What’s a Hedgehog Got to Do with Condensed Matter Physics?

By: Hannah Pell

Pictures are a helpful way to express abstract ideas. Whether through Gedanken experiments like the famous Schroedinger’s Cat or Feynman diagrams (some of which have been described as “penguin diagrams“), physicists often draw on everyday language, sketches, and well, animals, to characterize complex scientific theories. You can take a quick visit to the Particle Zoo and see more examples for yourself.

Hedgehogs have also entered the condensed matter physics vocabulary. Papers with titles such as “Topological Transport of Deconfined Hedgehogs in Magnets,” “Finding Spin Hedgehogs in Chiral Crystals,” and “Magnetic hedgehog lattices in noncentrosymmetric metals,” were published in Physical Review Letters last year. So you’re probably wondering (as was I): what does a small, pokey tiny, pokey animal have to do with condensed matter systems? The answer has to do with magnetism, thin films, and a very interesting particle called the skyrmion.

Image Credit: Advocator SY on Unsplash.
Skyrmions were first proposed by Tony Skyrme in his 1962 paper “A Unified Field Theory of Mesons and Baryons” for the journal Nuclear Physics. Skyrme’s model described the nucleus in terms of pions’ quantum field with inherent “twists” (represented by the skyrmions), and the number of such twists corresponded to the number of baryons. Although Skyrme’s original theory correctly predicted some aspects of the nucleus (that protons do not decay, for example), it would eventually be superseded by quantum chromodynamics, which is our modern way of understanding the fundamental constituents of the nucleus, namely, quarks and gluons.

Skyrmions have since been observed experimentally and are often described as “vortices” due to their swirling effect on the polar orientation of surrounding atoms as they move across magnetic material (visualized below). Topological insulators are a particularly useful type of materials for skyrmionics, whose interior behaves like an insulator (not easily conductive) however the surface contains conducting states which skyrmions could easily move along.

Video Credit: Science News.

The magnetic effects from skyrmions can demonstrate chirality, or not identical to their own mirror image, and are evident according to two different configurations: cycloidal (a) or helical (b). “Hedgehog skyrmions” are cycloidal and achiral; this configuration is also referred to as the “Néel-type” after French physicist Louis Néel. Helical and chiral magnetization patterns, also called “Bloch type” after physicist Felix Bloch, are caused by a “vortex skyrmion.” Neel and Bloch types refer to two types of transitions between domain walls in magnetism.

Can’t you see the resemblance between the field vectors and hedgehog spikes?

Figure Credit: Karin Everschor-Sitte and Matthias Sitte, CC BY-SA 3.0.

The future of skyrmionics seems bright. Due in part to their topological stability, skyrmions are predicted to be particularly well-suited for future data storage and computing applications, as well as optics and photonics research. More recently, researchers utilizing graphene to study superconductivity and the movement of electrons have shed additional light on skyrmionic behavior in 2D materials.

Although skyrmions may still be quite the mystery, visualizing the resemblance of their magnetic effects to hedgehogs just maybe can help those of us who aren’t condensed matter physicists understand them a little bit more.

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