Skip to main content
SpringerLink
Log in

Neutron scattering study of the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr2CuO2Cl2

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

We have carried out a neutron scattering investigation of the static structure factorS(q 2D ) (q 2D is the in-plane wave vector) in the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr2CuO2Cl2. For the spin correlation length ξ we find quantitative agreement with Monte Carlo results over a wide range of temperature. The combined Sr2CuO2Cl2-Monte Carlo data, which cover the length scale from ≈1 to 200 lattice constants, are predicted without adjustable parameteres by renormalized classical theory for the quantum nonlinear sigma model. For the structure factor peakS(0), on the other hand, we findS(0)∼ξ 2 for the reduced temperature range 0.16<T/2πρ s <0.36, whereas current theories predict that at low temperaturesS(0)∼T 2 ξ 2. This discrepancy has important implications for the interpretation of many derivative quantities such as NMR relaxation rates. In the ordered phase, we have measured the temperature dependence of the out-of-plane spin-wave gap. Its low-temperature value of 5.0 meV corresponds to an XY anisotropyJ XY /J=1.4×10−4. From measurements of the sublattice mangetization we obtain β=0.22±0.01 for the order parameter exponent. This may either reflect tricricality as in La2CuO4, or it may indicate finite-size two-dimensional XY behavior as suggested by Bramwell and Holdsworth. As in theS=1 system K2NiF4, the gap energy in Sr2CuO2Cl2 scales linearly with the order parameter up to the Néel temperature. We also reanalyze static structure factor data for K2NiF4 using the exact low temperature result for the correlation length of Hasenfratz and Niedermayer and including the Ising anisotropy explicitly. Excellent agreement between experiment and theory is obtained for the correlation length, albeit with the spin-stiffnessρ s reduced by ≈20% from the spin-wave value. As in Sr2CuO2Cl2 we find thatS(0)∼ξ 2 for the reduced temperature range 0.22<T/2πρ s <0.47.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bethe, H.A.: Z. Phys.71, 205 (1931)

    Google Scholar 

  2. Hulthén, L.: Ark. Mat. Astron. Fys.26A, (1) (1938)

    Google Scholar 

  3. des Cloizeaux, J., Pearson, J.J.: Phys. Rev.128, 2131 (1962)

    Google Scholar 

  4. Endoh, Y., Shirane, G., Birgeneau, R.J., Richards, P.M., Holt, S.L.: Phys. Rev. Lett.32, 170 (1974)

    Google Scholar 

  5. Mikesaka, H.J.: Phys. Rev. B12, 2794 (1975)

    Google Scholar 

  6. Orbach, R.L.: Phys. Rev.112, 309 (1958)

    Google Scholar 

  7. Haldane, F.D.M.: Phys. Lett.93A, 464 (1983)

    Google Scholar 

  8. Haldane, F.D.M.: Phys. Rev. Lett.50, 1153 (1983)

    Google Scholar 

  9. Holstein, T., Primakoff, H.: Phys. Rev.58, 1098 (1940)

    Google Scholar 

  10. Anderson, P.W.: Phys. Rev.86, 694 (1952)

    Google Scholar 

  11. Kubo, R.: Phys. Rev.87, 568 (1952)

    Google Scholar 

  12. Hohenberg, P.C.: Phys. Rev.158, 383 (1967)

    Google Scholar 

  13. Mermin, N.D., Wagner, H.: Phys. Rev. Lett.22, 1133 (1966)

    Google Scholar 

  14. Anderson, P.W.: Mater. Res. Bull.8, 153 (1973)

    Google Scholar 

  15. Anderson, P.W.: Science235, 1196 (1987)

    Google Scholar 

  16. de Jongh, L.J., Meidema, A.R.: Adv. Phys.23, 1 (1974)

