Editing Magnetic monopole (section)

== "Monopoles" in condensed-matter systems ==

Since around 2003, various [[condensed-matter physics]] groups have used the term "magnetic monopole" to describe a different and largely unrelated phenomenon.<ref name=TchernyshyovQuote/><ref name=GibneyQuote/>

A true magnetic monopole would be a new [[elementary particle]], and would violate [[Gauss's law for magnetism]] {{math|∇⋅'''B''' {{=}} 0}}. A monopole of this kind, which would help to explain the law of [[charge quantization]] as formulated by [[Paul Dirac]] in 1931,<ref>"[http://users.physik.fu-berlin.de/~kleinert/files/dirac1931.pdf Quantised Singularities in the Electromagnetic Field]" [[Paul Dirac]], ''Proceedings of the Royal Society'', May 29, 1931. Retrieved February 1, 2014.</ref> has never been observed in experiments.<ref>[http://pdg.lbl.gov/2016/reviews/rpp2016-rev-mag-monopole-searches.pdf Magnetic Monopoles], report from [[Particle data group]], updated August 2015 by D. Milstead and E.J. Weinberg. "To date there have been no confirmed observations of exotic particles possessing magnetic charge."</ref><ref>{{cite journal |title=The search for magnetic monopoles |doi=10.1063/PT.3.3328 |author=Arttu Rajantie |journal=Physics Today |date=2016 |volume=69 |issue=10 |page=40 |quote=Magnetic monopoles have also inspired condensed-matter physicists to discover analogous states and excitations in systems such as spin ices and Bose–Einstein condensates. However, despite the importance of those developments in their own fields, they do not resolve the question of the existence of real magnetic monopoles. Therefore, the search continues.|bibcode=2016PhT....69j..40R |doi-access=free }}</ref>

The monopoles studied by condensed-matter groups have none of these properties. They are not a new elementary particle, but rather are an [[emergent phenomenon]] in systems of everyday particles ([[proton]]s, [[neutron]]s, [[electron]]s, [[photon]]s); in other words, they are [[quasi-particle]]s. They are not sources for the [[magnetic field|{{math|'''B'''}}-field]] (i.e., they do not violate {{math|∇⋅'''B''' {{=}} 0}}); instead, they are sources for other fields, for example the [[magnetic field|{{math|'''H'''}}-field]],<ref name=Castelnovo/> the "{{math|'''B'''*}}-field" (related to [[superfluid]] vorticity),<ref name=Ray/><ref>{{cite journal |doi=10.1103/PhysRevX.7.021023 |title=Experimental Realization of a Dirac Monopole through the Decay of an Isolated Monopole |journal=Phys. Rev. X |date=2017 |author=T. Ollikainen |author2=K. Tiurev |author3=A. Blinova |author4=W. Lee |author5=D. S. Hall |author6=M. Möttönen |volume=7|issue=2 |pages=021023 |arxiv=1611.07766 |bibcode=2017PhRvX...7b1023O |s2cid=54028181 }}</ref> or various other quantum fields.<ref>{{cite journal|last1=Yakaboylu|first1=E.|last2=Deuchert|first2=A.|last3=Lemeshko|first3=M.|date=2017-12-06|title=Emergence of Non-Abelian Magnetic Monopoles in a Quantum Impurity Problem|journal=Physical Review Letters|volume=119|issue=23|pages=235301|doi=10.1103/PhysRevLett.119.235301|pmid=29286703|arxiv=1705.05162|bibcode=2017PhRvL.119w5301Y|s2cid=206304158}}</ref> They are not directly relevant to [[grand unified theories]] or other aspects of particle physics, and do not help explain [[charge quantization]]—except insofar as studies of analogous situations can help confirm that the mathematical analyses involved are sound.<ref name=Gibney/>

