Editing Skyrmion

{{short description|Type of topological solutions in non-linear sigma models}}
{{about|the model in particle physics|the vortex-like magnetic structure|magnetic skyrmion}}
In [[particle theory]], the '''skyrmion''' ({{IPAc-en|ˈ|s|k|ɜr|m|i|.|ɒ|n}}) is a topologically stable field configuration of a certain class of non-linear [[sigma model]]s. It was originally proposed as a model of the [[nucleon]] by (and named after) [[Tony Skyrme]] in 1961.<ref>{{Cite journal|last1=Skyrme|first1=T. H. R.|last2=Schonland|first2=Basil Ferdinand Jamieson|date=1961-02-07|title=A non-linear field theory|url=https://royalsocietypublishing.org/doi/10.1098/rspa.1961.0018|journal=Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences|volume=260|issue=1300|pages=127–138|doi=10.1098/rspa.1961.0018|bibcode=1961RSPSA.260..127S|s2cid=122604321|url-access=subscription}}</ref><ref>{{Cite journal |title = A unified field theory of mesons and baryons |journal = Nuclear Physics |last1 = Skyrme |first1 = T. |volume = 31 |pages = 556–569 |year = 1962 |doi = 10.1016/0029-5582(62)90775-7 |bibcode = 1962NucPh..31..556S }}</ref><ref>{{cite book |last1=[[Tony Skyrme]] and [[Gerald E. Brown]] |title=Selected Papers, with Commentary, of Tony Hilton Royle Skyrme |date=1994 |publisher=World Scientific |isbn=978-981-2795-9-22 |pages=456 |url=https://books.google.com/books?id=9gDwymeh0WIC |access-date=4 July 2017}}</ref><ref>Brown, G. E. (ed.) (1994) ''Selected Papers, with Commentary, of Tony Hilton Royle Skyrme''. World Scientific Series in 20th Century Physics: Volume 3. {{ISBN|978-981-4502-43-6}}.</ref> As a [[topological soliton]] in the [[pion]] [[field theory (physics)|field]], it has the remarkable property of being able to model, with reasonable accuracy, multiple low-energy properties of the nucleon, simply by fixing the nucleon radius. It has since found application in [[solid-state physics]], as well as having ties to certain areas of [[string theory]].

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 sphere|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 [[photon]]ic or [[Exciton-polaritons|polariton fluids]] the skyrmion topology corresponds to a full Poincaré beam<ref>{{Cite journal |title = Full Poincaré beams |url = https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-18-10-10777&id=199401 |last1 = Beckley |first1 = A. M. |last2 = Brown |first2 = T. G. |last3 = Alonso |first3 = M. A. |year = 2010 |journal = Opt. Express |doi = 10.1364/OE.18.010777 |volume=18 |issue = 10 |pages=10777–10785 |pmid = 20588931|bibcode = 2010OExpr..1810777B|doi-access = free}}</ref> (a [[Spin (physics)|spin]] [[quantum vortex|vortex]] comprising all the states of [[Polarization (waves)|polarization]] mapped by a stereographic projection of the [[Poincaré sphere (optics)|Poincaré sphere]] to the real plane).<ref>{{Cite journal |title = Twist of generalized skyrmions and spin vortices in a polariton superfluid |last1 = Donati |first1 = S. |last2 = Dominici |first2 = L. |last3 = Dagvadorj |first3 = G. |display-authors = etal |year = 2016 |journal = Proc. Natl. Acad. Sci. USA |doi = 10.1073/pnas.1610123114 |pmid = 27965393 |pmc = 5206528 |volume=113 |issue = 52 |pages=14926–14931 |arxiv = 1701.00157 |bibcode = 2016PNAS..11314926D|doi-access = free }}</ref> A dynamical pseudospin skyrmion results from the stereographic projection of a rotating polariton Bloch sphere in the case of dynamical full Bloch beams.<ref>{{Cite journal | title = Full-Bloch beams and ultrafast Rabi-rotating vortices | author = Dominici | display-authors=etal | journal = Physical Review Research | volume = 3 | pages = 013007  | year = 2021 | issue = 1 | doi = 10.1103/PhysRevResearch.3.013007 | doi-access = free | arxiv = 1801.02580 | bibcode = 2021PhRvR...3a3007D }}</ref><ref>{{cite journal |last1= Dominici|first1= L.|last2= Voronova |first2= N. |last3= Rahmani |first3= A. |display-authors = etal |arxiv= 2202.13210 |title= Coupled quantum vortex kinematics and Berry curvature in real space |journal= Communications Physics|date= 2023|volume= 6|issue= 1|page= 197|doi= 10.1038/s42005-023-01305-x|bibcode= 2023CmPhy...6..197D}}</ref>

