Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals

Significance While arising in theories in many branches of science, from particle physics to condensed matter and cosmology, stable three-dimensional topological solitons remained experimentally elusive until very recently. We now show that such solitons can be electrically and magnetically switched between states with the same or different Hopf indices. Richness and robustness of this switching promise technological applications in the new breeds of information displays and data storage devices, as well as may provide a test ground and new inspirations for the mathematical knot theory.