Domain wall motion refers to the movement of the boundary (or "domain wall") between two regions (domains) in a material where the alignment of a certain property—typically the magnetization or electric polarization—differs. This concept is particularly important in ferromagnetic, ferroelectric, and multiferroic materials, where regions of differing magnetization or polarization are separated by domain walls.

Here’s a more detailed breakdown:

### 1. Magnetic Domain Wall Motion
In a ferromagnetic material, the magnetization within each domain points in a uniform direction, but this direction can vary from one domain to another. The domain wall is the transition region between two such domains. Domain wall motion in this context refers to the movement of this boundary when an external magnetic field is applied. This motion occurs as the domains aligned with the applied magnetic field expand at the expense of oppositely aligned domains, reducing the system's magnetic energy.

There are two primary types of magnetic domain walls:
- Bloch walls: Where the magnetization rotates within the plane of the wall.
- Néel walls: Where the magnetization rotates perpendicular to the plane of the wall.

### 2. Electric Domain Wall Motion
In ferroelectric materials, domain walls separate regions with different orientations of electric polarization. An applied electric field can cause electric domain wall motion, where domains aligned with the external field grow at the expense of others, changing the material's overall polarization.

### 3. Factors Affecting Domain Wall Motion
- External fields: Magnetic fields drive magnetic domain walls, while electric fields drive ferroelectric domain walls.
- Defects and pinning: Imperfections in the material, such as impurities or dislocations, can pin domain walls, making their motion more difficult or requiring a stronger external field.