Skyrmions have been reported, but not conclusively proven, to appear in [[Bose–Einstein condensate]]s,<ref>{{cite journal |year=2001 |title=Skyrmions in a ferromagnetic Bose–Einstein condensate |journal=[[Nature (journal)|Nature]] |pmid=11418849 |volume= 411 |issue= 6840 |pages=918–920 |doi=10.1038/35082010 |bibcode = 2001Natur.411..918A |last1=Al Khawaja |first1=Usama |last2=Stoof |first2=Henk |arxiv=cond-mat/0011471 |hdl=1874/13699|s2cid=4415343 }}</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.|s2cid=118433956 }}</ref> and 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...2..246F |doi-access=free}}</ref> as well as in free-space optics.<ref>{{Cite journal |last1=Sugic |first1=Danica |last2=Droop |first2=Ramon |last3=Otte |first3=Eileen |last4=Ehrmanntraut |first4=Daniel |last5=Nori |first5=Franco |last6=Ruostekoski |first6=Janne |last7=Denz |first7=Cornelia |last8=Dennis |first8=Mark R. |date=2021-11-22 |title=Particle-like topologies in light |journal=Nature Communications |language=en |volume=12 |issue=1 |pages=6785 |doi=10.1038/s41467-021-26171-5 |issn=2041-1723 |pmc=8608860 |pmid=34811373|arxiv=2107.10810 |bibcode=2021NatCo..12.6785S }}</ref><ref>{{Cite journal |last1=Ehrmanntraut |first1=Daniel |last2=Droop |first2=Ramon |last3=Sugic |first3=Danica |last4=Otte |first4=Eileen |last5=Dennis |first5=Mark R. |last6=Denz |first6=Cornelia |date=2023-06-20 |title=Optical second-order skyrmionic hopfion |url=https://opg.optica.org/abstract.cfm?URI=optica-10-6-725 |journal=Optica |language=en |volume=10 |issue=6 |pages=725 |doi=10.1364/OPTICA.487989 |issn=2334-2536|doi-access=free |bibcode=2023Optic..10..725E }}</ref>

As a model of the [[nucleon]], the topological stability of the skyrmion can be interpreted as a statement that the baryon number is conserved; i.e. that the [[proton]] does not decay. The Skyrme Lagrangian is essentially a one-parameter model of the nucleon. Fixing the parameter fixes the proton radius, and also fixes all other low-energy properties, which appear to be correct to about 30%, a significant level of predictive power.<ref>{{cite journal |last1=Adkins |first1=Gregory S. |last2=Nappi |first2=Chiara R. |last3=Witten |first3=Edward |title=Static Properties of Nucleons in the Skyrme Model |journal=Nucl. Phys. B |date=1983 |volume=228 |pages=552 |doi=10.1016/0550-3213(83)90559-X}}</ref>

Hollowed-out skyrmions form the basis for the [[chiral bag model]] (Cheshire Cat model) of the nucleon. The exact results for the duality between the fermion spectrum and the topological winding number of the non-linear sigma model have been obtained by [[Dan Freed]]. This can be interpreted as a foundation for the duality between a [[quantum chromodynamics]] (QCD) description of the nucleon (but consisting only of quarks, and without gluons) and the Skyrme model for the nucleon.

