# Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures.

@article{Tai2018StaticHS, title={Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures.}, author={Jung-Shen B. Tai and Ivan I. Smalyukh}, journal={Physical review letters}, year={2018}, volume={121 18}, pages={ 187201 } }

Two-dimensional topological solitons, commonly called Skyrmions, are extensively studied in solid-state magnetic nanostructures and promise many spintronics applications. However, three-dimensional topological solitons dubbed hopfions have not been demonstrated as stable spatially localized structures in solid-state magnetic materials. Here we model the existence of such static solitons with different Hopf index values in noncentrosymmetric solid magnetic nanostructures with a perpendicular…

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Arising in many branches of physics, Hopf solitons are three-dimensional particle-like field distortions with nontrivial topology described by the Hopf map. Despite their recent discovery in colloids…

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Topological solitons have been studied for decades in classical field theories, and have started recently to impact condensed matter physics. Among those solitons, magnetic skyrmions are…

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Hopfions are three-dimensional (3D) topological states discovered in field theory, magnetics, and hydrodynamics that resemble particle-like objects in physical space. Hopfions inherit the topological…

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