There are a number of examples in [[condensed-matter physics]] where collective behavior leads to emergent phenomena that resemble magnetic monopoles in certain respects,<ref name=symmetrymagazine>[http://www.symmetrymagazine.org/breaking/2009/01/29/making-magnetic-monopoles-and-other-exotica-in-the-lab/ Making magnetic monopoles, and other exotica, in the lab], [[Symmetry Breaking]], January 29, 2009. Retrieved January 31, 2009.</ref><ref>{{cite journal |last1=Zhong |first1=Fang |last2=Nagosa |first2=Naoto |last3=Takahashi |first3=Mei S. |last4=Asamitsu |first4=Atsushi |last5=Mathieu |first5=Roland |last6=Ogasawara |first6=Takeshi |last7=Yamada |first7=Hiroyuki |last8=Kawasaki |first8=Masashi |last9=Tokura |first9=Yoshinori |last10=Terakura |first10=Kiyoyuki |year=2003 |title=The Anomalous Hall Effect and Magnetic Monopoles in Momentum Space |journal=Science |volume=302 |issue=5642| pages=92–95 |doi=10.1126/science.1089408 |pmid=14526076 |arxiv=cond-mat/0310232 |bibcode=2003Sci...302...92F |s2cid=41607978 }}</ref><ref>{{Cite journal |doi = 10.1126/science.1167747|pmid = 19179491|arxiv = 0811.1303|bibcode = 2009Sci...323.1184Q|title = Inducing a Magnetic Monopole with Topological Surface States|year = 2009|last1 = Qi|first1 = X.-L.|last2 = Li|first2 = R.|last3 = Zang|first3 = J.|last4 = Zhang|first4 = S.-C.|journal = Science|volume = 323|issue = 5918|pages = 1184–1187|s2cid = 206517194}}</ref><ref>{{cite web|url=https://www.sciencedaily.com/releases/2013/05/130531103910.htm|title=Artificial magnetic monopoles discovered|website=sciencedaily.com}}</ref> including most prominently the [[spin ice]] materials.<ref name=Castelnovo>{{cite journal |last1=Castelnovo |first1=C. |last2=Moessner |first2=R. |last3=Sondhi |first3=S. L. |date=January 3, 2008 |title=Magnetic monopoles in spin ice |journal=Nature |arxiv=0710.5515 |bibcode=2008Natur.451...42C |doi=10.1038/nature06433 |volume=451 |issue=7174 |pages=42–45 |pmid=18172493|s2cid=2399316 }}</ref><ref name=Bramwell>{{cite journal |last1=Bramwell |first1=S. T. |last2=Giblin |first2=S. R. |last3=Calder |first3=S. |last4=Aldus |first4=R. |last5=Prabhakaran |first5=D. |last6=Fennell |first6=T. |date=15 October 2009 |title=Measurement of the charge and current of magnetic monopoles in spin ice |journal=Nature |doi=10.1038/nature08500 |pmid=19829376 |arxiv=0907.0956 |bibcode=2009Natur.461..956B |volume=461 |issue=7266 |pages=956–959 |s2cid=4399620 }}</ref> While these should not be confused with hypothetical elementary monopoles existing in the vacuum, they nonetheless have similar properties and can be probed using similar techniques.

Some researchers use the term '''magnetricity''' to describe the manipulation of magnetic monopole quasiparticles in [[spin ice]],<ref name="monopole">{{cite web |url=https://www.sciencedaily.com/releases/2009/10/091015085916.htm |title='Magnetricity' Observed And Measured For First Time |website=[[Science Daily]] |date=15 October 2009 |access-date=10 June 2010 }}</ref><ref name="MonopoleReview">{{cite journal |author=M.J.P. Gingras |year=2009 |title=Observing Monopoles in a Magnetic Analog of Ice |journal=Science |volume=326 |issue=5951 |pages=375–376 |doi=10.1126/science.1181510 |pmid=19833948|arxiv=1005.3557 |s2cid=31038263 }}</ref><ref name=Bramwell /><ref name=Giblin /> in analogy to the word "electricity".