    Google Scholar 

  17. Skalyo, Jr., J., Shirane, G., Birgeneau, R.J., Guggenheim, H.J.: Phys. Rev. Lett.23, 1394 (1969)

    Google Scholar 

  18. Birgeneau, R.J., Skalyo, Jr., J., Shirane, G.: Phys. Rev. B3, 1736 (1971)

    Google Scholar 

  19. Birgeneau, R.J., Als-Nielsen, J., Shirane, G.: Phys. Rev. B16, 280 (1977)

    Google Scholar 

  20. Neves, E.J., Peres, J.F.: Phys. Lett.114A, 331 (1986)

    Google Scholar 

  21. Affleck, I., Kennedy, T., Lieb, E.H., Tasaki, H.: Commun. Math. Phys.115, 477 (1988)

    Google Scholar 

  22. Affleck, I., Zou, Z., Hsu, T., Anderson, P.W.: Phys. Rev. B38, 745 (1988)

    Google Scholar 

  23. For a recent review, see Manousakis, E.: Rev. Mod. Phys.63, 1 (1991)

    Google Scholar 

  24. Bednorz, J.C., Müller, K.A.: Z. Phys. B64, 189 (1986)

    Google Scholar 

  25. Vaknin, D., Sinha, S.K., Moncton, D.E., Johnston, D.C., Newsam, J.M., Safinya, C.R., King, H.E.: Phys. Rev. Lett.58, 2802 (1987)

    Google Scholar 

  26. Endoh, Y., Yamada, K., Birgeneau, R.J., Gabbe, D.R., Jennsen, H.P., Kastner, M.A., Peters, C.J., Picone, P.J., Thurston, T.R., Tranquada, J.M., Shirane, G., Hidaka, Y., Oda, M., Enomoto Y., Suzuki, M., Murakami, T.: Phys. Rev. B37, 7443 (1988)

    Google Scholar 

  27. Chakravarty, S., Halperin, B.I., Nelson, D.R.: Phys. Rev. Lett.60, 1057 (1988)

    Google Scholar 

  28. Chakravarty, S., Halperin, B.I., Nelson, D.R.: Phys. Rev. B39, 2344 (1989)

    Google Scholar 

  29. Tyć, S., Halperin, B.I., Chakravarty, S.: Phys. Rev. Lett.62, 835 (1989)

    Google Scholar 

  30. Hasenfratz, P., Niedermayer, F.: Phys. Lett. B268, 231 (1991)

    Google Scholar 

  31. Yamada, K., Kakurai, K., Endoh, Y., Thurston, T.R., Kastner, M.A., Birgeneau, R.J., Shirane, G., Hidaka, Y., Murakami, T.: Phys. Rev. B40, 4557 (1989)

    Google Scholar 

  32. Keimer, B., Belk, N., Birgeneau, R.J., Cassanho, A., Chen, C.Y., Greven, M., Kastner, M.A., Aharony, A., Endoh, Y., Erwin, R.W., Shirane, G.: Phys. Rev. B46, 14034 (1992)

    Google Scholar 

  33. Birgeneau, R.J.: Phys. Rev. B41, 2514 (1990)

    Google Scholar 

  34. Greven, M., Birgeneau, R.J., Endoh, Y., Kastner, M.A., Keimer, B., Matsuda, M., Shirane, G., Thurston, T.R.: Phys. Rev. Lett.72, 1096 (1994)

    Google Scholar 

  35. Greven, M., Birgeneau, R.J., Endoh, Y., Kastner, M.A., Keimer, B., Matsuda, M., Shirane, G., Thurston, T.R.: Physica B199–200, 642 (1994)

