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

$\left(\frac{SU(N)_L\times SU(N)_R}{SU(N)_\text{diag}}\right)$

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 S³Ã—R, then classical configurations can be classified by an integral winding number^[5] because the third homotopy group

$\pi_3\left(\frac{SU(N)_L\times SU(N)_R}{SU(N)_\text{diag}}\cong SU(N)\right)$

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]

External links

• Developments in Magnetic Skyrmions Come in Bunches, IEEE Spectrum 2015 web article

References

1. At later stages the model was also related to mesons.
2. Wong, Stephen (2002). "What exactly is a Skyrmion?". arXiv:hep-ph/0202250 [hep/ph].
3. M.R.Khoshbin-e-Khoshnazar,"Correlated Quasiskyrmions as Alpha Particles",Eur.Phys.J.A 14,207-209 (2002).
4. Chiral models stress the difference between "left-handedness" and "right-handedness".
5. 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.
6. 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.
7. Baskaran, G. (2011). "Possibility of Skyrmion Superconductivity in Doped Antiferromagnet K₂Fe₄Se₅". arXiv:1108.3562 [cond-mat.supr-con].
8. 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:1102.2726. Bibcode:2011JPhD...44M2001K. doi:10.1088/0022-3727/44/39/392001.
9. 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.
10. 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).
11. A. Fert, V. Cros, and J. Sampaio (2013). "Skyrmions on the track". Nature Nanotechnology 8: 152–156. doi:10.1038/nnano.2013.29.
12. 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. doi:10.1038/ncomms9193.
13. X.C. Zhang, M. Ezawa, Y. Zhou (2014). "Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions". Scientific Reports 5: 9400. doi:10.1038/srep09400.
14. 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 summary – phys.org (Aug 8, 2013).
15. 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. doi:10.1126/science.aaa1442. ISSN 0036-8075. PMID 26067256.
16. 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. doi:10.1038/ncomms9462. Lay summary – NIST.
17. 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. doi:10.1038/ncomms9462.
18. "A new way to create spintronic magnetic information storage | KurzweilAI". www.kurzweilai.net. October 9, 2015. Retrieved 2015-10-14.