Dynamical skyrmions and emergent electromagnetism of moving monopoles in magnetic nanostructures

Topological defects such as domain walls, vortices and skyrmions have gained prominence  as they owe their stability to their robustness against continuous deformations, similar to knots in a rope. Such static spin textures in various dimensions can be classified according to homotopy theory.  Remarkably, however, we also demonstrate that smooth spin textures such as domain wall pairs and skyrmions can also be stabilized entirely dynamically.  Such textures and in particular dynamical skyrmions  may serve as tuneable generators of microwave radiation and may even exist in DMI free materials. As a second example of topologically nontrival dynamical object in DMI free materials, we  discuss the rapid motion of hedgehogs in nanowires. The creation of such hedgehogs is intimately related to the irreversibility of magnetization reversal in generic nanoparticles. Their rapid motion gives rise to a substantial emergent electric field, thus characterizing these hedgehogs as bona-fide magnetic monopoles.