|
|
| Line 1: |
Line 1: |
| {{technical|date=December 2012}}
| | My name is Sung (25 years old) and my hobbies are Backpacking and Locksport.<br><br>Also visit my web page cpap machine ([http://xsnoring.com/ click the up coming website]) |
| In [[condensed matter physics]], '''quantum spin liquid''' is a [[states of matter|state]] that can be achieved in a system of interacting [[quantum spin]]s. The state is referred to as a "liquid" as it is a [[Order and disorder (physics)|disordered]] state in comparison to a [[ferromagnetic]] spin state,<ref name=io9>{{cite news|last=Wilkins|first=Alasdair|title=A Strange New Quantum State of Matter: Spin Liquids|url=http://io9.com/5831111/a-strange-new-quantum-state-of-matter-spin-liquids|accessdate=23 December 2012|newspaper=io9|date=August 15, 2011}}</ref> much in the way liquid water is in a disordered state compared to crystalline ice. However, unlike other disordered states, a quantum spin liquid state preserves its disorder to very low temperatures.<ref name="balents10" />
| |
| | |
| The quantum spin liquid state was first proposed by physicist [[Phil W. Anderson|Phil Anderson]] in 1973 as the ground state for a system of spins on a [[triangular lattice]] that interact with their nearest neighbors via the so-called [[antiferromagnetic]] interaction. Quantum spin liquids generated further interest when in 1987 Anderson proposed a theory that described [[high temperature superconductivity]] in terms of a disordered spin-liquid state.<ref name=mit-3-2011>{{cite news|last=Trafton|first=Anne|title=A new spin on superconductivity?|url=http://web.mit.edu/newsoffice/2011/quantum-spin-liquid-0329.html|accessdate=24 December 2012|newspaper=MIT News|date=March 28, 2011}}</ref>
| |
| A quantum spin liquid state in κ-(BEDT-TTF)<sub>2</sub>Cu<sub>2</sub>(CN)<sub>3</sub> was first thoroughly mapped using [[muon spin spectroscopy]] by a team led by Dr Francis Pratt at [[ISIS neutron source]], UK in March, 2011.<ref name=isisQSL>{{cite web|title=Quantum mapmakers complete first voyage through spin liquid|url=http://www.isis.stfc.ac.uk/science/physics/magnetism/quantum-mapmakers-complete-first-voyage-through-spin-liquid11788.html|work=ISIS neutron and muon source|accessdate=23 August 2013}}</ref>
| |
| | |
| ==Examples==
| |
| Several physical models have a disordered ground state that can be described as a quantum spin liquid.
| |
| | |
| ===Frustrated magnetic moments===
| |
| [[Image:Triangular ising spin.png|right|thumb|130px|Frustrated Ising spins on a triangle.]]
| |
| Localized spins are [[Geometrical frustration|frustrated]] if there exist competing exchange interactions that can not all be satisfied at the same time, leading to a large degeneracy of the system's ground state. A triangle of Ising spins (meaning the only possible orientations of the spins are "up" and "down"), which interact antiferromagnetically, is a simple example for frustration. In the ground state, two of the spins can be antiparallel but the third one cannot. This leads to an increase of possible orientations (six in this case) of the spins in the ground state, enhancing fluctuations and thus suppressing magnetic ordering.<br />
| |
| Some frustrated materials with different lattice structures and their [[Curie temperature|Curie-Weiss temperature]] are listed in the table.<ref name="balents10" /> All of them are proposed spin liquid candidates.
| |
| {| class="wikitable"
| |
| |-
| |
| ! Material !! Lattice !! <math>\Theta _{cw} [K]</math>
| |
| |-
| |
| | κ-(BEDT-TTF)<sub>2</sub>Cu<sub>2</sub>(CN)<sub>3</sub> || anisotropic triangular || -375
| |
| |-
| |
| | ZnCu<sub>3</sub>(OH)<sub>6</sub>Cl<sub>2</sub> ([[herbertsmithite]]) || [[Kagome lattice|Kagome]] || -241
| |
| |-
| |
| | BaCu<sub>3</sub>V<sub>2</sub>O<sub>8</sub>(OH)<sub>2</sub> ([[vesignieite]]) || [[Kagome lattice|Kagome]] ||
| |
| |-
| |
| | Na<sub>4</sub>Ir<sub>3</sub>O<sub>8</sub> || Hyperkagome || -650
| |
| |-
| |
| | Cu-(1,3-benzenedicarboxylate) || [[Kagome lattice|Kagome]] || -33 <ref>''A Structurally Perfect S = 1/2 Metal−Organic Hybrid Kagome Antiferromagnet'' Emily A. Nytko, Joel S. Helton, Peter Müller, and Daniel G. Nocera J. Am. Chem. Soc., 2008, 130 (10), pp 2922–2923 {{DOI|10.1021/ja709991u}}</ref>
| |
| |-
| |
| | Rb<sub>2</sub>Cu<sub>3</sub>SnF<sub>12</sub> || [[Kagome lattice|Kagome]] || <ref>''Pinwheel valence-bond solid and triplet excitations in the two-dimensional deformed kagome lattice'' K. Matan, T. Ono, Y. Fukumoto, T. J. Sato, J. Yamaura, M. Yano, K. Morita & H. Tanaka Nature Physics 6, 865–869 (2010) {{doi|10.1038/nphys1761}}</ref>
| |
| |}
| |
| | |
| ===Resonating valence bonds (RVB)===
| |
| {{main|Resonating valence bond theory}}
| |
| [[Image:Valence bond solid.png|right|thumb|Valence bond solid. The bonds form a specific pattern and consist of pairs of entangled spins.]]
