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An hour-glass magnetic spectrum in an insulating, hole-doped antiferromagnet


Superconductivity in layered copper oxide compounds emerges when charge carriers are added to antiferromagnetically ordered CuO2 layers1. The carriers destroy the antiferromagnetic order, but strong spin fluctuations persist throughout the superconducting phase and are intimately linked to superconductivity2. Neutron scattering measurements of spin fluctuations in hole-doped copper oxides have revealed an unusual ‘hour-glass’ feature in the momentum-resolved magnetic spectrum that is present in a wide range of superconducting and non-superconducting materials3,4,5,6,7,8,9,10,11,12,13,14,15. There is no widely accepted explanation for this feature. One possibility is that it derives from a pattern of alternating spin and charge stripes16, and this idea is supported by measurements on stripe-ordered La1.875Ba0.125CuO4 (ref. 15). Many copper oxides without stripe order, however, also exhibit an hour-glass spectrum3,4,5,6,7,8,9,10,11,12. Here we report the observation of an hour-glass magnetic spectrum in a hole-doped antiferromagnet from outside the family of superconducting copper oxides. Our system has stripe correlations and is an insulator, which means that its magnetic dynamics can conclusively be ascribed to stripes. The results provide compelling evidence that the hour-glass spectrum in the copper oxide superconductors arises from fluctuating stripes.

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Figure 1: Crystal structure and magnetic order of La5/3Sr1/3CoO4.
Figure 2: Neutron scattering intensity maps of the magnetic excitation spectrum of La5/3Sr1/3CoO4.
Figure 3: Dispersion of the magnetic excitation spectrum of La5/3Sr1/3CoO4.
Figure 4: Simulations of the magnetic spectrum of La5/3Sr1/3CoO4.

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  1. Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006)

    Article  CAS  ADS  Google Scholar 

  2. Chubukov, A. V., Pines, D. & Schmalian, J. in The Physics of Superconductors Vol. 1, Conventional and High-T c Superconductors (eds Bennemann, K. H. & Ketterson, J. B. ) 495–590 (Springer, 2003)

    Book  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  5. Hayden, S. M., Mook, H. A., Dai, P., Perring, T. G. & Doğan, F. The structure of the high-energy spin excitations in a high-transition-temperature superconductor. Nature 429, 531–534 (2004)

    Article  CAS  ADS  Google Scholar 

  6. Reznik, D. et al. Dispersion of magnetic excitations in optimally doped superconducting YBa2Cu3O6. 95 . Phys. Rev. Lett. 93, 207003 (2004)

    Article  CAS  ADS  Google Scholar 

  7. Stock, C. et al. From incommensurate to dispersive spin-fluctuations: the high-energy inelastic spectrum in superconducting YBa2Cu3O6. 5 . Phys. Rev. B 71, 024522 (2005)

    Article  ADS  Google Scholar 

  8. Hinkov, V. et al. Spin dynamics in the pseudogap state of a high-temperature superconductor. Nature Phys. 3, 780–785 (2007)

    Article  CAS  ADS  Google Scholar 

  9. Fauqué, B. et al. Dispersion of the odd magnetic resonant mode in near-optimally doped Bi2Sr2CaCu2O8+δ . Phys. Rev. B 76, 214512 (2007)

    Article  ADS  Google Scholar 

  10. Xu, G. et al. Testing the itinerancy of spin dynamics in superconducting Bi2Sr2CaCu2O8+δ . Nature Phys. 5, 642–646 (2009)

    Article  CAS  ADS  Google Scholar 

  11. Christensen, N. B. et al. Dispersive excitations in the high-temperature superconductor La2−x Sr x CuO4 . Phys. Rev. Lett. 93, 147002 (2004)

    Article  CAS  ADS  Google Scholar 

  12. Vignolle, B. et al. Two energy scales in the spin excitations of the high-temperature superconductor La2−x Sr x CuO4 . Nature Phys. 3, 163–167 (2007)

    Article  CAS  ADS  Google Scholar 

  13. Matsuda, M. et al. Magnetic dispersion of the diagonal incommensurate phase in lightly doped La2−x Sr x CuO4 . Phys. Rev. Lett. 101, 197001 (2008)

    Article  CAS  ADS  Google Scholar 

  14. Lipscombe, O. J., Vignolle, B., Perring, T. G., Frost, C. D. & Hayden, S. M. Emergence of coherent magnetic excitations in the high temperature underdoped La2−x Sr x CuO4 superconductor at low temperatures. Phys. Rev. Lett. 102, 167002 (2009)

