From: Hannah Pell

Images are a great way to express abstract ideas. Whether through thought experiments like the famous Schrödinger-Katzen- or Feynman-diagrams (some of which have been referred to as “penguin diagrams”), physicists often resort to everyday language, sketches and even animals to characterize complex scientific theories. You can take a quick visit to the Particle Zoo and see more examples.

Hedgehogs have also taken up the vocabulary of condensed matter physics. Articles 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. You are probably wondering (as I am): what does a tiny, tiny 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.

Skyrmions were first proposed by Tony Skyrme in his 1962 work “A Unified Field Theory of Mesons and Baryons” for the journal Nuclear Physics. Skyrme’s model described the core as a pion 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 (for example, that protons do not decay), it would eventually be replaced by quantum chromodynamics, which is our modern way of understanding the basic components of the nucleus, namely quarks and gluons.

Skyrmions have since been observed experimentally and are often referred to as “vortices” due to their vortex effect on the polar orientation of surrounding atoms when moving over magnetic material (see figure below). Topological insulators are a particularly useful type of material for skyrmionics, the inside of which behaves like an insulator (not easily conductive), but the surface contains conductive states along which skyrmions can easily move.

Video credit:: Science news.

The magnetic effects of skyrmions can show chirality or not be identical to their own mirror image and can be seen in two different configurations: cycloidal (a) or helical (b). “Hedgehog Skyrmions” are cycloidal and achiral; This configuration is also known as the “Néel type” after the French physicist Louis Néel. Helical and chiral magnetization patterns, also called “Bloch-type” after the 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 similarity between the field vectors and the hedgehog tips?

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

The future of skyrmionics looks promising. In part because of their topological stability, skyrmions are expected to be particularly well suited for future data storage and computing applications, as well as optics and photonics research. More recently, researchers using graphene to study superconductivity and the movement of electrons have shed additional light on skyrmionic behavior in 2D materials.

While skyrmions are still a mystery, perhaps visualizing the similarity of their magnetic effects to hedgehogs can help those of us who are not condensed matter physicists understand them a bit better.


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