| |
| To build a ground state without magnetic moment, valence bond states can be used, where two
| |
| electron spins form a spin 0 singlet due to the antiferromagnetic interaction. If every spin
| |
| in the system is bound like this, the state of the system as a whole has spin 0 too and is
| |
| non-magnetic. The two spins forming the bond are [[Maximally entangled state|maximally entangled]], while not being
| |
| entangled with the other spins.
| |
| If all spins are distributed to certain localized static bonds, this is called a '''valence bond solid''' (VBS).
| |
| | |
| There are two things that still distinguish a VBS from a spin liquid: First, by ordering the
| |
| bonds in a certain way, the lattice symmetry is usually broken, which is not the case for a spin liquid. Second, this ground state lacks long-range entanglement. To achieve this,
| |
| quantum mechanical fluctuations of the valence bonds must be allowed, leading to a ground
| |
| state consisting of a superposition of many different partitionings of spins into valence
| |
| bonds. If the partitionings are equally distributed (with the same quantum amplitude), there is no preference for any specific
| |
| partitioning ("valence bond liquid"). This kind of ground state wavefunction
| |
| was proposed by [[P. W. Anderson]] in 1973 as the ground state of spin liquids<ref name="anderson73" /> and is called a
| |
| '''resonating valence bond''' (RVB) state. These states are of great theoretical interest as
| |
| they are proposed to play a key role in high-temperature superconductor physics.<ref name="anderson87" />
| |
| | |
| <br /> | |
| <gallery>
| |
| File:Resonating_valence_bond1.png|One possible short-range pairing of spins in a RVB state.
| |
| File:Long_range_valence_bonds.png|Long-range pairing of spins.
| |
| </gallery>
| |
| | |
| ====Excitations====
| |
| [[Image:Spinon moving.png|right|thumb|130px|Spinon moving in spin liquids.]]
| |
| The valence bonds do not have to be formed by nearest neighbors only and their distributions
| |
| may vary in different materials. Ground states with large contributions of long range
| |
| valence bonds have more low-energy spin excitations, as those valence bonds are easier to
| |
| break up. On breaking, they form two free spins. Other excitations rearrange the valence bonds, leading to low-energy excitations even for short-range bonds.
| |
| Very special about spin liquids is, that they support '''exotic excitations''', meaning
| |
| excitations with fractional quantum numbers. A prominent example is the excitation of
| |
| [[spinon]]s which are neutral in charge and carry spin <math> S= 1/2</math>.
| |
| In spin liquids, a spinon is created if one spin is not paired in a valence bond. It can move by rearranging nearby valence bonds at low energy cost.
| |
| | |
| ====Realizations of (stable) RVB states====
| |
| The first discussion of the RVB state on square lattice using the RVB picture<ref>Steven A. Kivelson, Daniel S. Rokhsar, and James P. Sethna , [http://prb.aps.org/abstract/PRB/v35/i16/p8865_1 Phys. Rev. B 35, 8865 (1987)]</ref> only consider nearest neighbour bonds that connect different sub-lattices.
| |
| The constructed RVB state is an equal amplitude superposition of all the nearest-neighbour bond configurations. Such a RVB state is believed to contain emergent gapless <math>U(1)</math> gauge field which may confine the spinons etc. So the equal-amplitude nearest-neighbour RVB state on square lattice is unstable and may describe a critical phase transition point between two stable phases. A version of RVB state which is stable and contains deconfined spinons is the chiral spin state.<ref>
| |
| V. Kalmeyer and R. B. Laughlin,
| |
| ''Equivalence of the resonating-valence-bond and fractional quantum Hall states'',
| |
| Phys. Rev. Lett. '''59''' 2095 (1987)
| |
| </ref><ref>
| |
| Xiao-Gang Wen, F. Wilczek and A. Zee,
| |
| ''Chiral Spin States and Superconductivity'',
| |
| Phys. Rev. B '''39''' 11413 (1989).
