Skip to main content
SpringerLink
Log in
Book cover

Spin Physics in Semiconductors pp 211–243Cite as

Spin Hall Effect

  • Chapter

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 157))

Abstract

Since the electrons have an internal degree of freedom, spin, they are characterized not only by charge density and electric current, but also by spin density and spin current. The spin current is described by a tensor q ij , where the first index indicates the direction of flow, while the second one says which component of the spin is flowing. Thus, if all electrons with concentration n are completely spin-polarized along z and move with a velocity v in the x direction, the only non-zero component of q ij is q xz = nv.1

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.I. Dyakonov, V.I. Perel, Pis’ma Z. Eksp. Teor. Fiz. 13, 657 (1971); JETP Lett. 13, 467 (1971)

    ADS  Google Scholar 

  2. M.I. Dyakonov, V.I. Perel, Phys. Lett. A 35, 459 (1971)

    Article  ADS  Google Scholar 

  3. H. Senftleben, Z. Phys. 31, 822 (1930)

    Google Scholar 

  4. H. Senftleben, Z. Phys. 31, 961 (1930)

    Google Scholar 

  5. C.J. Gorter, Naturwissenschaften. 26, 140 (1938)

    Article  ADS  Google Scholar 

  6. L. Gorelik, Pis’ma Z. Eksp. Teor. Fiz. 33, 403 (1981); Sov. Phys. JETP Lett. 33, 387 (1981)

    ADS  Google Scholar 

  7. N.S. Averkiev, M.I. Dyakonov, Pis’ma Z. Eksp. Teor. Fiz. 35, 196 (1982); Sov. Phys. JETP Lett. 35, 242 (1982)

    ADS  Google Scholar 

  8. M.I. Dyakonov, Phys. Rev. Lett. 99, 126601 (2007)

    Article  ADS  Google Scholar 

  9. E.H. Hall, Philos. Mag. 10, 301 (1880)

    Google Scholar 

  10. E.H. Hall, Philos. Mag. 12, 157 (1881)

    Google Scholar 

  11. J. Smit, Physica. 17, 612 (1951)

    Article  ADS  Google Scholar 

  12. J. Smit, Physica. 21, 877 (1955)

    Article  ADS  Google Scholar 

  13. J. Smit, Physica. 24, 29 (1958)

    ADS  Google Scholar 

  14. R. Karplus, J.M. Luttinger, Phys. Rev. 95, 1154 (1954)

    Article  MATH  ADS  Google Scholar 

  15. J.N. Chazalviel, I. Solomon, Phys. Rev. Lett. 29, 1676 (1972)

    Article  ADS  Google Scholar 

  16. M.I. Miah, J. Phys. D: Appl. Phys. 40, 1659 (2007)

    Article  ADS  Google Scholar 

  17. N.S. Averkiev, M.I. Dyakonov, Fiz. Tekh. Poluprovodn. 17, 629 (1983); Sov. Phys. Semicond. 17, 393 (1983)

    Google Scholar 

  18. A.A. Bakun, B.P. Zakharchenya, A.A. Rogachev, M.N. Tkachuk, V.G. Fleisher, Pis’ma Z. Eksp. Teor. Fiz. 40, 464 (1984); Sov. Phys. JETP Lett. 40, 1293 (1984)

    ADS  Google Scholar 

  19. M.N. Tkachuk, B.P. Zakharchenya, V.G. Fleisher, Z. Eksp. Teor. Fiz. Pis’ma 44, 47 (1986); Sov. Phys. JETP Lett. 44, 59 (1986)

