Spin Hall effect

Short description: Transport phenomenon in physics

Schematic of the spin Hall effect Schematic of the inverse spin Hall effect

The spin Hall effect (SHE) is a transport phenomenon predicted by Russian physicists Mikhail I. Dyakonov and Vladimir I. Perel in 1971.[1][2] It consists of the appearance of spin accumulation on the lateral surfaces of an 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.

## Contents

* 1 Definition
* 2 History
* 3 Physical origin
* 4 Mathematical description
* 5 Spin Hall magnetoresistance
* 6 Swapping spin currents
* 7 Optical monitoring
* 8 Applications
* 9 Further reading
* 10 See also
* 11 References

## Definition

## History

In 1983 Averkiev and Dyakonov[3] 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.[4]

The term "spin Hall effect" was introduced by Hirsch[5] who re-predicted this effect in 1999. Experimentally, the (direct) spin Hall effect was observed in semiconductors[6][7] more than 30 years after the original prediction.[8]

## Physical origin

Two possible mechanisms give origin to the spin Hall effect, in which an 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 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 spin–orbit interaction as a consequence of the asymmetries in the material.[9]

## Mathematical description

The spin current is described[1][2] by a second-rank tensor , 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|qxy} -component of spin in the x-direction. Introduce also the vector qi of charge flow density (which is related to the normal current density j=eq), 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[10] by introducing a single dimensionless coupling parameter ʏ.  The phenomenological equations describing the spin Hall effect and the inverse spin Hall effect were first derived by Dyakonov and Perel in Refs.[1][2] In Refs.,[11][12] a quantum theory of electron spin transport was constructed, suitable for describing effects that arise due to spin-orbit scattering of conduction electrons on defects of the crystal lattice. The theory constructed in [11][12] can be used in studying the anomalous Hall effect, the external spin Hall effect, and the inverse external spin Hall effect.

## Spin Hall magnetoresistance

Main article: Physics:Spin Hall magnetoresistance

No 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 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[2] and later elaborated in more detail by Dyakonov.[10] 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 (qij → qji) was predicted by Lifshits and Dyakonov.[13] 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

More recently, the existence of both direct and inverse effects was demonstrated not only in semiconductors,[14] but also in metals.[15][16][17]

## 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.[18]

## Further reading

For a review of spin Hall effect, see for example:

* Dyakonov, Mikhail I. (2008). Spin Physics in Semiconductors. Springer Series in Solid-State Sciences. 157. Springer. doi:10.1007/978-3-540-78820-1. ISBN 978-3-540-78820-1. Bibcode: 2008sps..book.....D. https://cds.cern.ch/record/1252258.