| |
| </ref> Later, another version of stable RVB state with deconfined spinons, the Z2 spin liquid, is proposed,<ref>
| |
| N. Read and Subir Sachdev,
| |
| ''Large-N expansion for frustrated quantum antiferromagnets'',
| |
| Phys. Rev. Lett. '''66''' 1773 (1991)
| |
| </ref><ref>
| |
| Xiao-Gang Wen,
| |
| ''Mean Field Theory of Spin Liquid States with Finite Energy Gaps'',
| |
| Phys. Rev. B '''44''' 2664 (1991).
| |
| </ref> which realizes the simplest [[topological order]] -- [[Z2 topological order]]. Both chiral spin state and Z2 spin liquid state have RVB bonds that connect the same sub-lattice.
| |
| In chiral spin state, different bond configurations can have complex amplitudes, while
| |
| in Z2 spin liquid state, different bond configurations only have real amplitudes.
| |
| The RVB state on triangle lattice also realizes the Z2 spin liquid,<ref>R. Moessner, S. L. Sondhi, Phys. Rev. Lett 86, 1881 (2001); arXiv:cond-mat/0205029</ref> where
| |
| different bond configurations only have real amplitudes. The toric code model is yet another realization of
| |
| Z2 spin liquid (and [[Z2 topological order]]) that explicitly breaks the spin rotation symmetry and is exactly soluble.<ref>A. Yu. Kitaev, Annals Phys., 303, 2 (2003); arXiv:quant-ph/9707021</ref>
| |
| | |
| ==Identification in Experiments==
| |
| Since there is no single experimental feature which identifies a material as a spin liquid, several experiments have to be conducted to gain information on different properties which characterize a spin liquid. An indication is given by a large value of the '''frustration parameter''' <math>f > 100</math>, which is defined as
| |
| | |
| <math>
| |
| f = \frac{|\Theta_{cw}|}{T_{c}}
| |
| </math>
| |
| | |
| where <math>\Theta_{cw}</math> is the [[Curie temperature|Curie-Weiss temperature]] and <math>T_{c}</math> is the temperature below which magnetic order begins to develop.
| |
| | |
| One of the most direct evidence for absence of magnetic ordering give [[NMR]] or [[µSR]] experiments. If there is a local magnetic field present, the nuclear or muon spin would be affected which can be measured. <sup>1</sup>H-[[NMR]] measurements <ref name="shimizu03" /> on κ-(BEDT-TTF)<sub>2</sub>Cu<sub>2</sub>(CN)<sub>3</sub> have shown no sign of magnetic ordering down to 32 mK, which is four orders of magnitude smaller than the [[Heisenberg model|coupling constant]] J≈250 K<ref>In literature, the value of J is commonly given in units of temperature (<math>J/k_{B}</math>) instead of energy.</ref> between neighboring spins in this compound.
| |
| Further investigations include:
| |
| * '''Specific heat measurements''' give information about the low-energy density of states, which can be compared to theoretical models.
| |
| * '''Thermal transport measurements''' can determine if excitations are localized or itinerant.
| |
| * '''Neutron scattering''' gives information about the nature of excitations and correlations (e.g. [[spinon]]s).
