View source for Physics:Spin Hall effect

{{Short description|Transport phenomenon in physics}}
[[File:SpinHallEffect.png|440px|thumbnail|right|Schematic of the spin Hall effect]]
[[File:InverseSpinHall.png|440px|thumbnail|right|Schematic of the inverse spin Hall effect]]
The '''spin Hall effect''' (SHE) is a transport phenomenon predicted by Russian physicists [[Biography:Mikhail Dyakonov|Mikhail I. Dyakonov]] and Vladimir I. Perel<!-- Перель, Владимир Иделевич --> in 1971.<ref name="ref1">{{cite journal | author = M. I. Dyakonov and V. I. Perel | title = Possibility of orientating electron spins with current | journal = Sov. Phys. JETP Lett. | volume = 13 | pages = 467 | year = 1971 | url = http://www.jetpletters.ac.ru/ps/1587/article_24366.shtml | bibcode = 1971JETPL..13..467D }}</ref><ref name="ref2">{{cite journal |author1=M. I. Dyakonov  |author2=V. I. Perel |name-list-style=amp | title = Current-induced spin orientation of electrons in semiconductors | journal =  Phys. Lett. A | volume = 35  | issue = 6| pages = 459 | year = 1971 | doi = 10.1016/0375-9601(71)90196-4|bibcode = 1971PhLA...35..459D }}</ref> It consists of the appearance of [[Physics:Spin|spin]] accumulation on the lateral surfaces of an [[Physics:Electric current|electric current]]-carrying sample, the signs of the spin directions being opposite on the opposing boundaries.  In a cylindrical wire, the current-induced surface spins will wind around the wire. When the current direction is reversed, the directions of spin orientation is also reversed.

== Definition ==
The spin Hall effect is a transport phenomenon consisting of the appearance of spin accumulation on the lateral surfaces of a sample carrying electric current. The opposing surface boundaries will have spins of opposite sign. It is analogous to the classical [[Physics:Hall effect|Hall effect]], where ''charges'' of opposite sign appear on the opposing lateral surfaces in an electric-current  carrying sample in a [[Physics:Magnetic field|magnetic field]]. In the case of the classical Hall effect the charge build up at the boundaries is in compensation for the [[Physics:Lorentz force|Lorentz force]] acting on the charge carriers in the sample due to the magnetic field. No magnetic field is needed for the spin Hall effect which is a purely [[Physics:Spin|spin]]-based phenomenon. The spin Hall effect belongs to the same family as the [[Physics:Hall effect#Anomalous Hall effect|anomalous Hall effect]], known for a long time in [[Physics:Ferromagnet|ferromagnet]]s, which also originates from [[Physics:Spin–orbit interaction|spin–orbit interaction]].

== History ==
The spin Hall effect (direct and inverse) was predicted by Russian physicists Mikhail I. Dyakonov and Vladimir I. Perel<!-- Перель, Владимир Иделевич --> in 1971.<ref name="ref1"/><ref name="ref2"/> They also introduced for the first time the notion of ''spin current''.

In 1983 Averkiev and Dyakonov<ref name="ref3">{{cite journal | author = N. S. Averkiev and M. I. Dyakonov |journal =  Sov. Phys. JETP Lett.| title = Current due to non-homogeneous spin orientation in semiconductors | volume = 35 | pages = 196 | year = 1983}}</ref> proposed a way to measure the inverse spin Hall effect under optical spin orientation in semiconductors.  The first experimental demonstration of the inverse spin Hall effect, based on this idea, was performed by Bakun et al. in 1984<ref name="ref4">{{cite journal | author =  A. A. Bakun |author2=B. P. Zakharchenya |author3=A. A. Rogachev |author4=M. N. Tkachuk |author5=V. G. Fleisher | title = Detection of a surface photocurrent due to electron optical orientation in a semiconductor | journal = Sov. Phys. JETP Lett. | volume = 40 | pages = 1293 | year = 1984 | url = http://www.jetpletters.ac.ru/ps/1262/article_19087.shtml | bibcode =  1984JETPL..40.1293B}}</ref>

The term "spin Hall effect" was introduced by Hirsch<ref name="ref5">{{cite journal | author = J. E. Hirsch | title = Spin Hall Effect | journal = Phys. Rev. Lett. | volume = 83 | issue = 9 | pages = 1834–1837 | year = 1999 | doi =10.1103/PhysRevLett.83.1834 | bibcode=1999PhRvL..83.1834H|arxiv = cond-mat/9906160 | s2cid = 59332923 }}</ref> who re-predicted this effect in 1999.

