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Two-dimensional geometry of spin excitations in the high-transition-temperature superconductor YBa2Cu3O6+x

Nature volume 430, pages 650654 (05 August 2004) | Download Citation



The fundamental building block of the copper oxide superconductors is a Cu4O4 square plaquette. The plaquettes in most of these materials are slightly distorted to form a rectangular lattice, for which an influential theory predicts that high-transition-temperature (high-Tc) superconductivity is nucleated in ‘stripes’ aligned along one of the axes1,2,3. This theory received strong support from experiments that indicated a one-dimensional character for the magnetic excitations in the high-Tc material YBa2Cu3O6.6 (ref. 4). Here we report neutron scattering data on ‘untwinned’ YBa2Cu3O6+x crystals, in which the orientation of the rectangular lattice is maintained throughout the entire volume. Contrary to the earlier claim4, we demonstrate that the geometry of the magnetic fluctuations is two-dimensional. Rigid stripe arrays therefore appear to be ruled out over a wide range of doping levels in YBa2Cu3O6+x, but the data may be consistent with liquid-crystalline stripe order5. The debate about stripes has therefore been reopened.

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  1. 1.

    & Charged magnetic domain lines and the magnetism of high-Tc oxides. Phys. Rev. B 40, 7391–7394 (1989)

  2. 2.

    & Frustrated electronic phase separation and high-temperature superconductors. Physica C 209, 597–621 (1993)

  3. 3.

    , , , & Evidence for stripe correlations of spins and holes in copper oxide superconductors. Nature 375, 561–563 (1995)

  4. 4.

    , , & One-dimensional nature of the magnetic fluctuations in YBa2Cu3O6.6. Nature 404, 729–731 (2000)

  5. 5.

    , & Electronic liquid-crystal phases of a doped Mott insulator. Nature 393, 550–553 (1998)

  6. 6.

    et al. How to detect fluctuating stripes in the high-temperature superconductors. Rev. Mod. Phys. 75, 1201–1241 (2003)

  7. 7.

    et al. Spin fluctuations in YBa2Cu3O6.6. Nature 395, 580–582 (1998)

  8. 8.

    et al. Doping dependence of the spatially modulated dynamical spin correlations and the superconducting transition temperature in La2-xSrxCuO4. Phys. Rev. B 57, 6165–6172 (1998)

  9. 9.

    et al. Incommensurate spin dynamics of underdoped superconductor YBa2Cu3O6.7. Phys. Rev. Lett. 83, 608–611 (1999)

  10. 10.

    et al. The spin excitation spectrum in superconducting YBa2Cu3O6.85. Science 288, 1234–1237 (2000)

  11. 11.

    Reznik, D. et al. Dispersion of magnetic excitations in superconducting optimally doped YBa2Cu3O6.95. Preprint at 〈〉 (2003).

  12. 12.

    et al. Dynamic stripes and resonance in the superconducting and normal phases of YBa2Cu3O6.5 ortho-II superconductor. Phys. Rev. B 69, 014502 (2004)

  13. 13.

    , & Unified description of the resonance peak and incommensuration in high-Tc superconductors. Phys. Rev. B 64, 172508 (2001)

  14. 14.

    & Spin dynamics of stripes. Phys. Rev. B 67, 134512 (2003)

  15. 15.

    Fine, B. V. Hypothesis of two-dimensional stripe arrangement and its implications for the superconductivity in high-Tc cuprates. Preprint at 〈〉 (2003)

  16. 16.

    & Renormalized mean-field theory of neutron scattering in cuprate superconductors. Phys. Rev. B 65, 014502 (2001)

  17. 17.

    & Spin dynamics of a two-dimensional metal in a superconducting state: Application to the high-Tc cuprates. Phys. Rev. B 65, 054515 (2002)

  18. 18.

    , , & LDA energy bands, low-energy Hamiltonians, t′, t″, tperp(k) and Jperp(k). J. Phys. Chem. Solids 56, 1573–1591 (1995)

  19. 19.

    , & In-plane charge modulation below Tc and charge density-wave correlations in the chain layer in YBa2Cu3O7. Phys. Rev. Lett. 85, 1310–1313 (2000)

  20. 20.

    Feng, D. L. et al. Zooming-in on the charge ordering in YBa2Cu3O6.5. Preprint at 〈〉 (2004)

  21. 21.

    & Possible quasi-one-dimensional Fermi surface in La2-xSrxCuO4. J. Phys. Soc. Jpn 69, 332–335 (2000)

  22. 22.

    & D-wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model. Phys. Rev. Lett. 85, 5162–5165 (2000)

  23. 23.

    , & Quantum theory of a nematic Fermi liquid. Phys. Rev. B 64, 195109 (2001)

  24. 24.

    , , & Superconductivity-induced effects on phononic and electronic Raman scattering in twin-free YBa2Cu3O7-x single crystals. Phys. Rev. B 61, 12412–12419 (2000)

  25. 25.

    et al. Superconducting gap and strong in-plane anisotropy in untwinned YBa2Cu3O7-δ. Phys. Rev. Lett. 86, 4370–4373 (2001)

  26. 26.

    , & Growth of large and untwinned single crystals of YBCO. Physica C 195, 291–300 (1992)

  27. 27.

    & Thermomechanical detwinning of YBa2Cu3O7-x single crystals under reduced oxygen partial pressure. Physica C 218, 175–180 (1993)

  28. 28.

    On the resolution of slow-neutron spectrometers. IV. The triple-axis spectrometer resolution function, spatial effects included. Acta Crystallogr. A 31, 507–513 (1975)

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We thank B. Hennion, S. Kivelson, D. Manske, W. Metzner and H. Yamase for discussions, S. Lacher, H. Wendel, B. Baum and M. Bakr for crystal preparation, M. Ohl and W. Plenert for the design and manufacturing of the sample holder, H. Bender, C. Busch and H. Klann for technical support, and P. Baroni for technical support at the 2T spectrometer. We acknowledge support from the German Federal Ministry of Culture and Research (BMBF) and from the Deutsche Forschungsgemeinschaft.

Author information


  1. Max-Planck-Institut für Festkörperforschung, 70569 Stuttgart, Germany

    • V. Hinkov
    • , A. Kulakov
    • , C. T. Lin
    • , D. P. Chen
    • , C. Bernhard
    •  & B. Keimer
  2. Laboratoire Léon Brillouin, CEA-CNRS, CE-Saclay, 91191 Gif-sur-Yvette, France

    • S. Pailhès
    • , P. Bourges
    •  & Y. Sidis
  3. Institut Laue-Langevin, 156X, 38042 Grenoble cedex 9, France

    • A. Ivanov


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Competing interests

The authors declare that they have no competing financial interests.

Corresponding author

Correspondence to B. Keimer.

Supplementary information

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  1. 1.

    Supplementary Discussion

    We use an anisotropic, damped harmonic oscillator model to describe the data collected on detwinned YBa2Cu3O6.85. This model and its parameters are discussed here and a figure is provided showing the energy dependence of the damping parameter γ along both perpendicular directions a* and b*.

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