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Magnetic field density of perfect and imperfect flux line lattices in type II superconductors. I. Application of periodic solutions

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Abstract

The densityn(B) of the spatially varying magnetic fieldB inside a type II superconductor can be measured by nuclear magnetic resonance or muon-spin rotation (μ+SR). For a perfect flux-line latticen(B) exhibits van Hove singularities at the maximum, minimum, and saddle point values of the ideally periodicB(r). In a real superconductor, these singularities are smeared due to distortions of the flux-line lattice caused by, e.g., the interaction of flux lines with inhomogeneities in the material (pinning), structural defects in the flux-line lattice, the nonellipsoidal shape of the specimen, or fluctuations of the applied field and temperature. Such perturbations of the periodicity ofB(r) typically broaden the idealn(B) by convolution with a Gaussian whose width in general depends onB and which thus smears each singularity differently. Knowledge of the broadening is required for the interpretation of μ+SR experiments in the new ceramic superconductors and also in pure niobium, where it competes with the broadening caused by the diffusion of the positive muons. In this paper (Part I), the broadening ofn(B) is discussed in detail and some of its features are derived from the periodic solutions of the Ginzburg-Landau and BCS-Gorkov theories. Forthcoming parts will deal with the application of nonperiodic solutions and with computer simulations.

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References

  1. A. A. Abrikosov,Sov. Phys.-JETP 5, 1174 (1957).

    Google Scholar 

  2. D. Cribier, B. Jacrot, L. M. Rao, and B. Farnoux,Phys. Lett. 9, 106 (1964).

    Google Scholar 

  3. J. Schelten, H. Ullmaier, and W. Schmatz,Phys. Stat. Sol. (b)48, 619 (1971).

    Google Scholar 

  4. P. Thorel, P. Kahn, Y. Simon, and C. Cribier,J. Phys. (Paris)34, 447 (1973).

    Google Scholar 

  5. H. W. Weber, J. Schelten, and G. Lippmann,Phys. Stat. Sol. (b)57, 511 (1973).

    Google Scholar 

  6. J. R. Clem,J. Low Temp. Phys. 18, 427 (1975).

    Google Scholar 

  7. E. H. Brandt,Phys. Stat. Sol. (b)51, 345 (1972).

    Google Scholar 

  8. U. Essmann and H. Träuble,Phys. Lett. 24A, 526 (1967).

    Google Scholar 

  9. H. Träuble and U. Essmann,J. Appl. Phys. 39, 4052 (1968).

    Google Scholar 

  10. N. V. Sarma,Phil. Mag. 18, 171 (1968).

    Google Scholar 

  11. P. L. Gammel, D. J. Bishop, G. J. Dolan, J. R. Kwo, C. A. Murray, L. F. Schreemeyer, and J. V. Waszczak,Phys. Rev. Lett. 59, 2592 (1987).

    Google Scholar 

  12. A. G. Redfield,Phys. Rev. 162, 367 (1967).

    Google Scholar 

  13. J. M. Delrieu,J. Low Temp. Phys. 6, 197 (1972).

    Google Scholar 

  14. J. M. Delrieu,J. Phys. F: Metal Phys. 3, 893 (1973).

    Google Scholar 

  15. J. M. Delrieu, Thèse d'Etat, Université Paris-sud (1974).

  16. E. H. Brandt,Phys. Lett. 43A, 539 (1973).

    Google Scholar 

  17. E. H. Brandt,Phys. Stat. Sol. (b)64, 467 (1974).

    Google Scholar 

  18. I. I. Gurevich, E. A. Meleshko, I. A. Muratova, B. A. Nikolskij, V. S. Roganov, V. I. Selivanov, and B. V. Sokolov,Phys. Lett. 40A, 143 (1972).

