Journal of Low Temperature Physics

, Volume 112, Issue 1–2, pp 73–116 | Cite as

Neutron Diffraction Studies of Nuclear Magnetic Ordering in Silver

  • Kaj K. Nummila
  • Juha T. Tuoriniemi
  • Reko T. Vuorinen
  • Kim Lefmann
  • Albert Metz
  • Finn B. Rasmussen
Article
  • 30 Downloads

Abstract

Nuclear antiferromagnetism in fcc silver metal, already investigated by NMR measurements, has been studied in a single crystal of109Ag by neutron absorption and diffraction techniques. Below the Neel temperature TN, a (001) Bragg reflection with a resolution limited width demonstrates long range order in a simple type-I AFM structure with the ordering vectork = (2π/a)(001) (“up-down” structure). The entropy at the transition,\({\text{S}}_c = 0.54R\) ln 2 in zero magnetic field, corresponding to a critical polarization Pc= 0.75 and TN= 700 ± 80 pK. Magnetic field B versus entropy S phase diagrams of the (001) structure have been constructed for two directions ofB: [001] and \([\overline {0.8} {\text{ }}\overline {{\text{0}}{\text{.8}}} {\text{ }}1]{\text{.}}\) The critical field extrapolated to S = 0 is 100 ± 10 μT, and for both field directions Scis highest around B = 30 μT. The transition to the paramagnetic state is presumably of second order. The nuclear magnetization was measured by transmission of unpolarized neutrons, and the dimensionless static volume susceptibility in SI units was found to be 0.36 ± 0.01 in the ordered state independently of B and S. The ac susceptibility at 7.9 Hz showed a kink at the transition only when the sample was not exposed to neutrons.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    M. Goldman, Phys. Rep. 32, 1 (1977).Google Scholar
  2. 2.
    A. Abragam and M. Goldman, Nuclear Magnetism: Order and Disorder, Clarendon Press, Oxford (1982).Google Scholar
  3. 3.
    P. Hakonen, O. V. Lounasmaa, and A. S. Oja, J. Magn. & Magn. Mater. 100, 394 (1991).Google Scholar
  4. 4.
    A. S. Oja and O. V. Lounasmaa, Rev. Mod. Phys. 69, 1 (1997).Google Scholar
  5. 5.
    M. Steiner, Phys. Scripta 42, 367 (1990); Int. J. Mod. Phys. B 7, 2909 (1993).Google Scholar
  6. 6.
    T. Herrmannsdörfer, P. Smeibidl, B. Schröder-Smeibidl, and F. Pobell, Phys. Rev. Lett. 74, 1665 (1995).Google Scholar
  7. 7.
    W. P. Halperin, C. N. Archie, F. B. Rasmussen, R. A. Buhrmann, and R. C. Richardson, Phys. Rev. Lett. 44, 792 (1974).Google Scholar
  8. 8.
    A. Benoit, J. Bossy, and J. Flouquet, J. Physique Lett. 46, L923 (1985).Google Scholar
  9. 9.
    F. Pobell, T. Herrmannsdörfer, S. Rehmann, and W. Wendler, Czech. J. Phys. 46, 3279 (1996).Google Scholar
  10. 10.
    P.-A. Lindgård, X.-W. Wang, and B. N. Harmon, J. Magn. & Magn. Mater. 54–57, 1052 (1986); S. J. Frisken and D. J. Miller, Phys. Rev. Lett. 57, 1052 (1986); D. J. Miller and S. J. Frisken, J. Appl. Phys. 64, 5630 (1988).Google Scholar
  11. 11.
    B. N. Harmon, X.-W. Wang, and P.-A. Lindgard, J. Magn. & Magn. Mater 104–107, 2113 (1992).Google Scholar
  12. 12.
    M. T. Huiku, M. T. Loponen, Phys. Rev. Lett. 49, 1288 (1982).Google Scholar
  13. 13.
    P. J. Hakonen, S. Yin, and K. K. Nummila, Europhys. Lett. 15, 677 (1991).Google Scholar
  14. 14.
