Radha Balakrishnan (The Institute of Mathematical Sciences) Exact Knotted Hopfion Vortices in a 3D Heisenberg Ferromagnet

We begin with a general introduction to solitary waves/solitons, topological solitons, and the concept of topological invariants/charges. We then present our recent work on knotted magnetic solitons in an anisotropic, inhomo- geneous 3D Heisenberg ferromagnetic spin model. We obtain exact static soliton solutions for the spin field of this model. We show analytically that each soliton possesses an integer topological charge. We demonstrate that this integer can also be interpreted as a linking number. These topological solitons are closed hopfion vortices. Their underlying structure represents either unknots or nontrivial (chiral) knots. We calculate their exact energies. We further show that they are stable entities. Possible applications in other fields are also outlined.