Experimentally, the (direct) spin Hall effect was observed in [[Physics:Semiconductor|semiconductor]]s<ref name="ref6">{{cite journal | author = Y. Kato |author2=R. C. Myers |author3=A. C. Gossard |author4=D. D. Awschalom  | title = Observation of the Spin Hall Effect in Semiconductors | journal = Science | volume = 306 | issue = 5703 | pages = 1910–1913 | date = 11 November 2004 | url = http://www.sciencemag.org/cgi/content/full/sci;306/5703/1910 | doi = 10.1126/science.1105514 | pmid = 15539563|bibcode = 2004Sci...306.1910K |s2cid=21374868 }}</ref><ref name="ref7">{{cite journal | author =  J. Wunderlich |author2=B. Kaestner |author3=J. Sinova |author4=T. Jungwirth | title = Experimental Observation of the Spin-Hall Effect in a Two-DimensionalSpin-Orbit Coupled Semiconductor System | journal = Phys. Rev. Lett. | volume = 94 | issue = 4| pages = 047204 | year = 2005 | url = http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000094000004047204000001&idtype=cvips&gifs=yes | doi =10.1103/PhysRevLett.94.047204 | pmid = 15783592 | bibcode=2005PhRvL..94d7204W|arxiv = cond-mat/0410295 |s2cid=119357053 }}</ref> more than 30 years after the original prediction.<!-- discovered by Yuichiro Katō (加藤 雄一郎) et al. -->

== Physical origin  ==
Two possible mechanisms give origin to the spin Hall effect, in which an [[Physics:Electric current|electric current]] (composed of moving charges) transforms into a spin current (a current of moving spins without charge flow). The original (extrinsic) mechanism devised by Dyakonov and Perel consisted of spin-dependent [[Physics:Mott scattering|Mott scattering]], where carriers with opposite spin diffuse in opposite directions when colliding with impurities in the material. The second mechanism is due to intrinsic properties of the material, where the carrier's trajectories are distorted due to [[Physics:Spin–orbit interaction|spin–orbit interaction]] as a consequence of the asymmetries in the material.<ref>{{Cite journal|last1=Manchon|first1=A.|last2=Koo|first2=H. C.|last3=Nitta|first3=J.|last4=Frolov|first4=S. M.|last5=Duine|first5=R. A.|date=September 2015|title=New perspectives for Rashba spin–orbit coupling|journal=Nature Materials|language=En|volume=14|issue=9|pages=871–882|doi=10.1038/nmat4360|pmid=26288976|issn=1476-4660|arxiv=1507.02408|bibcode=2015NatMa..14..871M|s2cid=24116488}}</ref>

One can intuitively picture the intrinsic effect by using the classical analogy between an electron and a spinning tennis ball. The tennis ball deviates from its straight path in air in a direction depending on the sense of rotation, also known as the [[Physics:Magnus effect|Magnus effect]]. In a solid, the air is replaced by an effective electric field due to asymmetries in the material, the relative motion between the magnetic moment (associated to the spin) and the electric field creates a coupling that distorts the motion of the electrons.

Similar to the standard Hall effect, both the extrinsic and the intrinsic mechanisms lead to an accumulation of spins of opposite signs on opposing lateral boundaries.

== Mathematical description ==
The spin current is described<ref name="ref1"/><ref name="ref2"/> by a second-rank ''tensor'' {{not a typo|''q''<sub>''ij''</sub>}}, where the first index refers to the direction of flow, and the second one to the spin component that is flowing. Thus {{not a typo|''q''<sub>''xy''</sub>}} denotes the flow density of the ''y''-component of spin in the ''x''-direction. Introduce also the ''vector'' ''q''<sub>''i''</sub> of charge flow density (which is related to the normal current density '''j'''=''e'''''q'''), where ''e'' is the elementary charge. The coupling between spin and charge currents is due to spin-orbit interaction. It may be described in a very simple way<ref name="ref8"/> by introducing a single dimensionless coupling parameter ''ʏ''.

== Spin Hall magnetoresistance ==
{{main|Physics:Spin Hall magnetoresistance}}
No [[Physics:Magnetic field|magnetic field]] is needed for spin Hall effect. However, if a strong enough magnetic field is applied in the direction perpendicular to the orientation of the spins at the surfaces, spins will [[Physics:Precession|precess]] around the direction of the magnetic field and the spin Hall effect will disappear. Thus in the presence of magnetic field, the combined action of the direct and inverse spin Hall effect leads to a change of the sample resistance, an effect that is of second order in spin-orbit interaction. This was noted by Dyakonov and Perel already in 1971<ref name="ref2"/> and later elaborated in more detail by Dyakonov.<ref name="ref8">{{cite journal | author = M. I. Dyakonov | title = Magnetoresistance due to edge spin accumulation | journal =  Phys. Rev. Lett. | volume = 99 | issue = 12| pages = 126601 | year = 2007 | doi = 10.1103/PhysRevLett.99.126601 | pmid = 17930533 | bibcode=2007PhRvL..99l6601D|arxiv = 0705.2738 | s2cid = 22492919 }}</ref> In recent years, the spin Hall magnetoresistance was extensively studied experimentally both in magnetic and non-magnetic materials (heavy metals, such as Pt, Ta, Pd, where the spin-orbit interaction is strong).

