  Domain wall dynamics in a magnetoelectric antiferromagnet is analyzed, and
its implications for magnetoelectric memory applications are discussed.
Cr$_2$O$_3$ is used in the estimates of the materials parameters. It is found
that the domain wall mobility has a maximum as a function of the electric field
due to the gyrotropic coupling induced by it. In Cr$_2$O$_3$ the maximal
mobility of 0.1 m/(s$\times$Oe) is reached at $E\approx0.06$ V/nm. Fields of
this order may be too weak to overcome the intrinsic depinning field, which is
estimated for B-doped Cr$_2$O$_3$. These major drawbacks for device
implementation can be overcome by applying a small in-plane shear strain, which
blocks the domain wall precession. Domain wall mobility of about 0.7
m/(s$\times$Oe) can then be achieved at $E=0.2$ V/nm. A split-gate scheme is
proposed for the domain-wall controlled bit element; its extension to
multiple-gate linear arrays can offer advantages in memory density,
programmability, and logic functionality.