The skyrmion can be quantized to form a [[quantum superposition]] of baryons and resonance states.<ref>{{cite arXiv |first=Stephen |last=Wong |title=What exactly is a Skyrmion? |eprint=hep-ph/0202250 |year=2002}}</ref> It could be predicted from some nuclear matter properties.<ref>{{cite journal | last1= Khoshbin-e-Khoshnazar | first1 = M. R. |year = 2002 | title = Correlated Quasiskyrmions as Alpha Particles | journal = Eur. Phys. J. A | volume = 14 | issue = 2 | pages = 207–209 | doi = 10.1140/epja/i2001-10198-7 | bibcode = 2002EPJA...14..207K | s2cid = 121791891 }}</ref>

==Topological soliton==
In field theory, skyrmions are [[homotopy|homotopically]] non-trivial classical solutions of a [[nonlinear sigma model]]<ref>D.H. Tchrakian, "Topologically stable lumps in SO(d) gauged O(d+1) sigma models in d dimensions: d=2,3,4", Lett. Math. Phys. 40 (1997) 191-201; F. Navarro-Lerida, E. Radu and D.H. Tchrakian, "On the topological charge of SO(2) gauged Skyrmions in 2+1 and 3+1 dimensions," Phys. Lett. B 791 (2019) 287-292.</ref> 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]]

: <math>\left(\frac{\operatorname{SU}(N)_L \times \operatorname{SU}(N)_R}{\operatorname{SU}(N)_\text{diag}}\right),</math>

where SU(''N'')<sub>''L''</sub> and SU(''N'')<sub>''R''</sub> are the left and right chiral symmetries, and SU(''N'')<sub>diag</sub> is the [[diagonal subgroup]]. In [[nuclear physics]], for ''N'' = 2, the chiral symmetries are understood to be the [[isospin]] symmetry of the nucleon. For ''N'' = 3, the isoflavor symmetry between the up, down and strange [[quark]]s is more broken, and the skyrmion models are less successful or accurate.

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=1006–1007 |bibcode = 1968JAP....39.1006D }}</ref> because the third [[homotopy group]]

: <math>\pi_3\left(\frac{\operatorname{SU}(N)_L \times \operatorname{SU}(N)_R}{\operatorname{SU}(N)_\text{diag}} \cong \operatorname{SU}(N)\right)</math>

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 sector]]s in the quantised model. In (1 + 1)-dimensional spacetime, 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]].

== Lagrangian ==
The [[Lagrangian (field theory)|Lagrangian]] for the skyrmion, as written for the original chiral SU(2) [[effective Lagrangian]] of the nucleon-nucleon interaction (in (3 + 1)-dimensional spacetime), can be written as
: <math>\mathcal{L} =
  \frac{-f^2_\pi}{4}\operatorname{tr}(L_\mu L^\mu) + \frac{1}{32g^2} \operatorname{tr}[L_\mu, L_\nu] [L^\mu, L^\nu],
</math>
where <math>L_\mu = U^\dagger \partial_\mu U</math>, <math>U = \exp i\vec\tau \cdot \vec\theta</math>, <math>\vec\tau</math> are the [[isospin]] [[Pauli matrix|Pauli matrices]], <math>[\cdot, \cdot]</math> is the [[Lie bracket]] commutator, and tr is the matrix trace. The meson field ([[pion]] field, up to a dimensional factor) at spacetime coordinate <math>x</math> is given by <math>\vec\theta = \vec\theta(x)</math>. A broad review of the geometric interpretation of <math>L_\mu</math> is presented in the article on [[sigma model]]s.

When written this way, the <math>U</math> is clearly an element of the [[Lie group]] SU(2), and <math>\vec\theta</math> an element of the [[Lie algebra]] su(2). The pion field can be understood abstractly to be a [[Section (fiber bundle)|section]] of the [[tangent bundle]] of the [[principal fiber bundle]] of SU(2) over spacetime. This abstract interpretation is characteristic of all non-linear sigma models.

