Three-dimensionality of field-induced magnetism in a high-temperature superconductor

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Many physical properties of high-temperature superconductors are two-dimensional phenomena derived from their square-planar CuO2 building blocks. This is especially true of the magnetism from the copper ions. As mobile charge carriers enter the CuO2 layers, the antiferromagnetism of the parent insulators, where each copper spin is antiparallel to its nearest neighbours1, evolves into a fluctuating state where the spins show tendencies towards magnetic order of a longer periodicity. For certain charge-carrier densities, quantum fluctuations are sufficiently suppressed to yield static long-period order2,3,4,5,6, and external magnetic fields also induce such order7,8,9,10,11,12. Here we show that, in contrast to the chemically controlled order in superconducting samples, the field-induced order in these same samples is actually three-dimensional, implying significant magnetic linkage between the CuO2 planes. The results are important because they show that there are three-dimensional magnetic couplings that survive into the superconducting state, and coexist with the crucial inter-layer couplings responsible for three-dimensional superconductivity. Both types of coupling will straighten the vortex lines, implying that we have finally established a direct link between technical superconductivity, which requires zero electrical resistance in an applied magnetic field and depends on vortex dynamics, and the underlying antiferromagnetism of the cuprates.

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Figure 1: The experimental configuration and real-space interpretation of the results.
Figure 2: The field-induced signal in sample A for two different field directions.
Figure 3: Magnetic scattering from LSCO x=0.10 at different fields and temperatures for the two different samples.
Figure 4: Data collected for both samples as scans where the in-plane wavevector was varied for various fixed inter-planar wavevectors; each scan has been corrected for background and is represented by a different colour.


  1. 1

    Vaknin, D. et al. Antiferromagnetism in La2CuO4 . Phys. Rev. Lett. 58, 2802–2805 (1987).

  2. 2

    Suzuki, T. et al. Observation of modulated magnetic long-range order in La1.88Sr0.12CuO4 . Phys. Rev. B 57, R3229–R3232 (1998).

  3. 3

    Kimura, H. et al. Neutron-scattering study of static antiferromagnetic correlations in La2−xSrxCu1−yZnyO4 . Phys. Rev. B 59, 6517–6523 (1999).

  4. 4

    Lee, Y. S. et al. Neutron-scattering study of spin-density wave order in the superconducting state of excess-oxygen-doped La2CuO4+y . Phys. Rev. B 60, 3643–3654 (1999).

  5. 5

    Kimura, H. et al. Incommensurate geometry of the elastic magnetic peaks in superconducting La1.88Sr0.12CuO4 . Phys. Rev. B 61, 14366–14369 (2000).

  6. 6

    Wakimoto, S., Birgeneau, R. J., Lee, Y. S. & Shirane, G. Hole concentration dependence of the magnetic moment in superconducting and insulating La2−xSrxCuO4 . Phys. Rev. B 63, 172501–172504 (2001).

  7. 7

    Lake, B. et al. Spins in the vortices of a high-temperature superconductor. Science 291, 1759–1762 (2001).

  8. 8

    Lake, B. et al. Antiferromagnetic order induced by an applied magnetic field in a high-temperature superconductor. Nature 415, 299–302 (2002).

  9. 9

    Katano, S., Sato, M., Yamada, K., Suzuki, T. & Fukase, T. Enhancement of static antiferromagnetic correlations by magnetic field in a superconductor La2−xSrxCuO4 withx=0.12 . Phys. Rev. B 62, R14677–R14680 (2000).

  10. 10

    Khaykovich, B. et al. Enhancement of long-range magnetic order by magnetic field in superconducting La2CuO4+y . Phys. Rev. B 66, 014528–014535 (2002).

  11. 11

    Kang, H. J. et al. Antiferromagnetic order as the competing ground state in electron-doped Nd1.85Ce0.15CuO4 . Nature 423, 522–525 (2003).

  12. 12

    Sonier, J. E. et al. Superconductivity and field-induced magnetism in Pr2−xCexCuO4 single crystals. Phys. Rev. Lett. 91, 147002 (2003).

  13. 13

    Bednorz, J. G. & Müller, K. A. Possible high-Tc superconductivity in the Ba-La-Cu-O system. Z. Phys. B 64, 189–193 (1986).

  14. 14

    Hu, J.-P. & Zhang, S.-C. Theory of static and dynamic antiferromagnetic vortices in LSCO superconductors. J. Phys. Chem. Solids 63, 2277–2282 (2002).

