This recent paper describes how magnetic hopfions can be stabilized in chiral magnets. These are magnetic solitons characterized by the third homotopy group of the two sphere; this is different from skyrmions which are characterized by the second homotopy group of the two sphere. The third homotopy group is the integers so hopfions have a topological charge. Hopfions have been stabilized previously in liquid crystals. One can show that hopfions are unstable in a homogeneous bulk system so the presence of interfaces is crucial here.
https://arxiv.org/abs/1806.00453
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This topic was modified 5 years, 11 months ago by rowland.208.