The first term, <math>\operatorname{tr}(L_\mu L^\mu)</math> is just an unusual way of writing the quadratic term of the non-linear sigma model; it reduces to <math>-\operatorname{tr}(\partial_\mu U^\dagger \partial^\mu U)</math>. When used as a model of the nucleon, one writes

: <math>U = \frac{1}{f_\pi}(\sigma + i\vec\tau \cdot \vec\pi),</math>

with the dimensional factor of <math>f_\pi</math> being the [[pion decay constant]]. (In 1 + 1 dimensions, this constant is not dimensional and can thus be absorbed into the field definition.)

The second term establishes the characteristic size of the lowest-energy soliton solution; it determines the effective radius of the soliton. As a model of the nucleon, it is normally adjusted so as to give the correct radius for the proton; once this is done, other low-energy properties of the nucleon are automatically fixed, to within about 30% accuracy. It is this result, of tying together what would otherwise be independent parameters, and doing so fairly accurately, that makes the Skyrme model of the nucleon so appealing and interesting. Thus, for example, constant <math>g</math> in the quartic term is interpreted as the [[vector-pion coupling]] ρ–π–π between the [[rho meson]] (the nuclear [[vector meson]]) and the pion; the skyrmion relates the value of this constant to the baryon radius.

==Topological charge or winding number==
The local winding number density (or topological charge density) is given by
: <math>\mathcal{B}^\mu = \epsilon^{\mu\nu\alpha\beta} \operatorname{Tr} \{ L_\nu L_\alpha L_\beta \},</math>

where <math>\epsilon^{\mu\nu\alpha\beta}</math> is the totally antisymmetric [[Levi-Civita symbol]] (equivalently, the [[Hodge star]], in this context).

As a physical quantity, this can be interpreted as the baryon current; it is conserved: <math>\partial_\mu \mathcal{B}^\mu = 0</math>, and the conservation follows as a [[Noether current]] for the chiral symmetry.

The corresponding [[charge (physics)|charge]] is the baryon number:

: <math>B = \int d^3x\, \mathcal{B}^0(x).</math>
Which is conserved due to topological reasons and it is always an integer. For this reason, it is associated with the baryon number of the nucleus. 
As a conserved charge, it is time-independent: <math>dB/dt = 0</math>, the physical interpretation of which is that [[proton decay|protons do not decay]].

