Magnetic domains in an external field

A magnetic domain is a small region of a ferromagnetic (or ferrimagnetic) material in which all atomic magnetic moments are aligned in the same direction because of the exchange interaction, so the region is magnetized to saturation. Neighbouring domains are separated by domain walls. In an unmagnetized body the domains point in random directions and cancel.

Behaviour of domains in an external field

As the applied field $H$ increases, the magnetization changes in stages that match the parts of the initial B–H curve.

  B
  ^                 ______ saturation
  |            ___/  (3) rotation
  |          /
  |         / (2) irreversible wall
  |        /      motion (Barkhausen)
  |      _/
  |   _/  (1) reversible wall motion
  +-------------------------------> H

1. Zero field: domains are randomly oriented; net $M = 0$.
2. Weak field: reversible domain wall movement
   • Domains whose magnetization is close to $H$ have lower energy, so they grow by small shifts of their walls; unfavourable domains shrink.
   • If $H$ is removed, walls return to their original places. The curve is gentle and reversible.
3. Medium field: irreversible domain wall movement
   • Walls break free from impurities, voids and grain boundaries and move in sudden jumps (Barkhausen effect).
   • Favourable domains grow rapidly by eating unfavourable ones; $B$ rises steeply.
   • On removing $H$ the walls do not return completely; this gives remanence and hysteresis.
4. Strong field: domain rotation
   • Now most of the crystal is one domain, magnetized along an easy axis close to $H$.
   • Further increase in $H$ rotates the magnetization away from the easy axis into the exact direction of $H$, against anisotropy energy.
   • When all moments are parallel to $H$, the material reaches saturation $M_s$.

 H = 0        weak H ->     strong H ->   very strong
 [^][>]       [^ ][>>>]     [>>>>>>]      [-->-->-->]
 [<][v]       [< ][>>>]     [>>>>>>]      aligned with H
 random       walls move    one domain    rotated (Ms)

If the field is then reduced to zero, the domain structure does not fully go back, leaving residual magnetism $B_r$.