as a coating on a hard disk platter.

In this chapter, we take this work further, and simulate and observe the behaviour of a sphere (C. H. Stapper, 1969, Eisenstein and Aharoni, 1975, Lam, 1992), with a diameter $d$ of $200$nm and a flat cylinder (disc) of diameter $d=100$nm and height $2/5d = 80$nm; in both cases we use the material parameters for isotropic nickel ( $M_s = 493380$ A/m, $A = 8.5\times10^{-12}$ J/m, $K_1 = 0$ J) with a damping parameter $\alpha$ of 0.25 to assist with convergence. We also demonstrate the different magnetic microstructures when the height of the cylinder is altered, and perform a diameter dependence study with the cylinder.