Magnetic domain wall

A magnetic domain wall separates differently oriented magnetic domains. Its motion changes their volumes and average magnetization. It is a magnetic domain wall.

An original two-magnetic domain model makes the collective change explicit. Suppose opposite regions have magnetizations $+M_s$ and $-M_s$ along the measuring axis, where $M_s$ is the local saturation magnetization. If a magnetic domain wall sweeps volume $\Delta V$ from the negative region into the positive one, in a specimen of fixed volume $V$, thenThe factor two comes from replacing $-M_s$ by $+M_s$. The local magnitude $M_s$ stays fixed while the average magnetization changes; the event size depends on the swept volume, rather than a universal single-spin increment.

A trial domain pattern costs wall energy ${\gamma }_w{A}_w$ and can release stray energy $\Delta U$. For a stable uniform ground state, ${\gamma }_w{A}_w\ge \Delta U$ within that trial model. Substituting the entire initial stray energy assumes that it is nearly all removed; a numerical lower bound independent of the domain geometry does not follow from single-domain observation alone.

Spatial variations in energy, including crystal defects, can trap a magnetic domain wall. This is magnetic domain-wall pinning. Increasing the applied magnetic field can release the wall into a collective jump.