Closure domains and demagnetization

Closure domains

Closure domains are small triangular (prism-shaped) domains that form at the ends or surfaces of a ferromagnetic crystal, magnetized at 90° to the main domains, so that the magnetic flux forms a closed loop entirely inside the crystal. They remove free poles at the surface, making the external field and magnetostatic energy nearly zero.

Demagnetization by domain formation

A ferromagnetic crystal tends towards the state of lowest total energy. A single, fully magnetized domain has free poles and a large external field, which stores a large magnetostatic energy. The crystal reduces this energy by splitting into domains:

 (a) single     (b) two        (c) many        (d) closure
     domain         domains        domains         domains
 +--------+   +--------+     +--+--+--+--+   +--------+
 | ---->  |   | ---->  |     |^ |v |^ |v |   |\ <--- /|
 | N    S |   | <----  |     |  |  |  |  |   | v    ^ |
 +--------+   +--------+     +--+--+--+--+   |/ ---> \|
 large field  field halved   field small     +--------+
                                             no free poles

1. (a) Single domain: all moments parallel, poles at the ends, large external field and maximum magnetostatic energy $\left(\tfrac{\mu_0}{2}\int H^2 dV\right)$.
2. (b) Two antiparallel domains: part of the flux returns inside the crystal; the magnetostatic energy is roughly halved, at the cost of one domain wall.
3. (c) Many domains: with $N$ domains the energy falls to about $1/N$. Splitting stops when the energy of a new wall equals the magnetostatic energy saved.
4. (d) Closure domains: triangular domains at the ends, magnetized at 90° to the main domains, complete the flux loop inside the crystal. No free poles remain, the external field and magnetostatic energy are almost zero, and the net magnetization is zero: the crystal is demagnetized.

Energy balance

Total energy = exchange + magnetostatic + anisotropy + domain wall + magnetostrictive energy. Domains form only as long as the decrease in magnetostatic energy is larger than the extra wall energy needed. The result is a state in which domains are randomly oriented and flux is closed, which is why a piece of iron is normally unmagnetized. Demagnetizing a magnetized sample (AC field reduced slowly to zero, or heating above $T_C$) lets the material return to this low-energy domain pattern.