# Skyrmion

(Redirected from Skyrme model)

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. 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).[4]

## 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[5] 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[6] 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,[7] superconductors,[8] thin magnetic films[9] and in chiral nematic liquid crystals.[10]

## Magnetic materials/data storage

One particular form of skyrmions is magnetic skyrmions, found in magnetic materials that exhibit spiral magnetism due to the Dzyaloshinskii-Moriya interaction, double-exchange mechanism[11] or competing Heisenberg exchange interactions.[12] They form "domains" as small as 1 nm (e.g. in Fe on Ir(111)).[13] The small size and low energy consumption of magnetic skyrmions make them a good candidate for future data storage solutions and other spintronics devices.[14][15][16] Researchers could read and write skyrmions using scanning tunneling microscopy.[17] The topological charge, representing the existence and non-existence of skyrmions, can represent the bit states "1" and "0". Room temperature skyrmions were reported.[18][19]

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. 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 have been confirmed by magnetoresistance measurements.[20][21]

## References

1. ^ At later stages the model was also related to mesons.
2. ^ Wong, Stephen (2002). "What exactly is a Skyrmion?". arXiv: [hep/ph].
3. ^ Khoshbin-e-Khoshnazar, M.R. (2002). "Correlated Quasiskyrmions as Alpha Particles". Eur. Phys. J. A. 14: 207–209. doi:10.1140/epja/i2001-10198-7.
4. ^ Donati, S; Dominici, L; Dagvadorj, G; et al. (2016). "Twist of generalized skyrmions and spin vortices in a polariton superfluid". Proc Natl Acad Sci USA. doi:10.1073/pnas.1610123114.
5. ^ Chiral models stress the difference between "left-handedness" and "right-handedness".
6. ^ The same classification applies to the mentioned effective-spin "hedgehog" singularity": spin upwards at the northpole, but downward at the southpole.
See also Döring, W. (1968). "Point Singularities in Micromagnetism". Journal of Applied Physics. 39 (2): 1006. Bibcode:1968JAP....39.1006D. doi:10.1063/1.1656144.
7. ^ Al Khawaja, Usama; Stoof, Henk (2001). "Skyrmions in a ferromagnetic Bose–Einstein condensate". Nature. 411 (6840): 918–20. Bibcode:2001Natur.411..918A. doi:10.1038/35082010. PMID 11418849.
8. ^ Baskaran, G. (2011). "Possibility of Skyrmion Superconductivity in Doped Antiferromagnet K2Fe4Se5". arXiv: [cond-mat.supr-con].
9. ^ Kiselev, N. S.; Bogdanov, A. N.; Schäfer, R.; Rößler, U. K. (2011). "Chiral skyrmions in thin magnetic films: New objects for magnetic storage technologies?". Journal of Physics D: Applied Physics. 44 (39): 392001. arXiv:. Bibcode:2011JPhD...44M2001K. doi:10.1088/0022-3727/44/39/392001.
10. ^ Fukuda, J.-I.; Žumer, S. (2011). "Quasi-two-dimensional Skyrmion lattices in a chiral nematic liquid crystal". Nature Communications. 2: 246. Bibcode:2011NatCo...2E.246F. doi:10.1038/ncomms1250. PMID 21427717.
11. ^ Azhar, Maria; Mostovoy, Maxim (2017). "Incommensurate Spiral Order from Double-Exchange Interactions". Physical Review Letters. 118 (2). arXiv:. doi:10.1103/PhysRevLett.118.027203.
12. ^ Leonov, A. O.; Mostovoy, M. (2015-09-23). "Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet". Nature Communications. 6: 8275. doi:10.1038/ncomms9275. ISSN 2041-1723. PMC . PMID 26394924.
13. ^ Heinze, Stefan; Von Bergmann, Kirsten; Menzel, Matthias; Brede, Jens; Kubetzka, André; Wiesendanger, Roland; Bihlmayer, Gustav; Blügel, Stefan (2011). "Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions". Nature Physics. 7 (9): 713–718. Bibcode:2011NatPh...7..713H. doi:10.1038/NPHYS2045. Lay summary (Jul 31, 2011).
14. ^ A. Fert; V. Cros & J. Sampaio (2013). "Skyrmions on the track". Nature Nanotechnology. 8: 152–156. Bibcode:2013NatNa...8..152F. doi:10.1038/nnano.2013.29.
15. ^ Y. Zhou, E. Iacocca, A.A. Awad, R.K. Dumas, F.C. Zhang, H.B. Braun and J. Akerman (2015). "Dynamically stabilized magnetic skyrmions". Nature Communications. 6: 8193. Bibcode:2015NatCo...6E8193Z. doi:10.1038/ncomms9193. PMC . PMID 26351104.
16. ^ X.C. Zhang; M. Ezawa; Y. Zhou (2014). "Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions". Scientific Reports. 5: 9400. arXiv:. Bibcode:2015NatSR...5E9400Z. doi:10.1038/srep09400. PMC . PMID 25802991.
17. ^ Romming, N.; Hanneken, C.; Menzel, M.; Bickel, J. E.; Wolter, B.; Von Bergmann, K.; Kubetzka, A.; Wiesendanger, R. (2013). "Writing and Deleting Single Magnetic Skyrmions". Science. 341 (6146): 636–9. Bibcode:2013Sci...341..636R. doi:10.1126/science.1240573. PMID 23929977. Lay summaryphys.org (Aug 8, 2013).
18. ^ Jiang, Wanjun; Upadhyaya, Pramey; Zhang, Wei; Yu, Guoqiang; Jungfleisch, M. Benjamin; Fradin, Frank Y.; Pearson, John E.; Tserkovnyak, Yaroslav; Wang, Kang L. (2015-07-17). "Blowing magnetic skyrmion bubbles". Science. 349 (6245): 283–286. arXiv:. Bibcode:2015Sci...349..283J. doi:10.1126/science.aaa1442. ISSN 0036-8075. PMID 26067256.
19. ^ D.A. Gilbert, B.B. Maranville, A.L. Balk, B.J. Kirby, P. Fischer, D.T. Pierce, J. Unguris, J.A. Borchers, K. Liu (8 October 2015). "Realization of ground state artificial skyrmion lattices at room temperature". Nature Communications. 6: 8462. Bibcode:2015NatCo...6E8462G. doi:10.1038/ncomms9462. PMC . PMID 26446515. Lay summaryNIST.
20. ^ Gilbert, Dustin A.; Maranville, Brian B.; Balk, Andrew L.; Kirby, Brian J.; Fischer, Peter; Pierce, Daniel T.; Unguris, John; Borchers, Julie A.; Liu, Kai (2015-10-08). "Realization of ground-state artificial skyrmion lattices at room temperature". Nature Communications. 6: 8462. Bibcode:2015NatCo...6E8462G. doi:10.1038/ncomms9462. PMC . PMID 26446515.
21. ^ "A new way to create spintronic magnetic information storage | KurzweilAI". www.kurzweilai.net. October 9, 2015. Retrieved 2015-10-14.