Spacetime magnetic hopfions: from internal excitations and braiding of skyrmions
arxiv(2023)
Abstract
Spatial topology endows topological solitons, such as skyrmions and hopfions,
with fascinating dynamics. However, the temporal dimension has so far provided
a passive stage on which topological solitons evolve. Here we construct
spacetime magnetic hopfions: magnetic textures in two spatial dimensions that
when excited by a time-periodic drive develop spacetime topology. We uncover
two complementary construction routes using skyrmions by braiding their center
of mass position and by controlling their internal low-energy excitations.
Spacetime magnetic hopfions can be realized in nanopatterned grids to braid
skyrmions and in frustrated magnets under an applied AC electric field. Their
topological invariant, the spacetime Hopf index, can be tuned by the applied
electric field as demonstrated by our collective coordinate modeling and
micromagnetic simulations. The principles we have introduced to actively
control spacetime topology are not limited to magnetic solitons, opening
avenues to explore spacetime topology of general order parameters and fields.
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