  Spiral multiferroics exhibit a strong coupling between magnetic and
ferroelectric orders, allowing cross-control. Since the seminal work of Kimura
et al. in 2003, these materials have attracted great interest galvanized by the
prospect of new high-efficiency memory devices, where magnetic (electric) bits
are switched via an external electric (magnetic) field. Nevertheless, the
mechanism underlying such a switching process - the electric field-driven
dynamics of domain walls (DWs) - is still poorly understood. We address this
problem for meron DWs, which represent one of the main DW types in spiral
multiferroics and consist of an array of meron (half-skyrmion) strings. Minimum
energy walls feature merons with alternating topological charges and move as
relativistic massive particles, with the limiting velocity set by magnon speed.
Low-energy defects in this alternating charge sequence, which appear during
domain nucleation, can lead to DWs with net topological charge. This induces a
peculiar non-local dynamics where all the spins in the system rotate, merons
translate within the wall, and the DW mobility is suppressed. The topological
charge of the wall and the meron helicity can be easily modified via an
external magnetic and electric field, respectively, offering fine control over
DW dynamics. Defects within the meron strings, analogous to Bloch points, have
hedgehog-like spin texture and are strongly pinned to the lattice. The
fascinating interplay between domain wall motion, translation of merons within
the wall, and precession of spins in the entire domains opens a new playground
for the electric manipulation of topological spin textures.
