Domain theory of magnetism

The domain theory (Weiss, 1907) explains why a piece of ferromagnetic material such as iron can be unmagnetized and yet become strongly magnetized by a small field.

Main ideas

1. Domains: a ferromagnetic crystal is divided into small regions (about $10^{-6}$–$10^{-3}$ m) called domains. Inside each domain all atomic magnetic moments are aligned parallel by the strong exchange interaction, so each domain is magnetized to saturation.
2. Random orientation: in an unmagnetized specimen the directions of magnetization of different domains are random, so their effects cancel and net $M = 0$.
3. Domain walls (Bloch walls): domains are separated by transition layers a few hundred atoms thick in which the moment direction rotates gradually from one domain to the next.
4. Why domains form: a single domain would create a large external field with high magnetostatic energy. Splitting into domains (and closure domains at the ends) lowers this energy. The final size is set by the balance of magnetostatic, exchange, anisotropy, wall and magnetostrictive energies.

  Unmagnetized          Magnetized (H ->)
  +-----+-----+         +-----------+
  |  ^  |  -> |         | -> -> ->  |
  +-----+-----+   H     | -> -> ->  |
  | <-  |  v  |  ===>   | -> -> ->  |
  +-----+-----+         +-----------+

Magnetization process

On applying a field $H$:

1. Reversible wall motion (weak field): domains whose magnetization is nearly along $H$ grow, and others shrink, by small wall movement. Removing $H$ returns the walls.
2. Irreversible wall motion (medium field): walls jump past impurities and defects (Barkhausen jumps). Large rise in $B$; this is the steep part of the B–H curve and the cause of hysteresis.
3. Domain rotation (strong field): the remaining magnetization of domains rotates from the easy axis to the field direction, until the material saturates.

Explanations given by the theory

• Hysteresis and retentivity: walls stuck at defects do not return when $H$ is removed, leaving $B_r$.
• Curie temperature: above $T_C$ thermal energy destroys the exchange alignment, domains vanish, and the material becomes paramagnetic.
• Soft vs hard: pure, defect-free materials let walls move easily (soft); fine-grained, impure alloys pin walls (hard).