    ADS  Google Scholar 

  20. J.E. Hirsh, Phys. Rev. Lett. 83, 1834 (1999)

    Article  ADS  Google Scholar 

  21. Y.K. Kato, R.C. Myers, A.C. Gossard, D.D. Awschalom, Science 306, 1910 (2004)

    Article  ADS  Google Scholar 

  22. J. Wunderlich et al., Phys. Rev. Lett. 94, 047204 (2005)

    Article  ADS  Google Scholar 

  23. J. Shi, P. Zhang, D. Xiao, Q. Niu, Phys. Rev. Lett. 96, 076604 (2006)

    Article  ADS  Google Scholar 

  24. M.I. Dyakonov, A.V. Khaetskii, Z. Eksp. Teor. Fiz. 86, 1843 (1984); Sov. Phys. JETP 59, 1072 (1984)

    Google Scholar 

  25. A.V. Khaetskii, Fiz. Tekh. Poluprovodn 18, 1744 (1984); Sov. Phys. Semicond. 18, 1091 (1984)

    Google Scholar 

  26. N.F. Mott, H.S.W. Massey, The Theory of Atomic Collisions, 3rd edn. (Clarendon Press, Oxford, 1965)

    Google Scholar 

  27. M.I. Dyakonov, V.I. Perel, Fiz. Tekh. Poluprov. 10, 350 (1976); Sov. Phys. Semicond. 10, 208 (1976)

    Google Scholar 

  28. D.A. Abanin, A.V. Shytov, L.S. Levitov, B.I. Halperin, Nonlocal charge transport mediated by spin diffusion in the Spin-Hall Effect, arXiv:0708.0455 (2007)

    Google Scholar 

  29. E.L. Ivchenko, G.E. Pikus, Sov. Phys. JETP Lett. 27, 604 (1978)

    ADS  Google Scholar 

  30. V.I. Belinicher, Phys. Lett. A 66, 213 (1978)

    Article  ADS  Google Scholar 

  31. V.I. Belinicher, B.I. Sturman, Usp. Fiz. Nauk 130, 415 (1980)

    Google Scholar 

  32. V.M. Asnin, A.A. Bakun, A.M. Danishevskii, E.L. Ivchenko, G.E. Pikus, A.A. Rogachev, Solid State Commun. 30, 565 (1979)

    Article  ADS  Google Scholar 

  33. M.I. Dyakonov, V.Yu. Kachorovskii, Sov. Phys. Semicond. 20, 110 (1986)

    Google Scholar 

  34. Y.A. Bychkov, E.I. Rashba, J. Phys. C 17, 6039 (1984)

    Article  ADS  Google Scholar 

  35. V.K. Kalevich, V.I. Korenev, I.A. Merkulov, Solid State Commun. 91, 559 (1994)

    Article  ADS  Google Scholar 

  36. N.A. Sinitsyn, J. Phys. Condens. Matter. 20, 023201 (2008); arXiv:0712.0183

    Article  ADS  Google Scholar 

  37. H.-A. Engel, E.I. Rashba, B.I. Halperin, Handbook of Magnetism and Advanced Magnetic Materials, vol. 5 (Wiley, New York, 2006), p. 2858; arXiv:cond-mat/0603306