    Google Scholar 

  36. Makivić, M.S., Ding, H. -Q.: Phys. Rev. B43, 3562 (1991)

    Google Scholar 

  37. Sokol, A., Gleinister, R.L., Singh, R.R.P.: Phys. Rev. Lett.72, 1549 (1994)

    Google Scholar 

  38. Igarashi, J.: Phys. Rev. B46, 10763 (1992)

    Google Scholar 

  39. Manousakis, E., Salvador, R.: Phys. Rev. Lett.61, 1210 (1989)

    Google Scholar 

  40. Manousakis, E., Salvador, R.: Phys. Rev. B40, 2205 (1989)

    Google Scholar 

  41. Chakravarty, S.: (private communication)

  42. Chubukov, A.V., Sachdev, S.: Phys. Rev. Lett.71, 169 (1993)

    Google Scholar 

  43. Sachdev, S., Ye, J.: Phys. Rev. Lett.69, 2411 (1992)

    Google Scholar 

  44. Shenker, S.H., Tobochnik, J.: Phys. Rev. B22, 4462 (1980)

    Google Scholar 

  45. Halperin, B.I., Hohenberg, P.C.: Phys. Rev.177, 952 (1969)

    Google Scholar 

  46. Makivić, M., Jarrell, M.: Phys. Rev. Lett.68, 1770 (1992)

    Google Scholar 

  47. Wiese, U.-J., Ying, H.-P.: Z. Phys. B93, 147 (1994)

    Google Scholar 

  48. Miller, L.L., Wang, X.L., Wang, S.X., Stassis, C., Johnston, D.C., Faber, J., Loong, C.-K.: Phys. Rev. B41, 1921 (1990)

    Google Scholar 

  49. Bloch, D.: J. Phys. Chem. Solids27, 881 (1966)

    Google Scholar 

  50. Tokura, Y., Koshihara, S., Arima, T., Takagi, H., Ishibashi, S., Ido, T., Uchida, S.: Phys. Rev. B41, 11657 (1990)

    Google Scholar 

  51. Yildirim, T., Harris, A.B., Entin-Wohlman, O., Aharony, A.: Phys. Rev. Lett.72, 3710 (1994)

    Google Scholar 

  52. Yildirim, T., Harris, A.B., Entin-Wohlman, O., Aharaony, A.: (to be published).

  53. Vaknin, D., Sinha, S.K., Stassis, C., Miller, L.L., Johnston, D.C.: Phys. Rev. B41, 1926 (1990)

    Google Scholar 

  54. Shender, E.F.: Sov. Phys. JETP56, 178 (1982)

    Google Scholar 

  55. Keimer, B., Birgeneau, R.J., Cassanho, A., Endoh, Y., Greven, M., Kastner, M.A., Shirane, G.: Z. Phys. B91, 373 (1993)

    Google Scholar 

  56. Thio, T., Thurston, T.R., Preyer, N.W., Picone, P.J., Kastner, M.A., Jenssen, H.P., Gabbe, D.R., Chen, C.Y., Birgeneau, R.J., Aharony, A.: Phys. Rev. B38, 905 (1988)

    Google Scholar 

  57. Thio, T., Chen, C.Y., Freer, B.S., Gabbe, D.R., Jenssen, H.P., Kastner, M.A., Picone, P.J., Preyer, N.W., Birgeneau, R.J.: Phys. Rev. B41, 231 (1990)

    Google Scholar 

  58. Matsuda, M. et al.: (unpublished)

  59. Chubukov, A.V., Sachdev, S., Ye, J.: Phys. Rev. B49, 11919 (1994)

    Google Scholar 

  60. Sokol, A., Pines, D.: Phys. Rev. Lett.71, 2813 (1993)

    Google Scholar 

  61. Barzykin, V., Pines, D., Sokol, A., Thelen, D.: Phys. Rev. B49, 1544 (1994)

    Google Scholar 

  62. Imai, T., Schlichter, C.P., Yoshimura, K., Katoh, M., Kosuge, K.: Phys. Rev. Lett.71, 1254 (1993)

    Google Scholar 

  63. Ding, H.-Q., Makivić, M.S.: Phys. Rev. B42, 6827 (1990)

    Google Scholar 

  64. Kosterlitz, J.M., Thouless, D.J.: J. Phys. C6, 1181 (1973)

    Google Scholar 

  65. Matsuda, M., Yamada, K., Kadowaki, H., Thurston, T.R., Endoh, Y., Hidaka, Y., Birgeneau, R.J., Kastner, M.A., Gehring, P.M., Moudden, A.H., Shirane, G.: Phys. Rev. B42, 10098 (1990)

