# Skyrmion

In particle theory, the skyrmion (/ˈskɜːrmi.ɒn/) is a hypothetical particle related originally[1] to baryons. It was described by Tony Skyrme in 1962 and consists of a quantum superposition of baryons and resonance states.[2] It could be predicted from some nuclear matter properties.[3]

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.

## Mathematical definition

In field theory, skyrmions are homotopically non-trivial classical solutions of a nonlinear sigma model with a non-trivial target manifold topology – hence, they are topological solitons. An example occurs in chiral models[4] of mesons, where the target manifold is a homogeneous space of the structure group

${\displaystyle \left({\frac {SU(N)_{L}\times SU(N)_{R}}{SU(N)_{\text{diag}}}}\right)}$

where SU(N)L and SU(N)R are the left and right parts of the SU(N) matrix, and SU(N)diag is the diagonal subgroup.

If spacetime has the topology S3×R, then classical configurations can be classified by an integral winding number[5] because the third homotopy group

${\displaystyle \pi _{3}\left({\frac {SU(N)_{L}\times SU(N)_{R}}{SU(N)_{\text{diag}}}}\cong SU(N)\right)}$

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. 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.

Skyrmions have been reported, but not conclusively proven, to be in Bose-Einstein condensates,[6] superconductors,[7] thin magnetic films[8] and in chiral nematic liquid crystals.[9]

## Magnetic materials/data storage

One particular form of skyrmions is found in magnetic materials that break the inversion symmetry and where the Dzyaloshinskii-Moriya interaction plays an important role. They form "domains" as small as 1 nm (e.g. in Fe on Ir(111)).[10] The small size and low energy consumption of magnetic skyrmions make them a good candidate for future data storage solutions and other spintronics devices.[11][12][13] Researchers could read and write skyrmions using scanning tunneling microscopy.[14] The topological charge, representing the existence and non-existence of skyrmions, can represent the bit states "1" and "0". Room temperature skyrmions were reported.[15][16]

Skyrmions operate at magnetic fields 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. The device used arrays of magnetized cobalt disks as artificial Bloch skyrmion lattices atop a thin film of cobalt and palladium. Asymmetric magnetic nanodots were patterned with controlled circularity on an underlayer with perpendicular magnetic anisotropy (PMA). 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 via suppressing the PMA by a critical ion-irradiation step. The lattices are identified with polarized neutron reflectometry and confirmed by magnetoresistance measurements.[17][18]