Introduction

After IBM attained an areal recording density of 1Gbit/in$^2$ (Tsang et al., 1993, Tsang et al., 1990) -- half a million times greater than RAMAC -- the growth of areal density of a consumer hard disk drive has been approaching 100% every twelve months. Following current trends the next decade should witness the advent of an areal density of 1Tbit/in$^2$ (Tarnopolsky, 2004, Wood, 2000, Wood et al., 2002).

Since modern hard disk drive technology is converging on fundamental limits (see figures 2.1, 2.2) new approaches must be considered. Micromagnetic simulation is an important method of addressing these limits. Further discussion of the applications of micromagnetic modelling can be seen in section 2.10.

In sections 2.2 to 2.6 we provide an overview of micromagnetics.

In section 2.3 we describe the different interactions and associated energies of a system of magnetic moments $\mu$.

Section 2.4 describes the micromagnetic approach when the discrete, atomistic nature of matter is ignored and the magnetisation is represented as a continuous function of space.

In sections 2.5 and 2.6 the Landau-Lifshitz Gilbert equations and the Stoner-Wohlfarth model are introduced.

Sections 2.7 to 2.10 describe the simulation packages used in this work and associated hardware and software requirements.

Micromagnetism as a field -- i.e. that which deals specifically with the behaviour of ferromagnetic materials at fine ( $1\times 10^{-6}$ metre) length scales -- was introduced in 1963 when William Fuller Brown Jr. published his paper on antiparallel domain wall structure (Brown, 1963); however until comparatively recently computational micromagnetics -- particularly when three-dimensional problems are considered -- has been prohibitively expensive in terms of computational power, but now a modern desktop PC is capable of performing small micromagnetic simulations within a few days.