Motion of a Bloch domain wall

We study the velocity versus applied-field relation of a moving Bloch domain wall, using the ‘‘collective-coordinate’’ method employed in the theory of soliton motion. For a sufficiently large field, the wall emits spin waves, thereby self-limiting its velocity. That velocity is equal to the common value of the phase and group velocities of a particular spin wave, and may be above or below the Walker limit ${\mathit{V}}_{\mathit{W}}$, depending on the intrinsic damping.