The Present and Future of Magnetic Hopfions

Noah Kent

Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA

Hopfions are topological structures defined by a Hopf charge, Q [1]. Q is the number of times every field line in order parameter space wraps around each other. To clearly talk about three dimensional magnetic Hopfions and their possible future uses, I will first discuss topological mappings, why topologically protected three dimensional Skyrmions can’t exist in ferromagnetic systems [2], and give an overview of the various types of 3D Hopfions (e.g. Skyrmion tube, heliknoton [3]).
I will then talk about the experimental realization of magnetic Hopfions [4], and how they were identified by differentiating them from other possible magnetic structures using a combination of depth averaging magnetic transmission x-ray microscopy and surface sensitive photo-emission electron microscopy.
Finally, I will discuss why Hopfions have significant technological potential (e.g. unique interactivity, multiple structurally distinct hopfions for a given Q) and give a brief outline of future experimental goals that must be reached in order to realize this potential.

Fig.1. Structure and signal of a Q=1 skyrmion tube hopfion. (Left) Surface sensitive photeemission electron microscopy (PEEM) signal of this Hopfion. (Middle) Structural schematic for this Hopfion. The yellow region shows the approximate depth sensitivity of PEEM. (Right) Depth averaging Magnetic X-ray Microscopy signal for this Hopfion. Adapted from [4].

 

Reference(s)
[1] Nicholas Manton, Paul Sutcliffe, Topological Solitons, Cambridge University Press. 2004
[2] H.B. Braun, Topological effects in nanomagnetism: from superparamagnetism to chiral quantum solitons, Advances in Physics (2012).
[3] Tai J-SB, Smalyukh II. Three-dimensional crystals of adaptive knots. Science. 2019;365:1449–1453.
[4] Kent, N., Reynolds, N., Raftrey, D. et al. Creation and observation of Hopfions in magnetic multilayer systems. Nat Commun 12, 1562 (2021). https://doi.org/10.1038