    P. J. Hakonen, K. K. Nummila, R. T. Vuorinen, and O. V. Lounasmaa, Phys. Rev. Lett. 68, 365 (1992).Google Scholar
  15. 15.
    H. A. Bethe, Z. Phys. 71, 205 (1931); L. Hulthén, Arkiv Mat. Astro. Fys. 26A, No. 11, 1–105 (1938).Google Scholar
  16. 16.
    F. D. M. Haldane, Phys. Rev. Lett. 60, 635 (1988; B. S. Shastry, Phys. Rev. Lett. 60, 639 (1988).Google Scholar
  17. 17.
    K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986).Google Scholar
  18. 18.
    P. W. Anderson, Mat. Res. Bull. 8, 153 (1973).Google Scholar
  19. 19.
    K. Siemensmeyer and M. Steiner, Z. Phys. B 89, 305 (1992).Google Scholar
  20. 20.
    G. J. Ehnholm, J. P. Ekström, J. F. Jacquinot, M. T. Loponen, O. V. Lounasmaa, and J. K. Soini, Phys. Rev. Lett. 42, 1702 (1979).Google Scholar
  21. 21.
    M. T. Huiku, T. A. Jyrkkiö, and M. T. Loponen, Phys. Rev. Lett. 50, 1516 (1983).Google Scholar
  22. 22.
    M. T. Huiku, T. A. Jyrkkiö, J. M. Kyynäräinen, A. S. Oja, and O. V. Lounasmaa, Phys. Rev. Lett. 53, 1692 (1984); M. T. Huiku, T. A. Jyrkkiö, J. M. Kyynäräinen, M. T. Loponen, O. V. Lounasmaa, and A. S. Oja, J. Low Temp. Phys. 62, 433 (1986).Google Scholar
  23. 23.
    T. A. Jyrkkiö, M. T. Huiku, O. V. Lounasmaa, K. Siemensmeyer, K. Kakurai, M. Steiner, K. N. Clausen, and J. K. Kjems, Phys. Rev. Lett. 60, 2418 (1988).Google Scholar
  24. 24.
    T. A. Jyrkkiö, M. T. Huiku, K. Siemensmeyer, and K. N. Clausen, J. Low Temp. Phys. 74, 435 (1989).Google Scholar
  25. 25.
    A. J. Annila, K. N. Clausen, P.-A. Lindgard, O. V. Lounasmaa, A. S. Oja, K. Siemensmeyer, M. Steiner, J. T. Tuoriniemi, and H. Weinfurter, Phys. Rev. Lett. 64, 1421 (1990); A. J. Annila, K. N. Clausen, A. S. Oja, J. T. Tuoriniemi, and H. Weinfurter, Phys. Rev. B 45, 7772 (1992).Google Scholar
  26. 26.
    H. E. Viertiö and A. S. Oja, Phys. Rev. B 42, 6857 (1990).Google Scholar
  27. 27.
    A. S. Oja and H. E. Viertiö, Phys. Rev. B 47, 237 (1993).Google Scholar
  28. 28.
    H. E. Viertiö and A. S. Oja, Phys. Rev. B 48, 1062 (1993).Google Scholar
  29. 29.
    P. J. Hakonen and S. Yin, J. Low Temp. Phys. 85, 25 (1991).Google Scholar
  30. 30.
    A. S. Oja, A. J. Annila, and Y. Takano, J. Low Temp. Phys. 85, 1 (1991).Google Scholar
  31. 31.
    P. J. Hakonen and R. T. Vuorinen, J. Low Temp. Phys. 89, 177 (1992).Google Scholar
  32. 32.
    H. Glättli and M. Goldman, Neutron Scattering, in Methods of Experimental Physics, K. Sköld and D. L. Price (eds.), Academic Press, New York (1987), Ch. 21.Google Scholar
  33. 33.
    K. Lefmann, J. T. Tuoriniemi, K. K. Nummila, and A. Metz, Z. Phys. B 102, 439 (1997).Google Scholar
  34. 34.