In the [[chiral bag model]], one cuts a hole out of the center and fills it with quarks. Despite this obvious "hackery", the total baryon number is conserved: the missing charge from the hole is exactly compensated by the [[spectral asymmetry]] of the vacuum fermions inside the bag.<ref>{{cite journal |author = [[Gerald E. Brown]] and [[Mannque Rho]] |date=March 1979 |title = The little bag |journal = Phys. Lett. B |volume = 82 |issue = 2 |pages = 177–180| doi = 10.1016/0370-2693(79)90729-9 |bibcode = 1979PhLB...82..177B }}</ref><ref>{{cite journal
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==Magnetic materials/data storage==
One particular form of skyrmions is [[magnetic skyrmion]]s, found in magnetic materials that exhibit spiral magnetism due to the [[Dzyaloshinskii–Moriya interaction]], [[double-exchange mechanism]]<ref>{{Cite journal |last1=Azhar |first1=Maria |last2=Mostovoy |first2=Maxim |year=2017 |title=Incommensurate Spiral Order from Double-Exchange Interactions |journal=Physical Review Letters |volume=118 |issue=2 |pages=027203 |arxiv=1611.03689 |doi=10.1103/PhysRevLett.118.027203 |pmid=28128593 |bibcode=2017PhRvL.118b7203A|s2cid=13478577 }}</ref> or competing [[Heisenberg model (quantum)|Heisenberg exchange interactions]].<ref>{{Cite journal |last1=Leonov |first1=A. O. |last2=Mostovoy |first2=M. |date=2015-09-23 |title=Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet |journal=Nature Communications |language=en |volume=6 |doi=10.1038/ncomms9275 |issn=2041-1723 |pmc=4667438 |pmid=26394924 |page=8275 |arxiv=1501.02757 |bibcode=2015NatCo...6.8275L}}</ref> They form "domains" as small as 1&nbsp;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 |first2=Kirsten |last3=Menzel |first3=Matthias |last4=Brede |first4=Jens |last5=Kubetzka |first5=André |last6=Wiesendanger |first6=Roland |author-link6=Roland Wiesendanger |last7=Bihlmayer |first7=Gustav |last8=Blügel |first8=Stefan |issue=9 |bibcode = 2011NatPh...7..713H |s2cid=123676430}}</ref> The small size and low energy consumption of magnetic skyrmions make them a good candidate for future data-storage solutions and other spintronics devices.<ref name=Fert>{{cite journal
 |author1=A. Fert |author2=V. Cros |author3=J. Sampaio
 |year=2013
 |title=Skyrmions on the track
 |journal=Nature Nanotechnology
 |volume=8 |issue=3 |pages=152–156
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 |year=2015
 |title=Dynamically stabilized magnetic skyrmions
 |journal=Nature Communications
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}}</ref><ref name=xichao1>{{cite journal
 |author1=X. C. Zhang |author2=M. Ezawa |author3=Y. Zhou
 |year=2014
 |title=Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions
 |journal=Scientific Reports
 |volume=5 |pages=9400
 |bibcode= 2015NatSR...5E9400Z
 |doi=10.1038/srep09400
 |arxiv = 1410.3086 |pmid=25802991 |pmc=4371840}}</ref>
Researchers could 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. |author-link8=Roland Wiesendanger |journal=Science |volume=341 |issue=6146 |pages=636–639 |pmid=23929977 |bibcode = 2013Sci...341..636R |s2cid=27222755 |url=https://engagedscholarship.csuohio.edu/cgi/viewcontent.cgi?article=1200&context=sciphysics_facpub|url-access=subscription }}
*{{cite web |date=August 8, 2013 |title=Controlling skyrmions for better electronics |website=Phys.org |url=http://phys.org/news/2013-08-skyrmions-electronics.html}}</ref><ref>{{Cite journal |last1=Hsu |first1=Pin-Jui |last2=Kubetzka |first2=André |last3=Finco |first3=Aurore |last4=Romming |first4=Niklas |last5=Bergmann |first5=Kirsten von |last6=Wiesendanger |first6=Roland |title=Electric-field-driven switching of individual magnetic skyrmions |journal=Nature Nanotechnology |volume=12 |issue=2 |pages=123–126 |doi=10.1038/nnano.2016.234 |pmid=27819694 |arxiv=1601.02935 |bibcode=2017NatNa..12..123H |year=2017|s2cid=5921700 }}</ref> The topological charge, representing the existence and non-existence of skyrmions, can represent the bit states "1" and "0". Room-temperature skyrmions were reported.<ref>{{Cite journal |title = Blowing magnetic skyrmion bubbles |journal = Science |date = 2015-07-17 |issn = 0036-8075 |pmid = 26067256 |pages = 283–286 |volume = 349 |issue = 6245 |doi = 10.1126/science.aaa1442 |first1 = Wanjun |last1 = Jiang |first2 = Pramey |last2 = Upadhyaya |first3 = Wei |last3 = Zhang |first4 = Guoqiang |last4 = Yu |first5 = M. Benjamin |last5 = Jungfleisch |first6 = Frank Y. |last6 = Fradin |first7 = John E. |last7 = Pearson |first8 = Yaroslav |last8 = Tserkovnyak |first9 = Kang L. |last9 = Wang |arxiv = 1502.08028 |bibcode = 2015Sci...349..283J |s2cid = 20779848 }}</ref><ref>{{cite journal |author1=D. A. Gilbert |author2=B. B. Maranville |author3=A. L. Balk |author4=B. J. Kirby |author5=P. Fischer |author6=D. T. Pierce |author7=J. Unguris |author8=J. A. Borchers |author9=K. Liu |title=Realization of ground state artificial skyrmion lattices at room temperature |journal=[[Nature Communications]] |volume=6|page=8462|doi=10.1038/ncomms9462 |date=8 October 2015 |bibcode = 2015NatCo...6.8462G |pmid=26446515 |pmc=4633628}}
*{{cite web |date=October 8, 2015 |title=NIST, UC Davis Scientists Float New Approach to Creating Computer Memory |website=[[NIST]] |url=https://www.nist.gov/ncnr/20151008skyrmions.cfm}}</ref>