| |
| * '''Reflectance measurements''' can uncover [[spinon]]s, which couple via emergent gauge fields to the electromagnetic field, giving rise to a power-law optical conductivity.<ref name="ng07" />
| |
| [[Image:Herbertsmithite-herb03a.jpg|thumb|right|200px|[[Herbertsmithite]], the mineral whose ground state was shown to have QSL behaviour]]
| |
| | |
| ===Observation of fractionalization===
| |
| In 2012, Young Lee and his collaborators at MIT and the [[National Institute of Standards and Technology]] artificially developed a crystal of [[herbertsmithite]], a crystal with [[kagome lattice]] ordering, on which they were able to perform [[neutron scattering]] experiments.<ref name=extremetech>{{cite web|last=Anthony|first=Sebastian|title=MIT discovers a new state of matter, a new kind of magnetism|url=http://www.extremetech.com/extreme/143782-mit-discovers-a-new-state-of-matter-a-new-kind-of-magnetism|work=Extremetech|accessdate=23 August 2013}}</ref> The experiments revealed evidence for spin-state [[fractionalization]], a predicted property of quantum spin-liquid type states.<ref name=redorbit>{{cite news|title=Third State Of Magnetism Discovered By MIT Researchers|url=http://www.redorbit.com/news/science/1112752884/magnetism-mit-quantum-spin-liquid-herbertsmithite-122112/|accessdate=24 December 2012|newspaper=Red Orbit|date=December 21, 2012}}</ref> The observation has been described as a hallmark for the quantum spin liquid state in herbertsmithite.<ref name=young-lee-nature>{{cite journal|last=Han|first=Tiang-Heng|coauthors=Young S. Lee, et al.|title=Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet|journal=Nature|year=2012|volume=492|issue=7429|doi=10.1038/nature11659|url=http://www.nature.com/nature/journal/v492/n7429/full/nature11659.html|accessdate=24 December 2012|arxiv = 1307.5047 |bibcode = 2012Natur.492..406H }}</ref> Data indicate that the [[strongly correlated quantum spin liquid]], a specific form of quantum spin liquid, is realized in Herbertsmithite.
| |
| | |
| ==Applications==
| |
| Materials supporting quantum spin liquid states may have applications in data storage and memory.<ref name=gizmodo>{{cite news|last=Aguilar|first=Mario|title=This Weird Crystal Demonstrates a New Magnetic Behavior That Works Like Magic|url=http://gizmodo.com/quantum-spin-liquid/|accessdate=24 December 2012|newspaper=Gizmodo|date=December 20, 2012}}</ref> In particular, it is possible to realize [[topological quantum computation]] by means of spin-liquid states.<ref name=fendley-TQC>{{cite web|last=Fendley|first=Paul|title=Topological Quantum Computation from non-abelian anyons|url=http://rockpile.phys.virginia.edu/trieste08.pdf|publisher=University of Virginia|accessdate=24 December 2012}}</ref> Developments in quantum spin liquids may also help in the understanding of [[high temperature superconductivity]].<ref name=phys.org>{{cite news|last=Chandler|first=David|title=New kind of magnetism discovered: Experiments demonstrate 'quantum spin liquid'|url=http://phys.org/news/2012-12-kind-magnetism-quantum-liquid.html|accessdate=24 December 2012|newspaper=Phys.org|date=December 20, 2012}}</ref>
| |
| | |
| == References ==
| |
| {{Reflist|30em|refs=
| |
| <ref name="balents10">{{cite journal | author=Leon Balents| title=Spin liquids in frustrated magnets| journal=Nature| year=2010| volume=464| pages=199–208|bibcode = 2010Natur.464..199B |doi = 10.1038/nature08917| issue=7286| pmid=20220838}}</ref>
| |
| | |
| <ref name="ng07">{{cite journal | author=T. Ng and P. A. Lee| title=Power-Law Conductivity inside the Mott Gap: Application to κ-(BEDT-TTF)<sub>2</sub>Cu<sub>2</sub>(CN)<sub>3</sub>| journal=Phys. Rev. Lett.| year=2007| volume=99| issue=15| doi=10.1103/PhysRevLett.99.156402| bibcode=2007PhRvL..99o6402N|arxiv = 0706.0050 }}</ref>
| |
| | |
| <ref name="shimizu03">{{cite journal | author=Y. Shimizu, K. Miyagawa, K. Kanoda, M. Maesato, and G. Saito| title=Spin Liquid State in an Organic Mott Insulator with a Triangular Lattice| journal=Phys. Rev. Lett.| year=2003| volume=91| issue=10| doi=10.1103/PhysRevLett.91.107001| bibcode=2003PhRvL..91j7001S|arxiv = cond-mat/0307483 }}</ref>
| |
| | |
| <ref name="anderson73">{{cite journal | author=P. W. Anderson| title=Resonating valence bonds: A new kind of insulator?| journal=Mater. Res. Bull.| year=1973| volume=8| issue=2| doi=10.1016/0025-5408(73)90167-0}}</ref>
| |
| | |
| <ref name="anderson87">{{cite journal | author=P. W. Anderson| title=The resonating valence bond state in La<sub>2</sub>CuO<sub>4</sub> and superconductivity| journal=Science| year=1987| volume=235| issue=4793| pages=1196–1198|bibcode = 1987Sci...235.1196A |doi = 10.1126/science.235.4793.1196| pmid=17818979}}</ref>}}
| |
| | |
| | |
| | |
| <!--- Categories --->
| |
| | |
| [[Category:Articles created via the Article Wizard]]
| |
| [[Category:Liquids]]
| |
| [[Category:Phases of matter]]
| |