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| {{Technical|date=September 2010}}
| | Got nothing to tell about me really.<br>Hurrey Im here and a member of this community.<br>I really wish I am useful at all<br><br>my page; [http://janyaa.org/content/how-use-your-psychic-powers-sell-more-products electronic dog training collar] |
| <!-- {{Standard model of particle physics}} Here it would be essentially inadequate to introduced this well-known graphics! -->
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| In particle theory, the '''skyrmion''' is a hypothetical particle related originally<ref>At later stages the model was also related to [[meson]]s.</ref> to [[baryon]]s. It was described by [[Tony Skyrme]] and consists of a [[quantum superposition]] of baryons and resonance states.<ref>{{cite arXiv|first=Stephen|last=Wong|date=|title=What exactly is a Skyrmion?|class=hep/ph|eprint=hep-ph/0202250|year=2002}}</ref>
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| Skyrmions as topological objects are also important in [[solid state physics]], especially in the emerging technology of [[spintronics]]. A two-dimensional 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 sphere|Bloch point]]" singularity of homotopy degree +1) by a [[stereographic projection]], whereby the positive northpole spin is mapped onto a far-off edge circle of a 2d-disk, while the negative southpole spin is mapped onto the center of the disk.
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| ==Mathematical definition==
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| In field theory, skyrmions are [[homotopy|homotopically]] non-trivial classical solutions of a [[nonlinear sigma model]] with a non-trivial [[target manifold]] topology – hence, they are [[topological soliton]]s. An example occurs in [[chiral model]]s <ref>Chiral models stress the difference between "left-handedness" and "right-handedness".</ref> of mesons, where the target manifold is a [[homogeneous space]] of the [[structure group]]
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| <math>\left(\frac{SU(N)_L\times SU(N)_R}{SU(N)_\text{diag}}\right)</math>
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| where ''SU''(''N'')<sub>''L''</sub> and ''SU''(''N'')<sub>''R''</sub> are the left and right parts of the ''SU''(''N'') matrix, and ''SU''(''N'')<sub>diag</sub> is the [[diagonal subgroup]].
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| If [[spacetime]] has the topology S<sup>3</sup>×'''R''', then classical configurations can be classified by an integral [[winding number]]<ref>The same classification applies to the mentioned effective-spin "hedgehog" singularity": spin upwards at the northpole, but downward at the southpole.<br>See also {{Cite journal|doi=10.1063/1.1656144|title=Point Singularities in Micromagnetism|year=1968|last1=Döring|first1=W.|journal=Journal of Applied Physics|volume=39|issue=2|pages=1006 }}</ref> because the third [[homotopy group]]
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| <math>\pi_3\left(\frac{SU(N)_L\times SU(N)_R}{SU(N)_\text{diag}}\cong SU(N)\right)</math> | |
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| is equivalent to the ring of integers, with the congruence sign referring to [[homeomorphism]].
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| A topological term can be added to the chiral Lagrangian, whose integral depends only upon the [[homotopy class]]; this results in [[superselection sector]]s in the quantised model[[Skyrim|.]] 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]].
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| Skyrmions have been reported, but not conclusively proven, to be in [[Bose–Einstein condensate|Bose-Einstein condensates]],<ref>{{cite journal|year=2001|title=Skyrmions in a ferromagnetic Bose–Einstein condensate|journal=[[Nature (journal)|Nature]]|pmid=11418849|volume= 411|issue= 6840|pages=918–20|doi=10.1038/35082010|bibcode = 2001Natur.411..918A|last1=Al Khawaja|first1=Usama|last2=Stoof|first2=Henk}}</ref> [[superconductors]],<ref>{{Cite arXiv|last=Baskaran|first=G.|eprint=1108.3562|title=Possibility of Skyrmion Superconductivity in Doped Antiferromagnet K$_2$Fe$_4$Se$_5$|class=cond-mat.supr-con|year=2011}}</ref> thin magnetic films<ref>{{cite journal|title=Chiral skyrmions in thin magnetic films: New objects for magnetic storage technologies?|doi=10.1088/0022-3727/44/39/392001|year=2011|journal=Journal of Physics D: Applied Physics|volume=44|issue=39|page=392001|arxiv=1102.2726|bibcode=2011JPhD...44M2001K|last1=Kiselev|first1=N. S.|last2=Bogdanov|first2=A. N.|last3=Schäfer|first3=R.|last4=Rößler|first4=U. K.}}</ref> and also chiral nematic [[liquid crystals]].<ref>{{cite journal|title=Quasi-two-dimensional Skyrmion lattices in a chiral nematic liquid crystal|doi=10.1038/ncomms1250|year=2011|journal=Nature Communications|volume=2|page=246|last1=Fukuda|first1=J.-I.|last2=Žumer|first2=S.|pmid=21427717|bibcode = 2011NatCo...2E.246F }}</ref>
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| ==Skyrmions in an emerging technology==
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| One particular form of the 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 a 1 nm (e.g. in Fe on Ir(111)<ref>{{Cite journal|doi=10.1038/NPHYS2045|title=Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions|year=2011|last1=Heinze|first1=Stefan|last2= Von Bergmann|journal=Nature Physics|volume=7|pages=713–718|layurl=http://www.nature.com/nphys/journal/v7/n9/full/nphys2045.html|laydate=Jul. 31, 2011|first2=Kirsten|last3=Menzel|first3=Matthias|last4=Brede|first4=Jens|last5=Kubetzka|first5=André|last6=Wiesendanger|first6=Roland|last7=Bihlmayer|first7=Gustav|last8=Blügel|first8=Stefan|issue=9}}</ref>). The small size of magnetic skyrmions makes them a good candidate for future data storage solutions. Physicists at the University of Hamburg have managed to read and write skyrmions using scanning tunneling microscopy.<ref>{{Cite journal|doi=10.1126/science.1240573|title=Writing and Deleting Single Magnetic Skyrmions|year=2013|last1=Romming|first1=N.|last2=Hanneken|first2=C.|last3=Menzel|first3=M.|last4=Bickel|first4=J. E.|last5=Wolter|first5=B.|last6=Von Bergmann|first6=K.|last7=Kubetzka|first7=A.|last8=Wiesendanger|first8=R.|journal=Science|volume=341|issue=6146|pages=636–9|pmid=23929977|layurl=http://phys.org/news/2013-08-skyrmions-electronics.html
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| | laysource = phys.org | laydate = Aug 08, 2013 }}</ref> The topological charge, representing the existence and non-existence of skyrmions, can represent the bit states "1" and "0".
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| ==References==
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| {{reflist}}
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| {{Particles}}
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| [[Category:Particle physics]]
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| [[Category:Quantum chromodynamics]]
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Got nothing to tell about me really.
Hurrey Im here and a member of this community.
I really wish I am useful at all
my page; electronic dog training collar