    J. T. Tuoriniemi, K. K. Nummila, K. Lefmann, R. T. Vuorinen, and A. Metz, Z. Phys. B 102, 433 (1997).Google Scholar
  35. 35.
    J. T. Tuoriniemi, K. K. Nummila, R. T. Vuorinen, O. V. Lounasmaa, A. Metz, K. Siemensmeyer, M. Steiner, K. Lefmann, K. N. Clausen, and F. B. Rasmussen, Phys. Rev. Lett. 75, 3744 (1995).Google Scholar
  36. 36.
    K. K. Nummila, Czech. J. Phys. 46, 3271 (1996).Google Scholar
  37. 37.
    See, e.g., A. Abragam, The Principles of Nuclear Magnetism, Oxford University Press, London (1961); M. Goldman, Spin Temperature and Nuclear Magnetic Resonance in Solids, Oxford University Press, London, (1970).Google Scholar
  38. 38.
    M. T. Huiku. M. T. Loponen, T. A. Jyrkkiö, J. M. Kyynäräinen, A. S. Oja, and J. K. Soini, in Proceedings of the 17th International Conference on Low Temperature Physics, Vol. 133, U. Eckern, A. Schmid, W. Werber, and H. Wühl (eds.), Elsevier Science Publishers, Amsterdam (1984).Google Scholar
  39. 39.
    See, e.g., P. Jauho and P. V. Pirilä, Phys. Rev. B 1, 21 (1970); F. Bacon, J. A. Barclay, W. D. Brewer, D. A. Shirley, and J. E. Templeton, Phys. Rev. B 5, 2397 (1972); E. Klein, in Low-Temperature Nuclear Orientation, N. J. Stone and H. Postma (eds.), Elsevier Science Publishers, Amsterdam (1986), Ch. 12.Google Scholar
  40. 40.
    G. Breit and E. Wigner, Phys. Rev. 49, 519 (1936).Google Scholar
  41. 41.
    S. F. Mughabghab, M. Divadeenam, and N. E. Holden, Neutron resonance parameters and thermal cross sections, in Neutron Cross Sections 1, Part A, Z = 1–60, S. F. Mughabghab, R. R. Kinsey, and C. L. Dunford (eds.), Academic Press, New York (1981).Google Scholar
  42. 42.
    M. E. Rose, Phys. Rev. 75, 213 (1949).Google Scholar
  43. 43.
    R. I. Schermer, Phys. Rev. 130, 1907 (1963).Google Scholar
  44. 44.
    H. Postma, H. Marshak, V. L. Sailor, F. J. Shofe, and C. A. Reynolds, Phys. Rev. 126, 979 (1962).Google Scholar
  45. 45.
    L. Passell and R. I. Schermer, Phys. Rev. 150, 146 (1966).Google Scholar
  46. 46.
    H. Postma, in Low-Temperature Nuclear Orientation, N. J. Stone and H. Postma (eds.), Elsevier Science Publishers, Amsterdam (1986), Ch. 7.Google Scholar
  47. 47.
    Yu. M. Bunkov, Cryogenics 29, 938 (1989).Google Scholar
  48. 48.
    See, e.g., F. Pobell, Matter and Methods at Low Temperatures, Springer-Verlag, Berlin (1992).Google Scholar
  49. 49.
    D. Hechtfischer, Cryogenics 27, 503 (1987); J. Phys. E 20, 143 (1987).Google Scholar
  50. 50.
    See, e.g., P. M. Berglund, H. K. Collan, G. J. Ehnholm, R. G. Gylling, and O. V. Lounasmaa, J. Low Temp. Phys. 6, 357 (1972).Google Scholar
  51. 51.
    National Institute of Standards and Technology (NIST), Gaithersburgh, MD 20899, USA; former National Bureau of Standards (NBS).Google Scholar
  52. 52.
    S. Yin and P. Hakonen, Rev. Sci. Instrum. 62, 1370 (1991).Google Scholar
  53. 53.
    K. Gloos, C. Mitschka, F. Pobell, and P. Smeibidl, Cryogenics 30, 14 (1990).Google Scholar
  54. 54.