## See also

* Quantum spin Hall effect
* Spin Nernst effect

## References

1. ↑ 1.0 1.1 1.2 M. I. Dyakonov and V. I. Perel (1971). "Possibility of orientating electron spins with current". Sov. Phys. JETP Lett. 13: 467. Bibcode: 1971JETPL..13..467D. http://www.jetpletters.ac.ru/ps/1587/article_24366.shtml.
2. ↑ 2.0 2.1 2.2 2.3 M. I. Dyakonov; V. I. Perel (1971). "Current-induced spin orientation of electrons in semiconductors". Phys. Lett. A 35 (6): 459. doi:10.1016/0375-9601(71)90196-4. Bibcode: 1971PhLA...35..459D.
3. ↑ N. S. Averkiev and M. I. Dyakonov (1983). "Current due to non-homogeneous spin orientation in semiconductors". Sov. Phys. JETP Lett. 35: 196.
4. ↑ A. A. Bakun; B. P. Zakharchenya; A. A. Rogachev; M. N. Tkachuk; V. G. Fleisher (1984). "Detection of a surface photocurrent due to electron optical orientation in a semiconductor". Sov. Phys. JETP Lett. 40: 1293. Bibcode: 1984JETPL..40.1293B. http://www.jetpletters.ac.ru/ps/1262/article_19087.shtml. Retrieved 2008-06-24.
5. ↑ J. E. Hirsch (1999). "Spin Hall Effect". Phys. Rev. Lett. 83 (9): 1834–1837. doi:10.1103/PhysRevLett.83.1834. Bibcode: 1999PhRvL..83.1834H.
6. ↑ Y. Kato; R. C. Myers; A. C. Gossard; D. D. Awschalom (11 November 2004). "Observation of the Spin Hall Effect in Semiconductors". Science 306 (5703): 1910–1913. doi:10.1126/science.1105514. PMID 15539563. Bibcode: 2004Sci...306.1910K. http://www.sciencemag.org/cgi/content/full/sci;306/5703/1910.
7. ↑ J. Wunderlich; B. Kaestner; J. Sinova; T. Jungwirth (2005). "Experimental Observation of the Spin-Hall Effect in a Two-DimensionalSpin-Orbit Coupled Semiconductor System". Phys. Rev. Lett. 94 (4). doi:10.1103/PhysRevLett.94.047204. PMID 15783592. Bibcode: 2005PhRvL..94d7204W. http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRLTAO000094000004047204000001&idtype=cvips&gifs=yes.
8. ↑ discovered by Yuichiro Katō (加藤 雄一郎) et al.
9. ↑ Manchon, A.; Koo, H. C.; Nitta, J.; Frolov, S. M.; Duine, R. A. (September 2015). "New perspectives for Rashba spin–orbit coupling" (in En). Nature Materials 14 (9): 871–882. doi:10.1038/nmat4360. ISSN 1476-4660. PMID 26288976. Bibcode: 2015NatMa..14..871M.
10. ↑ 10.0 10.1 M. I. Dyakonov (2007). "Magnetoresistance due to edge spin accumulation". Phys. Rev. Lett. 99 (12). doi:10.1103/PhysRevLett.99.126601. PMID 17930533. Bibcode: 2007PhRvL..99l6601D.
11. ↑ 11.0 11.1 Ustinov V. V., Yasyulevich I. A. (2020). "Electron Spin Current and Spin-Dependent Galvanomagnetic Phenomena in Metals". Physics of Metals and Metallography 121 (3): 223–234. doi:10.1134/S0031918X20030072. Bibcode: 2020PMM...121..223U. https://link.springer.com/10.1134/S0031918X20030072.
12. ↑ 12.0 12.1 Ustinov V. V., Yasyulevich I. A., Bebenin N. G. (2023). "Playing Pure Spin Current in Helimagnets: Toward Chiral Spin-Orbitronics". Physics of Metals and Metallography 124 (14): 1745–1767. doi:10.1134/s0031918x23601968. https://link.springer.com/10.1134/S0031918X23601968.
13. ↑ M. B. Lifshits and M. I. Dyakonov (2009). "Swapping spin currents". Phys. Rev. Lett. 103 (18). doi:10.1103/PhysRevLett.103.186601. PMID 19905821. Bibcode: 2009PhRvL.103r6601L.
14. ↑ H. Zhao; E. J. Loren; H. M. van Driel; A. L. Smirl (2006). "Coherence Control of Hall Charge and Spin Currents". Phys. Rev. Lett. 96 (24). doi:10.1103/PhysRevLett.96.246601. PMID 16907264. Bibcode: 2006PhRvL..96x6601Z.
15. ↑ E. Saitoh; M. Ueda; H. Miyajima; G. Tatara (2006). "Conversion of spin current into charge current at room temperature: inverse spin-Hall effect". Applied Physics Letters 88 (18): 182509. doi:10.1063/1.2199473. Bibcode: 2006ApPhL..88r2509S.
16. ↑ S. O. Valenzuela; M. Tinkham (2006). "Direct Electronic Measurement of the Spin Hall Effect". Nature 442 (7099): 176–9. doi:10.1038/nature04937. PMID 16838016. Bibcode: 2006Natur.442..176V.
17. ↑ T. Kimura; Y. Otani; T. Sato; S. Takahashi; S. Maekawa (2007). "Room-Temperature Reversible Spin Hall Effect". Phys. Rev. Lett. 98 (15). doi:10.1103/PhysRevLett.98.156601. PMID 17501368. Bibcode: 2007PhRvL..98o6601K.
18. ↑ Yu. V. Pershin; N. A. Sinitsyn; A. Kogan; A. Saxena; D. Smith (2009). "Spin polarization control by electric stirring: proposal for a spintronic device". Appl. Phys. Lett. 95 (2): 022114. doi:10.1063/1.3180494. Bibcode: 2009ApPhL..95b2114P. https://scholarcommons.sc.edu/phys_facpub/74.

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