  15. 15

    Demler, E., Sachdev, S. & Zhang, Y. Spin-ordering quantum transitions of superconductors in a magnetic field. Phys. Rev. Lett. 87, 067202 (2001).

  16. 16

    Kivelson, S. A., Lee, D. H., Fradkin, E. & Oganesyan, V. Competing order in the mixed state of high-temperature superconductors. Phys. Rev. B 66, 144516–144523 (2002).

  17. 17

    Boebinger, G. S. et al. Insulator-to-metal crossover in the normal state of La2−xSrxCuO4 near optimal doping. Phys. Rev. Lett. 77, 5417–5420 (1996).

  18. 18

    Ando, Y. et al. Resistive upper critical fields and irreversibility lines of optimally doped high-T c cuprates. Phys. Rev. B 60, 12475–12479 (1999).

  19. 19

    Thio, T. et al. Magnetoresistance and the spin-flop transition in single-crystal La2CuO4+y . Phys. Rev. B 41, 231–239 (1990).

  20. 20

    Chiba, K. et al. 139La -NMR study of spin-flop and spin structure in La2−xSrxCuO4 (xl/8). J. Low Temp. Phys. 117, 479–483 (1999).

  21. 21

    Fukase, T. et al. Elastic anomalies induced by spin-flop in La1.88Sr0.12CuO4 . Physica B 284, 483–484 (2000).

  22. 22

    Ando, Y., Boebinger, G. S., Passner, A., Kimura, T. & Kishio, K. Logarithmic divergence of both in-plane and out-of-plane normal-state resistivities of superconducting La2−xSrxCuO4 in the zero-temperature limit. Phys. Rev. Lett. 75, 4662–4665 (1995).

  23. 23

    Suzuki, M. & Hikita, M. Resistive transition, magnetoresistance, and anisotropy in La2−xSrxCuO4 single-crystal thin films. Phys. Rev. B 44, 249–261 (1991).

  24. 24

    Shibauchi, T. et al. Anisotropic penetration depth in La2−xSrxCuO4 . Phys. Rev. Lett. 72, 2263–2266 (1994).

  25. 25

    Kimura, T. et al. In-plane and out-of-plane magnetoresistance in La2−xSrxCuO4 single crystals. Phys. Rev. B 53, 8733–8742 (1996).

  26. 26

    Goto, T., Kazama, S., Miyagawa, K. & Fukase, T. 63/65Cu/139La -NMR study on antiferromagnetic ordering in high-Tc oxides La2−xSrxCuO4 (x0.115) and La2−xBaxCuO4 (x0.125). J. Phys. Soc. Jpn 63, 3494–3503 (1994).

  27. 27

    Dai, P. C., Mook, H. A., Aeppli, G., Hayden, S. M. & Dogan, F. Resonance as a measure of pairing correlations in the high-Tc superconductor YBa2Cu3O6.6 . Nature 406, 965–968 (2000).

  28. 28

    Xu, G. Y. et al. Holes in a quantum spin liquid. Science 289, 419–422 (2000).

  29. 29

    Wan, Y. M., Hebboul, S. E., Harris, D. C. & Garland, J. C. Interlayer Josephson coupling of thermally excited vortices in Bi2Sr2CaCu2Oδ−y . Phys. Rev. Lett. 71, 157–160 (1993).

  30. 30

    Safar, H. et al. Observation of two-dimensional vortices in Bi2Sr2CaCu2Ox . Phys. Rev. B 46, 14238–14241 (1992).

  31. 31

    van der Marel, D. Interacting Electrons in Low Dimensions (Physics and Chemistry of Materials with Low-Dimensional Structures, Kluwer Academic, Dordrecht, 2003).

  32. 32

    Huecker, M., Klauss, H.-H. & Buechner, B. Strong dependence of the interlayer coupling on the hole mobility in antiferromagnetic La2−xSrxCOx (x<0.02). Phys. Rev. B 70, 220507(R) (2004).

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We thank N. H. Andersen, B. M. Andersen, A. B. Abrahamsen and S. Kivelson for discussions. Experiments at the Berlin Neutron Scattering Centre were made possible by the support of the European Community—Access to Research Infrastructure action of the Improving Human Potential Programme. Work in London was supported by Royal Society Wolfson Merit Awards.

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Correspondence to B. Lake.

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Lake, B., Lefmann, K., Christensen, N. et al. Three-dimensionality of field-induced magnetism in a high-temperature superconductor. Nature Mater 4, 658–662 (2005) doi:10.1038/nmat1452

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