Skyrme model

In particle theory, the skyrmion (/ˈskɜːrmi.ɒn/) is a topologically stable field configuration of a certain class of non-linear sigma models. It was originally proposed as a model of the nucleon by Tony Skyrme in 1962. As a topological soliton in the pion field, it has the remarkable property of being able to model, with reasonable accuracy, multiple low-energy properties of the nucleon, simply by fixing the nucleon radius. It has since found application in solid state physics, as well as having ties to certain areas of string theory.

Skyrmions as topological objects are important in solid state physics, especially in the emerging technology of spintronics. A two-dimensional magnetic skyrmion, as a topological object, is formed, e.g., from a 3D effective-spin "hedgehog" (in the field of micromagnetics: out of a so-called "Bloch point" singularity of homotopy degree +1) by a stereographic projection, whereby the positive north-pole spin is mapped onto a far-off edge circle of a 2D-disk, while the negative south-pole spin is mapped onto the center of the disk. In a spinor field such as for example photonic or polariton fluids the skyrmion topology corresponds to a full Poincaré beam (which is, a quantum vortex of spin comprising all the states of polarization).

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