Domain wall and domain wall motion

A domain wall (Bloch wall) is the thin boundary layer, typically a few hundred atomic spacings thick, between two magnetic domains magnetized in different directions. Inside the wall the atomic moments turn gradually, a little from atom to atom, from the direction of one domain to that of the next. A wall has energy (exchange + anisotropy), and its width is set by the balance between them: exchange energy favours a wide wall; anisotropy energy favours a narrow one.

 domain A        wall           domain B
 ^ ^ ^ ^ |  ^  /  ->  \   v  | v v v v
         |<- spins rotate ->|

How domain wall motion occurs

When an external field $H$ is applied, the domains magnetized close to the direction of $H$ have lower energy ($-\mu_0 M\cdot H$) than the others. The material lowers its energy by enlarging these favourable domains. This happens by moving the walls: spins at the edge of the wall rotate one after another towards the favourable direction, so the wall shifts into the unfavourable domain.

 H = 0         H ->              H -> (larger)
 [ ^ | v ]     [ ^ ^ | v ]       [ ^ ^ ^ |v]
  wall at       wall moves        favourable
  centre        right             domain grows

Stages

1. Reversible wall motion (low field): walls bulge or shift slightly but stay held by defects. Removing $H$ returns them; the initial part of the B–H curve is gentle.
2. Irreversible wall motion (medium field): walls break free from impurities, voids, dislocations and grain boundaries and jump suddenly to new positions. These jumps (Barkhausen effect) can be heard as clicks with a coil and amplifier. B rises steeply, and after $H$ is removed the walls stay in new positions, causing remanence and hysteresis loss.
3. Domain rotation (high field): after the walls have swept through, the remaining domain rotates into the field direction, giving saturation.

Importance: easy wall motion (pure, annealed, large-grain material) gives soft magnetic behaviour; walls pinned by fine particles and defects give hard magnetic behaviour.