    Google Scholar 

  66. Borsa, F., Corti, M., Goto, T., Rigamonti, A., Johnston, D.C., Chou, F.C.: Phys. Rev. B45, 5756 (1992)

    Google Scholar 

  67. Kopietz, P.: Phys. Rev. Lett.64, 2587 (1990)

    Google Scholar 

  68. Nakajima, K., Yamada, K., Hosoya, S., Endoh, Y., Greven, M., Birgeneau, R.J.: Z. Phys. B. (next article)

  69. Kim, J.H.: (Preprint.)

  70. Chakravarty, S., Orbach, R.: Phys. Rev. Lett.64, 224 (1990)

    Google Scholar 

  71. Imai, T., Schlichter, C.P., Yoshimura, K., Kosuge, K.: Phys. Rev. Lett.70, 1002 (1993)

    Google Scholar 

  72. Chubukov, A.V., Sachdev, S., Sokol, A.: Phys. Rev. B49, 9052 (1994)

    Google Scholar 

  73. Le, L.P., Luke, G.M., Sternlieb, B.J., Uemura, Y.J., Brewer, J.H., Riseman, T.M., Johnston, D.C., Miller, L.L.: Phys. Rev. B42, 2182 (1990)

    Google Scholar 

  74. Bramwell, S.T., Holdsworth, P.C.W.: J. Phys. Condens. Matter5, L53 (1993)

    Google Scholar 

  75. Bramwell, S.T., Holdsworth, P.C.W.: J. Appl. Phys.73, 6096 (1993)

    Google Scholar 

  76. Bramwell, S.T., Holdsworth, P.C.W.: Phys. Rev. B49, 8811 (1994)

    Google Scholar 

  77. Thio, T., Aharony, A.: Phys. Rev. Lett.73, 894 (1994)

    Google Scholar 

  78. Birgeneau, R.J., Guggenheim, H.J., Shirane, G.: Phys. Rev. Lett.22, 720 (1969)

    Google Scholar 

  79. Birgeneau, R.J., De Rosa, F., Guggenheim, H.J.: Solid State Commun.8, 13 (1970)

    Google Scholar 

  80. Tranquada, J.M., Shirane, G., Keimer, B., Shamoto, S., Sato, M.: Phys. Rev. B40, 4503 (1989)

    Google Scholar 

  81. Ding, H.-Q.: Phys. Rev. Lett.68, 1927 (1992)

    Google Scholar 

  82. Keimer, B., Aharony, A., Auerbach, A., Birgeneau, R.J., Cassanho, A., Endoh, Y., Erwin, R.W., Kastner, M.A., Shirane, G.: Phys. Rev. B45, 7430 (1992)

    Google Scholar 

  83. Arovas, D.P., Auerbach, A.: Phys. Rev. B38, 316 (1988)

    Google Scholar 

  84. Auerbach, A., Arovas, D.P.: Phys. Rev. Lett.61, 617 (1988)

    Google Scholar 

  85. Haldane, F.D.M.: J. Appl. Phys.57, 3359 (1985)

    Google Scholar 

  86. Hamer, C.J., Weihong, Z., Oitmaa, J.: Phys. Rev. B50, 6877 (1994)

    Google Scholar 

  87. Cowley, R.A., Shirane, G., Birgeneau, R.J., Guggenheim, H.J.: Phys. Rev. B15, 4292 (1977)

    Google Scholar 

Download references

Author information

Author notes

  1. M. Matsuda

    Present address: The Institute of Physical and Chemical Research, RIKEN, Wako, 351-01, Saitama, Japan

Authors and Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    M. Greven, R. J. Birgeneau & M. A. Kastner

  2. Brookhaven National Laboratory, 11973, Upton, NY, USA

    M. Greven, M. Matsuda & G. Shirane

  3. Department of Physics, Tohoku University, 980, Sendai, Japan

    Y. Endoh

Authors
  1. M. Greven
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. J. Birgeneau
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. Endoh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. A. Kastner
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. Matsuda
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. G. Shirane
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Greven, M., Birgeneau, R.J., Endoh, Y. et al. Neutron scattering study of the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr2CuO2Cl2 . Z. Physik B - Condensed Matter 96, 465–477 (1995). https://doi.org/10.1007/BF01313844

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01313844

PACS

Search

Navigation