    Google Scholar 

  38. N.F. Mott, Proc. R. Soc. A 124, 425 (1929)

    Article  ADS  Google Scholar 

  39. L. Berger, Phys. Rev. B 2, 4559 (1970)

    Article  ADS  Google Scholar 

  40. L. Berger, Phys. Rev. B 6, 1862 (1972)

    Article  ADS  Google Scholar 

  41. L.D. Landau, E.M. Lifshits, Quantum Mechanics. Non-relativistic Theory, 3rd edn. (Elsevier Science, Oxford, 1977)

    Google Scholar 

  42. V.N. Abakumov, I.N. Yassievich, Z. Eksp. Teor. Fiz. 61, 2571 (1971); Sov. Phys. JETP 34, 1375 (1971)

    Google Scholar 

  43. P. Nozières, C. Lewiner, J. Phys. (Paris) 34, 901 (1973)

    Google Scholar 

  44. S.K. Lyo, T. Holstein, Phys. Rev. Lett. 29, 423 (1972)

    Article  ADS  Google Scholar 

  45. V.F. Gantmakher, Y.B. Levinson, Carrier Scattering in Metals and Semiconductors (North-Holland, Amsterdam, 1987)

    Google Scholar 

  46. S. Murakami, N. Nagaosa, S.-C. Zhang, Science 301, 1348 (2003)

    Article  ADS  Google Scholar 

  47. J. Sinova, D. Culcer, Q. Niu, N.A. Sinitsyn, T. Jungwirth, A.H. MacDonald, Phys. Rev. Lett. 92, 126603 (2004)

    Article  ADS  Google Scholar 

  48. E.G. Mishchenko, A.V. Shytov, B.I. Halperin, Phys. Rev. Lett. 93, 226602 (2004)

    Article  ADS  Google Scholar 

  49. O.V. Dimitrova, Phys. Rev. B 71, 245327 (2005)

    Article  ADS  Google Scholar 

  50. R. Winkler, Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, Berlin, 2003)

    Google Scholar 

  51. A.V. Shytov, E.G. Mishchenko, H.-A. Engel, B.I. Halperin, Phys. Rev. B 73, 075316 (2006)

    Article  ADS  Google Scholar 

  52. A. Khaetskii, Phys. Rev. B 73, 115323 (2006)

    Article  ADS  Google Scholar 

  53. V.A. Zyuzin, P.G. Silvestrov, E.G. Mishchenko, Phys. Rev. Lett. 99, 106601 (2007)

    Article  ADS  Google Scholar 

  54. A.V. Khaetskii, E.V. Sukhorukov, to be published

    Google Scholar 

  55. V. Sih, V.H. Lau, R.C. Myers, V.R. Horowitz, A.C. Goassard, D.D. Awschalom, Phys. Rev. Lett. 97, 096605 (2006)

    Article  ADS  Google Scholar 

  56. K. Nomura, J. Wunderlich, J. Sinova, B. Kaestner, A.H. MacDonald, T. Jungwirth, Phys. Rev. B 72, 245330 (2005)

    Article  ADS  Google Scholar 

  57. V. Sih, R.C. Myers, Y.K. Kato, W.H. Lau, A.C. Gossard, D.D. Awschalom, Nat. Phys. 1, 31 (2005)

    Article  Google Scholar 

  58. S.O. Valenzuela, M. Tinkham, Nature 442, 176 (2006)

    Article  ADS  Google Scholar 

  59. T. Kimura, Y. Otani, T. Sato, S. Takahashi, S. Maekawa, Phys. Rev. Lett. 98, 156601 (2007)

    Article  ADS  Google Scholar 

  60. N.P. Stern, S. Ghosh, G. Xiang, M. Zhu, N. Samarth, D.D. Awschalom, Phys. Rev. Lett. 97, 126603 (2006)

    Article  ADS  Google Scholar 

  61. M.I. Dyakonov, V.I. Perel, Decay of atomic polarization moments, in: Proc. 6th Intern. Conf. on Atomic Physics, Riga, 1978, pp. 410

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique Théorique, et Astroparticules Université Montpellier II, CNRS, Place E. Bataillon, 34090, Montpellier, France

    M. I. Dyakonov

  2. Institute of Microelectronics, Technology Russian Academy of Sciences, 142432, Chernogolovka, Moscow District, Russia

    A. V. Khaetskii

Authors
  1. M. I. Dyakonov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Khaetskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratoire de Physique Théorique et Astroparticules, cc 070 Université Montpellier II, 34095, Montpellier, France

    Michel I. Dyakonov

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Dyakonov, M.I., Khaetskii, A.V. (2008). Spin Hall Effect. In: Dyakonov, M.I. (eds) Spin Physics in Semiconductors. Springer Series in Solid-State Sciences, vol 157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78820-1_8

Download citation

Publish with us

Policies and ethics

Search

Navigation