    Article  CAS  ADS  Google Scholar 

  15. Tranquada, J. M. et al. Quantum magnetic excitations from stripes in copper oxide superconductors. Nature 429, 534–538 (2004)

    Article  CAS  ADS  Google Scholar 

  16. Tranquada, J. M., Sternlieb, B. J., Axe, J. D., Nakamura, Y. & Uchida, S. Evidence for stripe correlations of spins and holes in copper oxide superconductors. Nature 375, 561–563 (1995)

    Article  ADS  Google Scholar 

  17. Hayden, S. M. in Superconductivity: Conventional and Unconventional Superconductors Vol. 2 (eds Bennemann, K. H. & Ketterson, J. B. ) 993–1029 (Springer, 2008)

    Book  Google Scholar 

  18. Moritomo, Y., Higashi, K., Matsuda, K. & Nakamura, A. Spin-state transition in layered perovskite cobalt oxides: La2−x Sr x CoO4 (0.4 ≤ x ≤ 1.0). Phys. Rev. B 55, R14725–R14728 (1997)

    Article  CAS  ADS  Google Scholar 

  19. Yamada, K. et al. Successive antiferromagnetic phase transitions in single-crystal La2CoO4 . Phys. Rev. B 39, 2336–2343 (1989)

    Article  CAS  ADS  Google Scholar 

  20. Cwik, M. et al. Magnetic correlations in La2−x Sr x CoO4 studied by neutron scattering: possible evidence for stripe phases. Phys. Rev. Lett. 102, 057201 (2009)

    Article  CAS  ADS  Google Scholar 

  21. Chen, C. H., Cheong, S.-W. & Cooper, A. S. Charge modulations in La2−x Sr x NiO4+y : ordering of polarons. Phys. Rev. Lett. 71, 2461–2464 (1993)

    Article  CAS  ADS  Google Scholar 

  22. Tranquada, J. M., Buttrey, D. J., Sachan, V. & Lorenzo, J. E. Simultaneous ordering of holes and spin in La2NiO4. 125 . Phys. Rev. Lett. 73, 1003–1006 (1994)

    Article  CAS  ADS  Google Scholar 

  23. Yoshizawa, H. et al. Stripe order at low temperatures in La2−x Sr x NiO4 with 0.289 ≤ x ≤ 0.5. Phys. Rev. B 61, R854–R857 (2000)

    Article  CAS  ADS  Google Scholar 

  24. Hollmann, N. et al. Anisotropic susceptibility of La2−x Sr x CoO4 related to the spin states of cobalt. N. J. Phys. 10, 023018 (2008)

    Article  Google Scholar 

  25. Helme, L. M. et al. Magnetic order and dynamics of the charge-ordered antiferromagnet La1. 5Sr0. 5CoO4 . Phys. Rev. B 80, 134414 (2009)

    Article  ADS  Google Scholar 

  26. Babkevich, P., Prabhakaran, D., Frost, C. D. & Boothroyd, A. T. Magnetic spectrum of the two-dimensional antiferromagnet La2CoO4 studied by inelastic neutron scattering. Phys. Rev. B 82, 184425 (2010)

    Article  ADS  Google Scholar 

  27. Yao, D. X., Carlson, E. W. & Campbell, D. K. Magnetic excitations of stripes near a quantum critical point. Phys. Rev. Lett. 97, 017003 (2006)

    Article  CAS  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  29. Vojta, M. Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity. Adv. Phys. 58, 699–820 (2009)

    Article  CAS  ADS  Google Scholar 

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We thank F. Essler and E.W. Carlson for discussions. This work was supported by the Engineering and Physical Sciences Research Council of Great Britain and the Paul Scherrer Institut, Switzerland.

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D.P. prepared and characterized the single-crystal samples. A.T.B., P.B. and P.G.F. performed the neutron scattering experiments. A.T.B. developed the theoretical model and P.B. performed the data analysis. A.T.B. wrote the manuscript.

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Correspondence to A. T. Boothroyd.

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The authors declare no competing financial interests.

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Boothroyd, A., Babkevich, P., Prabhakaran, D. et al. An hour-glass magnetic spectrum in an insulating, hole-doped antiferromagnet. Nature 471, 341–344 (2011).

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