    Google Scholar 

  19. A. Seeger,Phys. Lett. 77A, 259 (1979).

    Google Scholar 

  20. E. H. Brandt and A. Seeger,Adv. Phys. 35, 189 (1986).

    Google Scholar 

  21. C. P. Slichter,Principles of Magnetic Resonance, 2nd ed. (Springer, Heidelberg, 1980).

    Google Scholar 

  22. W. Schwarz, E. H. Brandt, K.-P. Döring, U. Essmann, K. Fürderer, M. Gladisch, D. Herlach, G. Majer, H.-J. Mundinger, H. Orth, A. Seeger, and M. Schmolz,Hyperfine Interact. 31, 257 (1987).

    Google Scholar 

  23. G. Aeppli, R. J. Cava, E. J. Ansaldo, J. H. Brewer, S. R. Kreitzman, G. M. Luke, D. R. Noakes, and R. F. Kiefl,Phys. Rev. B 35, 7129 (1987).

    Google Scholar 

  24. W. J. Kossler, J. R. Kempton, X. H. Yu, H. E. Schone, Y. J. Uemura, A. R. Moodenbaugh, M. Suenaga, and C. E. Stronach,Phys. Rev. B 35, 7133 (1987).

    Google Scholar 

  25. D. R. Harschman, G. Aeppli, E. J. Ansaldo, B. Batlogg, J. H. Brewer, J. F. Carolan, R. J. Cava, M. Celio, A. C. D. Chaklader, W. N. Hardy, S. R. Kreitzman, G. M. Luke, D. R. Noakes, and M. Senba,Phys. Rev. B 36, 2386 (1987).

    Google Scholar 

  26. F. N. Gygax, B. Hitti, E. Lippelt, A. Schenck, D. Cattani, J. Cors, M. Decroux, Ø. Fischer, and S. Barth,Europhys. Lett. 4, 473 (1987).