    A. C. Anderson, R. E. Peterson, and J. E. Robichaux, Phys. Rev. Lett. 20, 459 (1968); E. R. Rumbo, J. Phys. F 6, 85 (1976).Google Scholar
  55. 55.
    Vacuumschmelze GMBH, Postfach 2253, D-63412, Germany.Google Scholar
  56. 56.
    Newport Corporation, 18235 Mt. Baldy Circle, Fountain Valley, CA 92728-8020 USA.Google Scholar
  57. 57.
    K. K. Nummila, Numerical Simulations on the Feasibility of Neutron Diffraction Experiments on Ordered Silver Nuclei (1991, unpublished).Google Scholar
  58. 58.
    Medgenics Diagnostics, Lise-Meitner Strasse 4a, 4030 Ratingen, Germany.Google Scholar
  59. 59.
    L. Koester, H. Rauch, and E. Seymann, At. Data and Nucl. Data Tables 49, 65 (1991).Google Scholar
  60. 60.
    G. J. Ehnholm, J. P. Ekström, J. F. Jacquinot, M. T. Loponen, O. V. Lounasmaa, and J. K. Soini, J. Low Temp. Phys. 39, 417 (1980).Google Scholar
  61. 61.
    A. J. Annila, K. N. Clausen, P. J. Hakonen, P.-A. Lindgard, O. V. Lounasmaa, K. K. Nummila, A. S. Oja, K. Siemensmeyer, M. Steiner, J. T. Tuoriniemi, H. Weinfurter, and H. E. Viertiö, Report Risø-M-2874 (1990).Google Scholar
  62. 62.
    M. A. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954).Google Scholar
  63. 63.
    L. H. Kjäldman and J. Kurkijärvi, Phys. Lett. 71A, 454 (1979).Google Scholar
  64. 64.
    A. S. Oja and P. Kumar, J. Low Temp. Phys. 66, 155 (1987).Google Scholar
  65. 65.
    H. E. Viertiö and A. S. Oja, Phys. Rev. B 36, 3805 (1987).Google Scholar
  66. 66.
    H. E. Viertiö, Theoretical Studies on Nuclear Magnetic Ordering in Copper and Silver, Ph.D. thesis, Helsinki University of Technology (1992).Google Scholar
  67. 67.
    P.-A. Lindgard, Phys. Rev. Lett. 61, 629 (1988).Google Scholar
  68. 68.
    M. T. Heinilä and A. S. Oja, Phys. Rev. B 48, 7227 (1993).Google Scholar
  69. 69.
    H. E. Viertiö, Phys. Scripta T 33, 168 (1990).Google Scholar
  70. 70.
    H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, Oxford University Press (1971).Google Scholar
  71. 71.
    F. B. Rasmussen, K. Baklanov, T. Hassekram, S. Pedersen, C. B. Sørensen, P. E. Lindelof, R. T. Vuorinen, and L. Lipinski, Czech. J. Phys. 46, 2773 (1996).Google Scholar
  72. 72.
    R. L. Haese, F. E. Bertrand, B. Harmatz, and M. J. Martin, Nucl. Data Sheets 37, 289 (1982).Google Scholar
  73. 73.
    P. de Gelder, E. Jacobs, and D. de Frenne, Nucl. Data Sheets 38, 545 (1983).Google Scholar
  74. 74.
    E. Storm and H. I. Israel, Nucl. Data Tables A 7, 565 (1970).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Kaj K. Nummila
    • 1
  • Juha T. Tuoriniemi
    • 1
  • Reko T. Vuorinen
    • 1
  • Kim Lefmann
    • 2
  • Albert Metz
    • 3
  • Finn B. Rasmussen
    • 4
  1. 1.Low Temperature LaboratoryHelsinki University of TechnologyHUTFinland.
  2. 2.Dept. of Condensed Matter Physics and Chemistry, Risiø National LaboratoryRoskildeDenmark.
  3. 3.Hahn-Meitner InstitutBerlinGermany
  4. 4.Niels Bohr InstituteUniversity of CopenhagenCopenhagen ØDenmark

Personalised recommendations