== Swapping spin currents ==
A transformation of spin currents consisting in interchanging (''swapping'') of the spin and flow directions (''q''<sub>''ij''</sub> → ''q''<sub>''ji''</sub>) was predicted by Lifshits and Dyakonov.<ref name="ref9">{{cite journal | author = M. B. Lifshits and M. I. Dyakonov | title = Swapping spin currents| journal =  Phys. Rev. Lett. | volume = 103 | issue = 18| pages = 186601 | year = 2009 | doi = 10.1103/PhysRevLett.103.186601 | pmid = 19905821|arxiv = 0905.4469| bibcode = 2009PhRvL.103r6601L| s2cid = 28816808}}</ref> Thus a flow in the ''x''-direction of spins polarized along ''y'' is transformed to a flow in the ''y''-direction of spins polarized along ''x''. This prediction has yet not been confirmed experimentally.

== Optical monitoring==
The direct and inverse spin Hall effect can be monitored by optical means. The spin accumulation induces [[Astronomy:Circular polarization|circular polarization]] of  the emitted [[Physics:Light|light]], as well as  the  [[Physics:Faraday effect|Faraday]] (or Kerr) polarization rotation of the transmitted (or reflected) light. Observing the polarization of emitted light allows the spin Hall effect to be observed.

More recently, the existence of both direct and inverse effects was demonstrated not only in [[Physics:Semiconductor|semiconductor]]s,<ref name="ref10">{{cite journal | author = H. Zhao |author2=E. J. Loren |author3=H. M. van Driel |author4=A. L. Smirl  | title = Coherence Control of Hall Charge and Spin Currents | journal = Phys. Rev. Lett. | volume = 96 | pages = 246601 | year = 2006 | doi = 10.1103/PhysRevLett.96.246601 | pmid = 16907264 | issue = 24 | bibcode=2006PhRvL..96x6601Z}}</ref> but also in [[Chemistry:Metal|metal]]s.<ref name="ref11">{{cite journal | author = E. Saitoh |author2=M. Ueda |author3=H. Miyajima |author4=G. Tatara  | title = Conversion of spin current into charge current at room temperature: inverse spin-Hall effect | journal = Applied Physics Letters | volume = 88 | issue = 18 | pages = 182509 | year = 2006 | doi = 10.1063/1.2199473|bibcode = 2006ApPhL..88r2509S }}</ref><ref name="ref12">{{cite journal | author = S. O. Valenzuela |author2=M. Tinkham  | title = Direct Electronic Measurement of the Spin Hall Effect | journal = Nature | volume = 442 | pages = 176–9 | year = 2006 | doi = 10.1038/nature04937 | pmid = 16838016 | issue = 7099 |arxiv = cond-mat/0605423 |bibcode = 2006Natur.442..176V |s2cid=4304951 }}</ref><ref name="ref13">{{cite journal | author = T. Kimura |author2=Y. Otani |author3=T. Sato |author4=S. Takahashi |author5=S. Maekawa  | title = Room-Temperature Reversible Spin Hall Effect | journal = Phys. Rev. Lett. | volume = 98 | pages = 156601 | year = 2007 | doi = 10.1103/PhysRevLett.98.156601 | pmid = 17501368 | issue = 15 | bibcode=2007PhRvL..98o6601K|arxiv = cond-mat/0609304 |s2cid=38362364 }}</ref>

== Applications ==
The spin Hall effect can be used to manipulate electron spins electrically. For example, in combination with the electric stirring effect, the spin Hall effect leads to spin polarization in a localized conducting region.<ref name="ref14">{{cite journal |author=Yu. V. Pershin |author2=N. A. Sinitsyn |author3=A. Kogan |author4=A. Saxena |author5=D. Smith | title = Spin polarization control by electric stirring: proposal for a spintronic device | journal = Appl. Phys. Lett. | volume = 95 | issue = 2 | pages = 022114 | year = 2009 | arxiv = 0906.0039 | doi = 10.1063/1.3180494|bibcode = 2009ApPhL..95b2114P |s2cid=67771810 |url=https://scholarcommons.sc.edu/phys_facpub/74 }}</ref>

== Further reading ==
For a review of spin Hall effect, see for example: 
* {{Cite book|title=Spin Physics in Semiconductors|volume = 157|last=Dyakonov|first=Mikhail I.|publisher=Springer|year=2008|isbn=978-3-540-78820-1|doi=10.1007/978-3-540-78820-1|series = Springer Series in Solid-State Sciences|bibcode = 2008sps..book.....D|url = https://cds.cern.ch/record/1252258}}

==See also==
*[[Physics:Quantum spin Hall effect|Quantum spin Hall effect]]
*[[Physics:Spin Nernst Effect|Spin Nernst effect]]

== References ==
{{reflist}}

[[Category:Hall effect]]
[[Category:Condensed matter physics]]
[[Category:Spintronics]]

{{Sourceattribution|Spin Hall effect}}