Introduction

Lithographic techniques have allowed researchers to create ordered structures on the sub-micron scale (Cowburn et al., 1997, Hehn et al., 1996, Van Roy et al., 1993, Fruchart et al., 1999, Martín et al., 2003), either as well-formed small magnetic elements such as the cylindrical and spherical objects described in chapters 3 and 5 or as regular arrays of holes in magnetic films. Antidots are the `opposite' of the nanodots discussed in the previous chapter. If one creates a hole in a thin sample, the hole can be considered to be an antidot. Lithographic techniques generally yield cylindrical holes, but emerging self-assembly techniques (Bartlett et al., 2002) promise a wider range of shapes.

Figure 6.1 shows the single-template self-assembly technique. Electrochemical deposition can be used to create nanoscale magnetic materials by creating an ordered template from polystyrene latex spheres of size order 50nm $\leq d \leq$ 1000nm (Xu et al., 2000, Bartlett et al., 2003b). Initially, an aqueous solution of monodisperse latex spheres is deposited on a glass substrate. On this substrate sputtered buffer layers of chromium and gold have been deposited, with thicknesses of 10nm and 200nm respectively.

Figure 6.1: The single-template self-assembly technique. Latex spheres of diameter $d$ are poured on to a substrate (left). As the water evaporates, the latex spheres become close-packed, forming a template (centre) which can then be filled with a magnetic material from the substrate upwards to a height $h$ (right).

Over a period of between three and five days the evaporation of the water leads to the formation of the template: the combination of the electrostatic repulsion between the latex spheres and the attractive capillary forces provided by the evaporation of the water produces a well-ordered close-packed structure (Bartlett et al., 2002, Bartlett et al., 2000, Bartlett et al., 2003b).

Using electrodeposition from the gold layer, the electrodeposited material fills the spaces between the latex spheres, using the spheres as a mould. By dissolving the latex spheres in toluene, 3D antidot arrays with spherical holes are formed.

Different thicknesses of antidot arrays can be formed by adjusting the charge during the electrodeposition process, while the period of the antidots is controlled by altering the diameter of the latex spheres.

Figure 6.2 shows a scanning electron microscope image of an antidot array created through the self-assembly template method, and demonstrates the regular structure formed with this process.

Figure 6.3 shows the experimentally-measured coercivity of Ni$_{50}$Fe$_{50}$ antidot arrays with a diameter $d$ of 550nm when the external field is applied in-plane. The coercivity oscillates as a function of height (thickness) $h$. When the height of the film is close to the sphere centres, the coercivity reaches a local maximum. This oscillatory behaviour is what we wish to understand and explain in this chapter.

Figure 6.2: Scanning electron microscope image of an antidot array created by the self-assembly template method. The image on the left shows the top of the array; the right-hand image shows the honeycomb-like structure at the edge of the sample

Figure 6.3: Experimentally observed coercivity oscillation in Ni$_{50}$Fe$_{50}$ antidot arrays of $d$=550nm against the height (thickness) $h$ of the film. The dashed lines indicate the positions of sphere centres for each layer in the close-packed structure. The coercivity shows maxima close to the sphere centres. The solid line is a guide to the eye