One example of the work on magnetic monopole quasiparticles is a paper published in the journal ''[[Science (journal)|Science]]'' in September 2009, in which researchers described the observation of [[quasiparticle]]s resembling magnetic monopoles. A single crystal of the [[spin ice]] material [[dysprosium titanate]] was cooled to a temperature between 0.6 [[kelvin]] and 2.0 kelvin. Using observations of [[neutron scattering]], the magnetic moments were shown to align into interwoven tubelike bundles resembling [[Dirac string]]s. At the [[crystallographic defect|defect]] formed by the end of each tube, the magnetic field looks like that of a monopole. Using an applied magnetic field to break the symmetry of the system, the researchers were able to control the density and orientation of these strings. A contribution to the [[heat capacity]] of the system from an effective gas of these quasiparticles was also described.<ref name=sciencedaily>
{{cite web
 |url=https://www.sciencedaily.com/releases/2009/09/090903163725.htm
 |title=Magnetic Monopoles Detected in a Real Magnet for the First Time
 |publisher=[[Science Daily]]
 |date=September 4, 2009
 |access-date=September 4, 2009
}}</ref><ref>
{{cite journal
 |doi=10.1126/science.1178868
 |title=Dirac Strings and Magnetic Monopoles in Spin Ice Dy<sub>2</sub>Ti<sub>2</sub>O<sub>7</sub>
 |author1=D.J.P. Morris |author2=D.A. Tennant |author3=S.A. Grigera |author4=B. Klemke |author5=C. Castelnovo |author6=R. Moessner |author7=C. Czter-nasty |author8=M. Meissner |author9=K.C. Rule |author10=J.-U. Hoffmann |author11=K. Kiefer |author12=S. Gerischer |author13=D. Slobinsky |author14=R.S. Perry  |name-list-style=amp
 |journal=[[Science (journal)|Science]]
 |orig-date=2009-07-09
 |date=September 3, 2009
 |bibcode = 2009Sci...326..411M
 |pmid=19729617|arxiv = 1011.1174
 |volume=326
 |issue=5951
 |pages=411–4
 |s2cid=206522398
}}</ref>
This research went on to win the 2012 Europhysics Prize for condensed matter physics.

In another example, a paper in the February 11, 2011 issue of ''[[Nature Physics]]'' describes creation and measurement of long-lived magnetic monopole quasiparticle currents in spin ice. By applying a magnetic-field pulse to crystal of dysprosium titanate at 0.36 K, the authors created a relaxing magnetic current that lasted for several minutes. They measured the current by means of the electromotive force it induced in a solenoid coupled to a sensitive amplifier, and quantitatively described it using a chemical kinetic model of point-like charges obeying the Onsager–Wien mechanism of carrier dissociation and recombination. They thus derived the microscopic parameters of monopole motion in spin ice and identified the distinct roles of free and bound magnetic charges.<ref name=Giblin>{{cite journal |last1=Giblin |first1=S. R. |last2=Bramwell |first2=S. T. |last3=Holdsworth |first3=P. C. W. |last4=Prabhakaran |first4=D. |last5=Terry |first5=I. |date=February 13, 2011 |title=Creation and measurement of long-lived magnetic monopole currents in spin ice |journal=[[Nature Physics]] |doi=10.1038/nphys1896 |bibcode=2011NatPh...7..252G |volume=7 |issue=3 |pages=252–258}}</ref>

In [[superfluid]]s, there is a field {{math|'''B'''*}}, related to superfluid vorticity, which is mathematically analogous to the magnetic {{math|'''B'''}}-field. Because of the similarity, the field {{math|'''B'''*}} is called a "synthetic magnetic field". In January 2014, it was reported that monopole quasiparticles<ref>{{cite journal |last1=Pietilä |first1=Ville |last2=Möttönen |first2=Mikko |year=2009 |title=Creation of Dirac Monopoles in Spinor Bose–Einstein Condensates |journal=Phys. Rev. Lett. |volume=103 |issue=3 |page=030401 |doi=10.1103/physrevlett.103.030401 |arxiv=0903.4732 |bibcode=2009PhRvL.103c0401P |pmid=19659254}}</ref> for the {{math|'''B'''*}} field were created and studied in a spinor Bose–Einstein condensate.<ref name=Ray/> This constitutes the first example of a quasi-magnetic monopole observed within a system governed by quantum field theory.<ref name=Gibney>{{cite journal |doi=10.1038/nature.2014.14612 |author=Elizabeth Gibney |journal=Nature |date=29 January 2014 |title=Quantum cloud simulates magnetic monopole|s2cid=124109501 }}</ref>

Updates to the theoretical and experimental searches in matter can be found in the reports by G. Giacomelli (2000) and by S. Balestra (2011) in the Bibliography section.