Magnetic domain

A magnetic domain is a region — typically 0.1 to 100 micrometres across — inside a ferromagnetic material where every atomic moment points in the same direction. Inside one domain the magnetization is uniform and saturated, carrying the full M_s the material is capable of; outside, in the next domain, the magnetization points a different way. Bulk ferromagnets at rest are carved up into millions of domains in a pattern that, averaged over macroscopic scales, often gives near-zero net magnetization. This is why a bar of "unmagnetised" iron does not lift nails even though each of its iron atoms is strongly ferromagnetic.

Domains exist because they lower the total magnetic energy of the sample. A uniformly magnetised block of iron would create enormous external field lines wrapping around from one pole to the other — field energy scaling with the cube of the sample size. Breaking the block into oppositely-pointing domains lets the flux close inside the material, dramatically reducing the external field energy. The cost is a network of domain walls, thin regions (100 Å thick in iron) where the magnetization direction rotates from one domain's orientation to the next. The equilibrium domain pattern balances the two: enough walls to shut off the external field, not so many that the wall energy exceeds what is saved.

Applying an external magnetic field doesn't flip atomic moments one by one; it pushes the domain walls. Domains aligned with the field grow by absorbing neighbouring misaligned domains; walls sweep through the material like ripples through water. At low fields the walls move reversibly; above the coercive field H_c they jump abruptly across pinning sites and the process becomes irreversible — the fingerprint of hysteresis. Pierre Weiss predicted domains in 1907 from energy arguments; Francis Bitter first imaged them in 1931 by sprinkling fine ferromagnetic powder on a polished iron surface. Today, magnetic-force microscopy, Kerr-effect imaging, and X-ray magnetic circular dichroism give direct pictures of domains in nanometre detail, and domain-wall engineering is the basis of almost every modern magnetic memory technology.