Merons, hedgehogs and magnetoelectric switching in spiral multiferroics

In spiral multiferroics, magnetism induces ferroelectricity, thus holding a promise for novel memory devices where an electric field switches magnetic bits. However, such a switching process, in which magnetic domain walls are moved electrically, is still poorly understood. We find multiferroic domain walls containing arrays of meron (half-skyrmion) strings with a plethora of topological defects, which profoundly affect wall dynamics. Minimum energy walls have alternating meron topological charges and move as relativistic massive particles, with velocity limited by the magnon speed. During domain nucleation, walls with non-alternating meron charges appear. Such defects result in a peculiar non-local dynamics where all the spins in the system rotate, and the wall mobility is suppressed. Meron strings possess 0D hedgehog defects, analogous to Bloch points, that pin the wall to the lattice. This fascinating interplay of magnetoelectric switching with a variety of topological defects and non-local spin dynamics opens a new playground for the electric manipulation of spins.