    Google Scholar 

  27. E. H. Brandt,Phys. Rev. B 37, 2349 (1988).

    Google Scholar 

  28. R. Labusch,Phys. Stat. Sol. (b)69, 359 (1975).

    Google Scholar 

  29. E. H. Brandt,Phys. Rev. B 18, 6022 (1978).

    Google Scholar 

  30. E. H. Brandt,Phys. Stat. Sol. 36, 381, 393 (1969).

    Google Scholar 

  31. V. G. Kogan,J. Low Temp. Phys. 32, 419 (1978).

    Google Scholar 

  32. E. H. Brandt,J. Low Temp. Phys. 28, 263 (1977).

    Google Scholar 

  33. E. H. Brandt,J. Low Temp. Phys. 28, 291 (1977).

    Google Scholar 

  34. E. H. Brandt,Phys. Rev. Lett. 50, 1599 (1983);J. Low Temp. Phys. 53, 41, 71 (1983).

    Google Scholar 

  35. A. M. Campbell and J. E. Evetts,Adv. Phys. 21, 199 (1972).

    Google Scholar 

  36. E. H. Brandt,J. Low Temp. Phys. 26, 709, 735 (1977).

    Google Scholar 

  37. A. I. Larkin and Yu. N. Ovchinnikov,J. Low Temp. Phys. 43, 409 (1979).

    Google Scholar 

  38. E. H. Brandt,Phys. Rev. B 14, 6514 (1986).

    Google Scholar 

  39. E. H. Brandt and U. Essmann,Phys. Stat. Sol. (b)144, 13 (1987).

    Google Scholar 

  40. A. M. Campbell,Jpn. J. Appl. Phys. 26, 2053 (1987).

    Google Scholar 

  41. P. H. Kes,Physica C 153–155, 1121 (1988).

    Google Scholar 

  42. W. Pesch and L. Kramer,J. Low Temp. Phys. 15, 367 (1974).

    Google Scholar 

  43. E. H. Brandt,Phys. Stat. Sol. (b)77, 105 (1976).

    Google Scholar 

  44. U. Klein,J. Low Temp. Phys. 69, 1 (1987).

    Google Scholar 

  45. E. H. Brandt, to be published.

  46. E. H. Brandt,Phys. Stat. Sol. (b)65, 469 (1974).

    Google Scholar 

  47. G. Eilenberger,Z. Phys. 214, 195 (1968).

    Google Scholar 

  48. L. Kramer and W. Pesch,Z. Phys. 269, 59 (1974).

    Google Scholar 

  49. K. Maki and T. Tsuzuki,Phys. Rev. A 139, 868 (1965).

    Google Scholar 

  50. G. Eilenberger,Phys. Rev. 153, A2584 (1967).

    Google Scholar 

  51. V. G. Kogan and J. R. Clem,Phys. Rev. B 24, 1572 (1981);Jpn. J. Appl. Phys. 26, 1159 (1987).

    Google Scholar 

  52. A. V. Balatskij, L. I. Burlachkov, and L. P. Gorkov,Sov. Phys.-JETP 63, 866 (1986).

    Google Scholar 

  53. M. Celio, T. M. Riseman, J. H. Brewer, and R. F. Kiefl,Physica C 153–155, 753 (1988).

    Google Scholar 

  54. E. H. Brandt,Phys. Rev. Lett. 56, 1381 (1986).

    Google Scholar 

  55. R. Schmucker and E. H. Brandt,Phys. Stat. Sol. (b)79, 479 (1977).

    Google Scholar 

  56. H. Träuble and U. Essmann,Phys. Stat. Sol. 25, 373 (1968).

    Google Scholar 

  57. R. Schmucker,Phil Mag. 35, 431, 453 (1977).

    Google Scholar 

  58. P. H. Kes and C. C. Tsuei,Phys. Rev. Lett. 47, 1930 (1981);Phys. Rev. B 28, 5126 (1983).

    Google Scholar 

  59. R. Wördenweber and P. H. Kes,Phys. Rev. B 34, 494 (1986).

    Google Scholar 

  60. E. H. Brandt,J. Low Temp. Phys. 64, 375 (1986).

    Google Scholar 

  61. R. Wördenweber and P. H. Kes,J. Low Temp. Phys. 67, 1 (1987).

    Google Scholar 

  62. E. H. Brandt,Phys. Rev. Lett. 56, 1381 (1986).

    Google Scholar 

  63. G. M. Eliashberg,Sov. Phys.-JETP 11, 696 (1960);16, 780 (1963).

    Google Scholar 

  64. G. E. Zwicknagl and J. W. Wilkins,Phys. Rev. Lett. 53, 1276 (1984).

    Google Scholar 

  65. G. E. Zwicknagl,Physica 135B, 267 (1985).

    Google Scholar 

  66. E. V. Thuneberg, J. Kurkijärvi, and D. Rainer,Phys. Rev. Lett. 48, 1853 (1982);Phys. Rev. B 29, 3913 (1984).

    Google Scholar 

  67. E. V. Thuneberg,J. Low Temp. Phys. 57, 415 (1984);62, 27 (1986).

    Google Scholar 

  68. R. Labusch,Phys. Stat. Sol. 32, 439 (1969).

    Google Scholar 

  69. E. H. Brandt,Phys. Stat. Sol. (b)77, 551 (1976).

    Google Scholar 

  70. E. H. Brandt,Phil. Mag. B 37, 293 (1978).

    Google Scholar 

  71. A. Seeger,Handbuch der Physik, Vol. VII, Parts 1 and 2 (Springer, Berlin, 1955, 1958).

    Google Scholar 

  72. R. Labusch,Phys. Lett. 22, 9 (1966).

    Google Scholar 

  73. J. P. Hirth and J. Lothe,Theory of Dislocations, 2nd ed. (Wiley, New York, 1982).

    Google Scholar 

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  1. Max-Planck-Institut für Metallforschung, Institut für Physik, Stuttgart, Germany

    E. H. Brandt

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Brandt, E.H. Magnetic field density of perfect and imperfect flux line lattices in type II superconductors. I. Application of periodic solutions. J Low Temp Phys 73, 355–390 (1988). https://doi.org/10.1007/BF00683568

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