Braiding with magnetic octupoles

T. Lachner, D. de las Heras, and T. M. Fischer
Phys. Rev. Research, 3, 013043, (2021)     DOI: 10.1103/PhysRevResearch.3.013043
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We simulate the trajectories of magnetic octupole colloids driven by periodic loops of an external magneticfield and placed above a two-dimensional threefold symmetric magnetic pattern. The octupoles avoid thethreefold symmetric points above the lattice, either in a topologically trivial way, or by nontrivially windingaround these high symmetry points both with respect to their position and with respect to their orientation.We calculate the full dynamical phase space of this winding behavior by changing both lattice symmetries andmodulation loops. We further use the nontrivial topology to braid with octupoles and we supply a protocol forboth braiding and weaving with such microscopic particles. Our classical external field command should workequally well for quantum mechanical octupoles on magnetic nanopatterns, providing an explicit protocol for theexchange of anyonic quantum particles.

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