In particle theory, the skyrmion (/ˈskɜːrmi.ɒn/) is a topologically stable field configuration of a certain class of non-linear sigma models.
[1][2][3][4] 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[5] (a spin vortex comprising all the states of polarization mapped by a stereographic projection of the Poincaré sphere to the real plane).
[7][8] Skyrmions have been reported, but not conclusively proven, to appear in Bose–Einstein condensates,[9] thin magnetic films,[10] and chiral nematic liquid crystals,[11] as well as in free-space optics.
[12][13] As a model of the nucleon, the topological stability of the skyrmion can be interpreted as a statement that the baryon number is conserved; i.e. that the proton does not decay.
The exact results for the duality between the fermion spectrum and the topological winding number of the non-linear sigma model have been obtained by Dan Freed.
The skyrmion can be quantized to form a quantum superposition of baryons and resonance states.
For N = 3, the isoflavor symmetry between the up, down and strange quarks is more broken, and the skyrmion models are less successful or accurate.
If spacetime has the topology S3×R, then classical configurations can be classified by an integral winding number[19] because the third homotopy group is equivalent to the ring of integers, with the congruence sign referring to homeomorphism.
A topological term can be added to the chiral Lagrangian, whose integral depends only upon the homotopy class; this results in superselection sectors in the quantised model.
In (1 + 1)-dimensional spacetime, a skyrmion can be approximated by a soliton of the Sine–Gordon equation; after quantisation by the Bethe ansatz or otherwise, it turns into a fermion interacting according to the massive Thirring model.
is just an unusual way of writing the quadratic term of the non-linear sigma model; it reduces to
It is this result, of tying together what would otherwise be independent parameters, and doing so fairly accurately, that makes the Skyrme model of the nucleon so appealing and interesting.
is the totally antisymmetric Levi-Civita symbol (equivalently, the Hodge star, in this context).
The corresponding charge is the baryon number: Which is conserved due to topological reasons and it is always an integer.
In the chiral bag model, one cuts a hole out of the center and fills it with quarks.
Despite this obvious "hackery", the total baryon number is conserved: the missing charge from the hole is exactly compensated by the spectral asymmetry of the vacuum fermions inside the bag.
[25] The small size and low energy consumption of magnetic skyrmions make them a good candidate for future data-storage solutions and other spintronics devices.
[31][32] Skyrmions operate at current densities that are several orders of magnitude weaker than conventional magnetic devices.
In 2015 a practical way to create and access magnetic skyrmions under ambient room-temperature conditions was announced.
Polarity is controlled by a tailored magnetic-field sequence and demonstrated in magnetometry measurements.
The vortex structure is imprinted into the underlayer's interfacial region by suppressing the PMA by a critical ion-irradiation step.
The lattices are identified with polarized neutron reflectometry and have been confirmed by magnetoresistance measurements.
[36] In 2020, a team of researchers from the Swiss Federal Laboratories for Materials Science and Technology (Empa) has succeeded for the first time in producing a tunable multilayer system in which two different types of skyrmions – the future bits for "0" and "1" – can exist at room temperature.