Introduction

Magnetostatics is the study of stationary patterns of magnetization in magnetic media. The central role in these studies is played by domains and domain walls. Domains are regions of uniform magnetization that are large on the atomic scale, but may be small in comparison with the dimensions of the medium under consideration. The walls are narrow regions that separate adjacent domains. In uniform media, the primary source of the spontaneous breakdown of magnetization into domains is the long-range dipole–dipole interaction, commonly referred to as the demagnetizing effect. Breakdown into domains provides a means of lowering the energy of demagnetization at the expense of increased exchange and anisotropy energies. Since within the domains the magnetization is fairly uniform and often aligned with an easy axis, it is at the site of the domain walls that the excess energies of exchange and anisotropy accumulate, as though the walls were endowed with an energy of their own. This chapter is devoted to the study of domains and domain walls and their structure and energy, as well as their magnetostatic interactions.

The basic tenets of magnetism were reviewed in Chapter 12, and the fundamental notions of magnetic field, magnetization, exchange and anisotropy were introduced. In the present chapter we shall confine attention to homogeneous thin-film media, where the magnetization M is treated as a continuous function of position r over the volume of the material (see Fig. 13.1).