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). [[Magnetic polarity|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 by suppressing the PMA by a critical [[Ion irradiation|ion-irradiation]] step. The lattices are identified with polarized [[neutron reflectometry]] and have been confirmed by [[magnetoresistance]] measurements.<ref>{{Cite journal |title = Realization of ground-state artificial skyrmion lattices at room temperature |journal = Nature Communications |date = 2015-10-08 |volume = 6 |doi = 10.1038/ncomms9462 |first1 = Dustin A. |last1 = Gilbert |first2 = Brian B. |last2 = Maranville |first3 = Andrew L. |last3 = Balk |first4 = Brian J. |last4 = Kirby |first5 = Peter |last5 = Fischer |first6 = Daniel T. |last6 = Pierce |first7 = John |last7 = Unguris |first8 = Julie A. |last8 = Borchers |first9 = Kai |last9 = Liu |bibcode = 2015NatCo...6.8462G |pages=8462 |pmid=26446515 |pmc=4633628}}</ref><ref>{{Cite web |title = A new way to create spintronic magnetic information storage |url = http://www.kurzweilai.net/a-new-way-to-create-spintronic-magnetic-information-storage |website = KurzweilAI |access-date = 2015-10-14 |date = October 9, 2015}}</ref>

A recent (2019) study<ref>{{Cite journal |last1=Ma |first1=Chuang |last2=Zhang |first2=Xichao |last3=Xia |first3=Jing |last4=Ezawa |first4=Motohiko |last5=Jiang |first5=Wanjun |last6=Ono |first6=Teruo |last7=Piramanayagam |first7=S. N. |last8=Morisako |first8=Akimitsu |last9=Zhou |first9=Yan |date=2018-12-12 |title=Electric Field-Induced Creation and Directional Motion of Domain Walls and Skyrmion Bubbles |journal=Nano Letters |volume=19 |issue=1 |pages=353–361 |language=en |doi=10.1021/acs.nanolett.8b03983 |pmid=30537837 |arxiv=1708.02023|s2cid=54481333 }}</ref> demonstrated a way to move skyrmions, purely using electric field (in the absence of electric current). The authors used Co/Ni multilayers with a thickness slope and Dzyaloshinskii–Moriya interaction and demonstrated skyrmions. They showed that the displacement and velocity depended directly on the applied voltage.<ref>{{Cite AV media |publisher=YouTube |url=https://www.youtube.com/watch?v=3vI76ojMdsA  |archive-url=https://ghostarchive.org/varchive/youtube/20211212/3vI76ojMdsA| archive-date=2021-12-12 |url-status=live|title=Breakthrough in manipulation of skyrmions using electric field |date=2019-03-12 |author=Prem Piramanayagam}}{{cbignore}}</ref>

In 2020, a team of researchers from the [[Swiss Federal Laboratories for Materials Science and Technology]] (Empa) has succeeded for the first time in producing a tunable multilayer system in which two different types of skyrmions – the future bits for "0" and "1" – can exist at room temperature.<ref>{{Cite web|url=https://www.empa.ch/web/s604/skyrmions|title=Empa - Communication - Skyrmions|website=www.empa.ch}}</ref>

== See also ==
* [[Hopfion]], 3D counterpart of skyrmions

==References==
{{reflist|30em}}

==Further reading==
* [https://spectrum.ieee.org/developments-in-magnetic-skyrmions-come-in-bunches Developments in Magnetic Skyrmions Come in Bunches], [[IEEE Spectrum]] 2015 web article
* {{cite book|
last1=Manton|first1=N.|author-link1=Nicholas Manton
|title=Skyrmions - A Theory of Nuclei
|year=2022
|publisher=[[World Scientific]]
|isbn=978-1800612471
}}

{{Particles}}

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[[Category:Hypothetical particles]]
[[Category:Quantum chromodynamics]]