From Wikipedia, the free encyclopedia
  (Redirected from Skyrme model)
Jump to: navigation, search

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[edit]

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

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

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[edit]

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]


  1. ^ At later stages the model was also related to mesons.
  2. ^ Wong, Stephen (2002). "What exactly is a Skyrmion?". arXiv:hep-ph/0202250Freely accessible [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:1108.3562Freely accessible [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:1102.2726Freely accessible. 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:1611.03689Freely accessible. 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 4667438Freely accessible. 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 4579603Freely accessible. 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:1410.3086Freely accessible. Bibcode:2015NatSR...5E9400Z. doi:10.1038/srep09400. PMC 4371840Freely accessible. 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 (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:1502.08028Freely accessible. 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 4633628Freely accessible. 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 4633628Freely accessible. PMID 26446515. 
  21. ^ "A new way to create spintronic magnetic information storage | KurzweilAI". October 9, 2015. Retrieved 2015-10-14. 

Further reading[edit]