Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Observation of spin Coulomb drag in a two-dimensional electron gas


An electron propagating through a solid carries spin angular momentum in addition to its mass and charge. Of late there has been considerable interest in developing electronic devices based on the transport of spin that offer potential advantages in dissipation, size and speed over charge-based devices1. However, these advantages bring with them additional complexity. Because each electron carries a single, fixed value (- e) of charge, the electrical current carried by a gas of electrons is simply proportional to its total momentum. A fundamental consequence is that the charge current is not affected by interactions that conserve total momentum, notably collisions among the electrons themselves2. In contrast, the electron's spin along a given spatial direction can take on two values, ± /2 (conventionally ↑,↓), so that the spin current and momentum need not be proportional. Although the transport of spin polarization is not protected by momentum conservation, it has been widely assumed that, like the charge current, spin current is unaffected by electron–electron (ee) interactions. Here we demonstrate experimentally not only that this assumption is invalid, but also that over a broad range of temperature and electron density, the flow of spin polarization in a two-dimensional gas of electrons is controlled by the rate of ee collisions.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Figure 1: Spin-grating decay at various wavevectors ( q ) and temperatures ( T ) for the sample with Fermi temperature 400 K.
Figure 2: Time dependence of the spin grating's amplitude.
Figure 3: Comparison of motion of spin and charge, for samples with the Fermi temperatures ( T F ) shown.
Figure 4: A representation of e e scattering that does not conserve spin-current.
Figure 5: Relation between suppression of spin diffusion and spin drag resistance.


  1. Awschalom, D. D., Loss, D. & Samarth, N. (eds) Semiconductor Spintronics and Quantum Computation (Springer, Berlin, 2002)

  2. Ziman, J. M. Electrons and Phonons: The Theory of Transport Phenomena in Solids (Oxford Univ. Press, New York, 2001)

    Book  Google Scholar 

  3. Cameron, A. R., Riblet, P. & Miller, A. Spin gratings and the measurement of electron drift mobility in multiple quantum well semiconductors. Phys. Rev. Lett. 76, 4793–4796 (1996)

    Article  ADS  CAS  Google Scholar 

  4. Meier, F. & Zakharchenya, B. Optical Orientation (North-Holland, Amsterdam, 1984)

    Google Scholar 

  5. Bar-Ad, S. & Bar-Joseph, I. Exciton spin dynamics in GaAs heterostructures. Phys. Rev. Lett. 68, 349–352 (1992)

    Article  ADS  CAS  Google Scholar 

  6. Rammer, J. Quantum Transport Theory (Perseus Books, Reading, Massachusetts, 1998)

    MATH  Google Scholar 

  7. Castellani, C., DiCastro, C., Kotliar, G., Lee, P. A. & Strinati, G. Thermal conductivity in disordered interacting-electron systems. Phys. Rev. Lett. 59, 477–480 (1987)

    Article  ADS  CAS  Google Scholar 

  8. Yarlagadda, S. & Giuliani, G. F. Spin susceptibility in a two-dimensional electron gas. Phys. Rev. B 40, 5432–5440 (1989)

    Article  ADS  CAS  Google Scholar 

  9. Kwon, Y., Ceperley, D. M. & Martin, R. M. Quantum Monte Carlo calculation of the Fermi liquid parameters in the two-dimensional electron gas. Phys. Rev. B 50, 1684–1694 (1994)

    Article  ADS  CAS  Google Scholar 

  10. D'Amico, I. & Vignale, G. Spin diffusion in doped semiconductors: The role of Coulomb interactions. Europhys. Lett. 55, 566–572 (2001)

    Article  ADS  CAS  Google Scholar 

  11. Kato, Y. K., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Observation of the spin Hall effect in semiconductors. Science 306, 1910–1913 (2004)

    Article  ADS  CAS  Google Scholar 

  12. Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Experimental observation of the spin Hall effect in a two-dimensional spin-orbit coupled semiconductor system. Phys. Rev. Lett. 94, 047204 (2005)

    Article  ADS  CAS  Google Scholar 

  13. Flensberg, K., Jensen, T. S. & Mortensen, N. A. Diffusion equation and spin drag in spin-polarized transport. Phys. Rev. B 64, 245308 (2001)

    Article  ADS  Google Scholar 

  14. D'Amico, I. & Vignale, G. Spin Coulomb drag in the two-dimensional electron liquid. Phys. Rev. B 68, 045307 (2003)

    Article  ADS  Google Scholar 

  15. Kikkawa, J. M. & Awschalom, D. D. Lateral drag of spin coherence in gallium arsenide. Nature 397, 139–141 (1999)

    Article  ADS  CAS  Google Scholar 

  16. Vohringer, P. & Scherer, N. F. Transient grating optical heterodyne detected impulsive stimulated Raman-scattering in simple liquids. J. Phys. Chem. 99, 2684–2695 (1995)

    Article  Google Scholar 

  17. Chang, Y. J., Cong, P. & Simon, J. D. Optical heterodyne-detection of impulsive stimulated Raman-scattering in liquids. J. Phys. Chem. 99, 7857–7859 (1995)

    Article  CAS  Google Scholar 

  18. Gedik, N. & Orenstein, J. Absolute phase measurement in heterodyne detection of transient gratings. Opt. Lett. 29, 2109–2111 (2004)

    Article  ADS  Google Scholar 

Download references


We thank I. D'Amico and G. Vignale for sending us numerical evaluations of their integral expression for the spin drag resistance. This work was funded by the US DOE, DARPA, and NSFDMR. We also acknowledge support from the Fannie and John Hertz Foundation (C.P.W.) and the Hellman Foundation (J.E.M.).

Author information

Authors and Affiliations


Corresponding author

Correspondence to C. P. Weber.

Ethics declarations

Competing interests

Reprints and permissions information is available at The authors declare no competing financial interests.

Supplementary information

Supplementary Figure 1

The q = 0 spin-relaxation rate as a function of temperature for the sample with Fermi temperature 400 K. (PDF 1061 kb)

Supplementary Discussion

A discussion of the measurement of the q = 0 spin-relaxation rate, and of the derivation of the non-interacting susceptibility of a two-dimensional electron gas. (PDF 46 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Weber, C., Gedik, N., Moore, J. et al. Observation of spin Coulomb drag in a two-dimensional electron gas. Nature 437, 1330–1333 (2005).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing