Advertisement

Journal of Low Temperature Physics

, Volume 76, Issue 5–6, pp 287–386 | Cite as

SQUID magnetometers for low-frequency applications

  • Tapani Ryhänen
  • Heikki Seppä
  • Risto Ilmoniemi
  • Jukka Knuutila
Article

Abstract

We present a novel formulation for SQUID operation, which enables us to evaluate and compare the sensitivity and applicability of different devices. SQUID magnetometers for low-frequency applications are analyzed, taking into account the coupling circuits and electronics. We discuss nonhysteretic and hysteretic single-junction rf SQUIDs, but the main emphasis is on the dynamics, sensitivity, and coupling considerations of dc-SQUID magnetometers. A short review of current ideas on thin-film, dc-SQUID design presents the problems in coupling and the basic limits of sensitivity. The fabrication technology of tunnel-junction devices is discussed with emphasis on how it limits critical current densities, specific capacitances of junctions, minimum linewidths, conductor separations, etc. Properties of high-temperature superconductors are evaluated on the basis of recently published results on increased flux creep, low density of current carriers, and problems in fabricating reliable junctions. The optimization of electronics for different types of SQUIDs is presented. Finally, the most important low-frequency applications of SQUIDs in biomagnetism, metrology, geomagnetism, and some physics experiments demonstrate the various possibilities that state-of-the-art SQUIDs can provide.

Keywords

Magnetic Material Specific Capacitance Physics Experiment Critical Current Density Current Idea 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Barone and G. Paterno,Physics and Applications of the Josephson Effect (Wiley, New York, 1982).Google Scholar
  2. 2.
    T. Van Duzer and C. W. Turner,Principles of Superconductive Devices and Circuits (Elsevier North-Holland, New York, 1981).Google Scholar
  3. 3.
    J. C. Gallop,Metrologia 18, 67 (1982).Google Scholar
  4. 4.
    K. K. Likharev,Dynamics of Josephson Junctions and Circuits (Gordon and Breach, New York, 1986).Google Scholar
  5. 5.
    O. V. Lounasmaa,Experimental Principles and Methods Below 1K (Academic Press, New York, 1974).Google Scholar
  6. 6.
    L. Solymar,Superconductive Tunnelling and Applications (Chapman and Hall, London, 1972).Google Scholar
  7. 7.
    M. Tinkham,Introduction to Superconductivity (McGraw-Hill, New York, 1975).Google Scholar
  8. 8.
    R. C. Jaklevic, J. Lambe, A. H. Silver, and J. E. Mercereau,Phys. Rev. Lett. 12, 159 (1964).Google Scholar
  9. 9.
    R. C. Jaklevic, J. Lambe, J. E. Mercereau, and A. H. Silver,Phys. Rev. A 140, 1628 (1965).Google Scholar
  10. 10.
    J. Clarke,Philos. Mag. 13, 115 (1966).Google Scholar
  11. 11.
    J. Clarke, W. M. Goubau, and M. B. Ketchen,J. Low Temp. Phys. 25, 99 (1976).Google Scholar
  12. 12.
    C. D. Tesche and J. Clarke,J. Low Temp. Phys. 29, 301 (1977).Google Scholar
  13. 13.
    A. H. Silver and J. E. Zimmerman,Phys. Rev. 157, 317 (1967).Google Scholar
  14. 14.
    J. G. Bednorz and K. A. Müller,Z. Phys. B 64, 189 (1986).Google Scholar
  15. 15.
    R. Ilmoniemi, J. Knuutila, T. Ryhänen, and H. Seppä, inProgress in Low Temperature Physics, Vol. XII, D. Brewer, ed. (Elsevier, New York, 1989).Google Scholar
  16. 16.
    J. Bardeen, L. N. Cooper, and J. R. Schrieffer,Phys. Rev. 108, 1175 (1957).Google Scholar
  17. 17.
    B. D. Josephson,Phys. Lett. 1, 251 (1962).Google Scholar
  18. 18.
    V. Ambegaokar and A. Baratoff,Phys. Rev. Lett. 10, 486 (1963), erratum;Phys. Rev. Lett. 11, 104 (1963).Google Scholar
  19. 19.
    B. D. Josephson,Rev. Mod. Phys. 36, 216 (1964).Google Scholar
  20. 20.
    B. D. Josephson,Adv. Phys. 14, 419 (1965).Google Scholar
  21. 21.
    P. W. Anderson and J. M. Rowell,Phys. Rev. Lett. 10, 230 (1963).Google Scholar
  22. 22.
    J. M. Rowell, P. W. Anderson, and D. E. Thomas,Phys. Rev. Lett. 10, 334 (1963).Google Scholar
  23. 23.
    J. M. Rowell,Phys. Rev. Lett. 11, 200 (1963).Google Scholar
  24. 24.
    B. N. Taylor and E. Burstein,Phys. Rev. Lett. 10, 14 (1963).Google Scholar
  25. 25.
    C. J. Adkins,Philos. Mag. 8, 1051 (1963).Google Scholar
  26. 26.
    N. F. Pedersen, T. F. Finnegan and D. N. Langenberg, inProceedings of the 13th International Conference on Low Temperature Physics, Boulder, Vol. 3, K. D. Timmerhaus, W. J. O'Sullivan, and E. F. Hammel, eds. (Plenum, New York, 1972), p. 268.Google Scholar
  27. 27.
    C. M. Falco, W. H. Parker and S. E. Trullinger,Phys. Rev. Lett. 31, 933 (1973), erratum;Phys. Rev. Lett. 31, 1476 (1973).Google Scholar
  28. 28.
    J. M. Rowell,IEEE Trans. Magn. MAG-23, 380 (1987).Google Scholar
  29. 29.
    N. F. Pedersen and K. Saermark,Physica (Utrecht)69, 572 (1973).Google Scholar
  30. 30.
    D. A. Vincent and B. S. Deaver, Jr.,Phys. Rev. Lett. 32, 212 (1974).Google Scholar
  31. 31.
    J. Hansma,J. Appl. Phys. 44, 4191 (1973).Google Scholar
  32. 32.
    M. Nisenoff,Rev. Phys. Appl. 5, 21 (1970).Google Scholar
  33. 33.
    R. Rifkin, D. A. Vincent, B. S. Deaver, Jr., and P. K. Hansma,J. Appl. Phys. 47, 2645 (1976).Google Scholar
  34. 34.
    S. N. Erné, H. Luther, and H. J. Scheer, inSQUID '80, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1980), p. 109.Google Scholar
  35. 35.
    S. N. Erné and H. Luther,J. Appl. Phys. 52, 2918 (1981).Google Scholar
  36. 36.
    D. E. McCumber,J. Appl. Phys. 7, 3113 (1968).Google Scholar
  37. 37.
    W. C. Stewart,Appl. Phys. Lett. 12, 277 (1968).Google Scholar
  38. 38.
    J. Kurkijärvi and V. Ambegaokar,Phys. Lett. 31A, 314 (1970).Google Scholar
  39. 39.
    J. A. Ketoja, J. Kurkijärvi, and R. K. Ritala,Phys. Lett. 105A, 425 (1985).Google Scholar
  40. 40.
    H. A. Kramers,Physica 7, 284 (1940).Google Scholar
  41. 41.
    V. Ambegaokar and B. I. Halperin,Phys. Rev. Lett. 22, 1364 (1969).Google Scholar
  42. 42.
    R. F. Voss,J. Low Temp. Phys. 42, 151 (1981).Google Scholar
  43. 43.
    V. V. Danilov, K. K. Likharev, and A. B. Zorin,IEEE Trans. Magn. MAG-19, 572 (1983).Google Scholar
  44. 44.
    H. Seppä,J. Appl. Phys. 55, 1578 (1984).Google Scholar
  45. 45.
    R. J. Soulen, Jr. and D. Van Vechten,Phys. Rev. B 36, 239 (1987).Google Scholar
  46. 46.
    W. C. Scott,Appl. Phys. Lett. 17, 166 (1970).Google Scholar
  47. 47.
    W. C. Stewart,J. Appl. Phys. 45, 452 (1974).Google Scholar
  48. 48.
    K. Matsuo,Suppl. Prog. Theor. Phys. 69, 301 (1980).Google Scholar
  49. 49.
    A. B. Zorin, K. K. Likharev, and S. I. Turovets,IEEE Trans. Magn. MAG-19, 629 (1983).Google Scholar
  50. 50.
    R. E. Harris,J. Appl. Phys. 48, 5188 (1977).Google Scholar
  51. 51.
    R. I. Gayley,J. Appl. Phys. 52, 1411 (1981).Google Scholar
  52. 52.
    V. K. Semenov, A. A. Odintsov and A. B. Zorin, inSQUID '85, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1985), p. 71.Google Scholar
  53. 53.
    H. Kratz and W. Jutzi,IEEE Trans. Magn. MAG-23, 731 (1987).Google Scholar
  54. 54.
    W. Jutzi, E. Crocoll and J. Marz,Jpn. J. Appl. Phys. 26-3, 1589 (1987).Google Scholar
  55. 55.
    M. J. Stephen,Phys. Rev. Lett. 21, 1629 (1968).Google Scholar
  56. 56.
    M. J. Stephen,Phys. Rev. 182, 531 (1969).Google Scholar
  57. 57.
    M. J. Stephen,Phys. Rev. 186, 393 (1969).Google Scholar
  58. 58.
    D. J. Scalapino, in Proceedings of the Symposium on the Physics of Superconducting Devices, B. S. Deaver, Jr, ed. (University of Virginia Press, Charlottesville, 1968).Google Scholar
  59. 59.
    A. J. Dahm, A. Denestein, D. N. Langenberg, W. H. Parker, D. Rogovin, and D. J. Scalapino,Phys. Rev. Lett. 22, 1416 (1969).Google Scholar
  60. 60.
    D. Rogovin and D. J. Scalapino,Ann. Phys. 86, 1 (1974).Google Scholar
  61. 61.
    K. K. Likharev,Rev. Mod. Phys. 51, 101 (1979).Google Scholar
  62. 62.
    Y. Aharonov and D. Bohm,Phys. Rev. 115, 485 (1959).Google Scholar
  63. 63.
    R. G. Chambers,Phys. Rev. Lett. 5, 3 (1960).Google Scholar
  64. 64.
    M. Büttiker, inSQUID '85, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1985), p. 529.Google Scholar
  65. 65.
    R. A. Webb, S. Washburn, C. P. Umbach, and R. B. Laibowitz, inSQUID '85, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1985), p. 561.Google Scholar
  66. 66.
    A. van der Ziel,J. Appl. Phys. 19, 999 (1948).Google Scholar
  67. 67.
    L. A. Blackwell and K. L. Kotzebue,Semiconductor-Diode Parametric Amplifiers (Prentice-Hall, Englewood Cliffs, New Jersey, 1961).Google Scholar
  68. 68.
    K. K. N. Chang,Parametric and Tunnel Diodes (Prentice-Hall, Englewood Cliffs, New Jersey, 1964).Google Scholar
  69. 69.
    S. N. Erné, H.-D. Hahlbohm, and H. Lübbig,J. Appl. Phys. 47, 5440 (1976).Google Scholar
  70. 70.
    V. V. Danilov, K. K. Likharev, and O. V. Snigirev, inSQUID '80, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1980), p. 473.Google Scholar
  71. 71.
    I. M. Dmitrenko, G. M. Tsoi, V. I. Shnyrkov, and V. V. Kartsovnik,J. Low Temp. Phys. 49, 417 (1982).Google Scholar
  72. 72.
    H. A. Notarys, R. H. Wang, and J. E. Mercereau,Proc. IEEE 61, 79 (1973).Google Scholar
  73. 73.
    D. Pascal and M. Sauzade,J. Appl. Phys. 45, 3085 (1974).Google Scholar
  74. 74.
    R. A. Buhrman and L. D. Jackel,IEEE Trans. Magn. MAG-13, 879 (1977).Google Scholar
  75. 75.
    O. H. Soerensen,J. Appl. Phys. 47, 5030 (1976).Google Scholar
  76. 76.
    A. Callegari and B. S. Deaver, Jr.,J. Appl. Phys. 48, 5328 (1977).Google Scholar
  77. 77.
    V. I. Shnyrkov, V. A. Khlus, and G. M. Tsoi,J. Low Temp. Phys. 39, 477 (1980).Google Scholar
  78. 78.
    M. Nisenoff and S. Wolf,Phys. Rev. B 12, 1712 (1975).Google Scholar
  79. 79.
    T. A. Fulton, L. N. Dunkleberger, and R. C. Dynes,Phys. Rev. B 6, 855 (1972).Google Scholar
  80. 80.
    B. V. Vasilev, V. V. Danilov, and K. K. Likharev,IEEE Trans. Magn. MAG-11, 743 (1975).Google Scholar
  81. 81.
    R. A. Buhrman, inSQUID '76, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1977), p. 395.Google Scholar
  82. 82.
    G. J. Ehnholm,J. Low Temp. Phys. 29, 1 (1977).Google Scholar
  83. 83.
    J. E. Zimmerman, P. Thiene, and J. T. Harding,J. Appl. Phys. 41, 1572 (1970).Google Scholar
  84. 84.
    J. E. Mercereau,Rev. Phys. Appl. 5, 13 (1970).Google Scholar
  85. 85.
    W. W. Webb,IEEE Trans. Magn. MAG-8, 51 (1972).Google Scholar
  86. 86.
    R. P. Giffard, R. A. Webb, and J. C. Wheatley,J. Low Temp. Phys. 6, 533 (1972).Google Scholar
  87. 87.
    J. Clarke,Proc. IEEE 61, 8 (1973).Google Scholar
  88. 88.
    L. D. Jackel and R. A. Buhrman,J. Low Temp. Phys. 19, 201 (1975).Google Scholar
  89. 89.
    M. B. Simmonds and W. H. Parker,J. Appl. Phys. 42, 38 (1971).Google Scholar
  90. 90.
    J. Kurkijärvi,Phys. Rev. B 6, 832 (1972).Google Scholar
  91. 91.
    J. Kurkijärvi and W. W. Webb, inProceedings of the 1972 Applied Superconductivity Conference (IEEE, New York, 1972), p. 581.Google Scholar
  92. 92.
    J. Kurkijärvi,J. Appl. Phys. 44, 3729 (1973).Google Scholar
  93. 93.
    A. V. Gusev and V. N. Rudenko,Zh. Eksp. Teor. Fiz. 72, 1217 (1977).Google Scholar
  94. 94.
    J. Hough, J. R. Pugh, W. A. Edelstein, and W. Martin,J. Phys. E 10, 993 (1977).Google Scholar
  95. 95.
    J. N. Hollenhorst and R. P. Giffard,J. Low Temp. Phys. 39, 477 (1980).Google Scholar
  96. 96.
    J. Kurkijärvi,J. Low Temp. Phys. 45, 37 (1981).Google Scholar
  97. 97.
    H. Ahola, G. J. Ehnholm, S. T. Islander, and B. Rantala, XXth Congress Ampere, Tallinn (1978).Google Scholar
  98. 98.
    A. Hoffman and B. Buchholz,J. Phys. E 17, 1035 (1984).Google Scholar
  99. 99.
    H. Seppä, P. Immonen, and J. Räihä,IEEE Trans. Instrum. Meas. IM-37, 2 (1988).Google Scholar
  100. 100.
    A. P. Long, T. D. Clark, and R. J. Prance,Rev. Sci. Instrum. 51, 8 (1980).Google Scholar
  101. 101.
    R. J. Prance, A. P. Long, T. D. Clark, and F. Goodall,J. Phys. E 15, 101 (1982).Google Scholar
  102. 102.
    R. Keränen and J. Kurkijärvi,J. Low Temp. Phys. 65, 279 (1986).Google Scholar
  103. 103.
    R. A. Kamper and M. B. Simmonds,Appl. Phys. Lett. 20, 270 (1972).Google Scholar
  104. 104.
    J. M. Pierce, J. E. Opfer, and L. H. Rorden,IEEE Trans. Magn. MAG-11, 599 (1975).Google Scholar
  105. 105.
    H. Kanter and F. L. Vernon, Jr.,IEEE Trans. Magn. MAG-13, 389 (1977).Google Scholar
  106. 106.
    J. N. Hollenhorst and R. P. Giffard,IEEE Trans. Magn. MAG-15, 474 (1979).Google Scholar
  107. 107.
    A. P. Long, T. D. Clark, R. J. Prance, and M. G. Richards,Rev. Sci. Instrum. 50, 1376 (1979).Google Scholar
  108. 108.
    F. J. Rachford and J. Cukauskas,Appl. Phys. Lett. 35, 881 (1979).Google Scholar
  109. 109.
    H. Seppä,IEEE Trans. Instrum. Meas. 32, 253 (1983).Google Scholar
  110. 110.
    O. G. Vendik, Yu. N. Gorin, and M. G. Stepanova,Pis'ma Zh. Tekh. Fiz. 9, 1007 (1983).Google Scholar
  111. 111.
    L. S. Kuzmin, K. K. Likharev, V. V. Migulin, E. A. Polunin, and N. A. Simonov, inSQUID '85, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1985), p. 1029.Google Scholar
  112. 112.
    A. D. Smith, R. W. Simon, J. F. Durch, R. D. Sandell, and A. H. Silver,IEEE Trans. Magn. Mag-23 1079 (1987).Google Scholar
  113. 113.
    T. Ryhänen and H. Seppä,IEEE Trans. Magn. MAG-25, 881 (1989).Google Scholar
  114. 114.
    H. K. Olsson and T. Claeson,J. Appl. Phys. 64, 5234 (1988).Google Scholar
  115. 115.
    R. A. Kamper, C. A. Simmonds, C. A. Hoer and R. T. Adain,Proc. IEEE 61, 121 (1973).Google Scholar
  116. 116.
    B. W. Petley, K. Morris, R. W. Yell, and R. N. Clarke,Electron. Lett. 12, 237 (1976).Google Scholar
  117. 117.
    D. B. Sullivan, R. T. Adain, and N. V. Frederick,Proc. IEEE 66, 454 (1978).Google Scholar
  118. 118.
    R. A. Kamper and J. E. Zimmerman,J. Appl. Phys. 42, 132 (1971).Google Scholar
  119. 119.
    R. J. Soulen, Jr. and H. Marshak,Cryogenics 7, 408 (1980).Google Scholar
  120. 120.
    R. J. Soulen, Jr., R. L. Rusby, and D. Van Vechten,J. Low Temp. Phys. 40, 553 (1980).Google Scholar
  121. 121.
    J. G. Park and A. Vaidya,IEEE Trans. Magn. MAG-17, 845 (1981).Google Scholar
  122. 122.
    A. H. Silver, R. D. Sandell, and J. Z. Wilcox,IEEE Trans. Magn. MAG-19, 625 (1983).Google Scholar
  123. 123.
    H. Seppä,J. Appl. Phys. 55, 1572 (1984).Google Scholar
  124. 124.
    S. N. Erné and H. Luther,PTB-Mitteilungen 94, 989 (1984).Google Scholar
  125. 125.
    M. Van Veldhuizen and H. A. Fowler,Phys. Rev. B 31 5805 (1985).Google Scholar
  126. 126.
    R. L. Peterson,J. Appl. Phys. 52, 7321 (1981).Google Scholar
  127. 127.
    K. K. Likharev and V. K. Semenov,Zh. Eksp. Teor. Fiz. 15, 625 (1972),JETP Lett. 15, 442 (1972).Google Scholar
  128. 128.
    R. P. Giffard, P. F. Michelson, and R. J. Soulen, Jr.,IEEE Trans. Magn. MAG-15, 276 (1979).Google Scholar
  129. 129.
    R. J. Soulen, Jr., D. Van Vechten, and H. Seppä,Rev. Sci. Instrum. 53, 1355 (1982).Google Scholar
  130. 130.
    H. Seppä,J. Low Temp. Phys. 62, 329 (1986).Google Scholar
  131. 131.
    R. A. Webb, R. P. Giffard, and J. C. Wheatley,J. Low Temp. Phys. 13, 383 (1973).Google Scholar
  132. 132.
    M. L. Roukes, R. S. Germain, M. R. Freeman, and R. C. Richardson, inProceedings of the 17th International Conference on Low Temperature Physics LT-17, U. Eckern, A. Schmid, W. Weber, and H. Wühl, eds. (North-Holland, Amsterdam, 1984), p. 1177.Google Scholar
  133. 133.
    S. N. Erné, H. Koch, and H. Luther, inSQUID '85, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1985), p. 165.Google Scholar
  134. 134.
    J. E. Zimmerman and A. H. Silver,Phys. Rev. 141, 367 (1966).Google Scholar
  135. 135.
    J. Clarke and T. A. Fulton,J. Appl. Phys. 40, 4470 (1969).Google Scholar
  136. 136.
    J. Clarke,IEEE Trans. Electron Dev. ED-27, 1896 (1980).Google Scholar
  137. 137.
    J. M. Jaycox and M. B. Ketchen,IEEE Trans. Magn. MAG-17, 400 (1981).Google Scholar
  138. 138.
    M. B. Ketchen,IEEE Trans. Magn. MAG-17, 387 (1981).Google Scholar
  139. 139.
    M. B. Ketchen, W. M. Goubau, J. Clarke, and G. B. Donaldson,J. Appl. Phys. 49, 4111 (1978).Google Scholar
  140. 140.
    M. B. Ketchen and J. M. Jaycox,Appl. Phys. Lett. 40, 736 (1982).Google Scholar
  141. 141.
    C. D. Tesche,J. Low Temp. Phys. 47, 385 (1982).Google Scholar
  142. 142.
    P. Carelli and V. Foglietti,J. Appl. Phys. 53, 7592 (1982).Google Scholar
  143. 143.
    B. Muhlfelder, J. A. Beall, M. W. Cromar, R. H. Ono, and W. W. Johnson,IEEE Trans. Magn. MAG-21, 427 (1985).Google Scholar
  144. 144.
    K. Enpuku, K. Sueoka, K. Yoshida, and F. Irie,J. Appl. Phys. 57, 1691 (1985).Google Scholar
  145. 145.
    V. J. de Waal and T. M. Klapwijk,Appl. Phys. Lett. 41, 669 (1982).Google Scholar
  146. 146.
    J. Knuutila, A. Ahonen, and C. Tesche,J. Low Temp. Phys. 68, 269 (1987).Google Scholar
  147. 147.
    D. Drung and W. Jutzi, inSQUID '85, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1985), p. 807.Google Scholar
  148. 148.
    H. Seppä and T. Ryhänen,IEEE Trans. Magn. MAG-23, 1083 (1987).Google Scholar
  149. 149.
    E. Ben-Jacob and Y. Imry,J. Appl. Phys. 52, 6806 (1981).Google Scholar
  150. 150.
    J. A. Ketoja, J. Kurkijärvi, and R. K. Ritala,Phys. Rev. B 30, 3757 (1984).Google Scholar
  151. 151.
    J. A. Ketoja, J. Kurkijärvi, T. Ryhänen, and H. Seppä,Phys. Rev. B 35, 404 (1987).Google Scholar
  152. 152.
    A. Th. A. M. de Waele and R. de Bruyn Ouboter,Physica 41, 225 (1968).Google Scholar
  153. 153.
    R. L. Peterson and D. G. McDonald,J. Appl. Phys. 54, 992 (1983).Google Scholar
  154. 154.
    C. Hilbert and J. Clarke,J. Low Temp. Phys. 61, 237 (1985).Google Scholar
  155. 155.
    A. D. Wentzell and M. I. Freidlin,Russian Math. Surveys 25, 1 (1970).Google Scholar
  156. 156.
    M. I. Freidlin and A. D. Wentzell,Random Perturbations of Dynamical Systems (Springer, New York, 1984).Google Scholar
  157. 157.
    E. Ben-Jacob, D. J. Bergman, Y. Imry, B. J. Matkowsky, and Z. Schuss,J. Appl. Phys. 54, 6533 (1983).Google Scholar
  158. 158.
    E. Ben-Jacob, D. J. Bergman, B. J. Matkowsky, and Z. Schuss, inSQUID '85, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1985), p. 219.Google Scholar
  159. 159.
    J. Kurkijärvi, inSQUID '85, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1985), p. 377.Google Scholar
  160. 160.
    I. O. Kulik,Zh. Eksp. Teor. Fiz. 37, 157 (1967).Google Scholar
  161. 161.
    Y. Imry and P. M. Marcus,IEEE Trans. Magn. MAG-13, 868 (1977).Google Scholar
  162. 162.
    J. J. P. Bruines, V. J. de Waal, and J. E. Mooij,J. Low Temp. Phys. 46, 383 (1982).Google Scholar
  163. 163.
    V. J. de Waal, P. Schrijner, and R. Llurba,J. Low Temp. Phys. 54, 215 (1984).Google Scholar
  164. 164.
    R. Leoni, P. Carelli, and V. Foglietti,Phys. Rev. B 35, 400 (1987).Google Scholar
  165. 165.
    S. Chandrasekhar,Rev. Mod. Phys. 15, 1 (1943).Google Scholar
  166. 166.
    H. Risken and H. D. Vollmer,Phys. Lett. 69A, 387 (1979).Google Scholar
  167. 167.
    H. D. Vollmer and H. Risken,Z. Phys. B 34, 313 (1979).Google Scholar
  168. 168.
    Y. Imry and L. S. Schulman,J. Appl. Phys. 49, 749 (1978).Google Scholar
  169. 169.
    E. Ben-Jacob, D. J. Bergman, Z. Schuss,Phys. Rev. B 25, 519 (1982).Google Scholar
  170. 170.
    C. D. Tesche,J. Low Temp. Phys. 44, 119 (1981).Google Scholar
  171. 171.
    H. Risken,The Fokker-Planck Equation (Springer-Verlag, New York, 1984).Google Scholar
  172. 172.
    Z. Schuss,SIAM J. Review 22, 119 (1980).Google Scholar
  173. 173.
    H. Suhl,Phys. Rev. Lett. 60, 473 (1988).Google Scholar
  174. 174.
    F. Sharifi, J. L. Gavilano, and D. J. van Harlingen,Phys. Rev. Lett. 61, 742 (1988).Google Scholar
  175. 175.
    C. Grebogi, E. Ott, and J. A. Yorke,Phys. Rev. Lett. 50, 935 (1983).Google Scholar
  176. 176.
    J. Guckenheimer and P. Holmes,Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).Google Scholar
  177. 177.
    A. J. Lichtenberg and M. A. Lieberman,Regular and Stochastic Motion (Springer-Verlag, New York, 1983).Google Scholar
  178. 178.
    E. Ben-Jacob, D. J. Bergman, B. J. Matkowsky and Z. Schuss,Phys. Rev. A 26, 2805 (1982).Google Scholar
  179. 179.
    M. R. Beasley, D. D'Humieres and B. A. Huberman,Phys. Rev. Lett. 50, 1328 (1983).Google Scholar
  180. 180.
    R. L. Kautz,J. Appl. Phys. 58, 424 (1985).Google Scholar
  181. 181.
    R. L. Kautz,Phys. Lett. 125A, 315 (1987).Google Scholar
  182. 182.
    R. L. Kautz,Phys. Rev. A 38, 2066 (1988).Google Scholar
  183. 183.
    J. E. Zimmerman,J. Appl. Phys. 42, 4483 (1971).Google Scholar
  184. 184.
    M. S. Gupta,Phys. Rev. A 18, 2725 (1978).Google Scholar
  185. 185.
    M. S. Gupta,Proc. IEEE 70, 788 (1982).Google Scholar
  186. 186.
    Y. Netzer,Proc. IEEE 62, 404 (1974).Google Scholar
  187. 187.
    Y. Netzer,Proc. IEEE 69, 728 (1981).Google Scholar
  188. 188.
    J. H. Claassen,J. Appl. Phys. 46, 2268 (1975).Google Scholar
  189. 189.
    J. Knuutila, M. Kajola, H. Seppä, R. Mutikainen, and J. Salmi,J. Low Temp. Phys. 71, 369 (1988).Google Scholar
  190. 190.
    R. F. Voss, R. B. Laibowitz, A. N. Broers, S. I. Raider, C. M. Knoedler, and J. M. Viggiano,IEEE Trans. Magn. MAG-17, 395 (1981).Google Scholar
  191. 191.
    M. W. Cromar and P. Carelli,Appl. Phys. Lett. 38, 723 (1981).Google Scholar
  192. 192.
    R. H. Koch, D. J. Van Harlingen, and J. Clarke,Appl. Phys. Lett. 38, 380 (1981).Google Scholar
  193. 193.
    D. J. Van Harlingen, R. H. Koch, and J. Clarke,Appl. Phys. Lett. 41, 197 (1982).Google Scholar
  194. 194.
    R. T. Wakai and D. J. Van Harlingen,Appl. Phys. Lett. 49, 593 (1986).Google Scholar
  195. 195.
    C. D. Tesche, K. H. Brown, A. C. Callegari, M. M. Chen, J. H. Greiner, H. C. Jones, M. B. Ketchen, K. K. Kim, A. W. Kleinsasser, H. A. Notarys, G. Proto, R. H. Wang, and T. Yogi,IEEE Trans. Magn. MAG-21, 1032 (1985).Google Scholar
  196. 196.
    G. D. Vendelin,Microwave Journal 13, 63 (1970).Google Scholar
  197. 197.
    J. R. James and A. Henderson,IEEE Journal on Microwaves, Optics and Acoustics 3, 205 (1979).Google Scholar
  198. 198.
    A. Longacre, Jr.,J. Appl. Phys. 50, 6451 (1979).Google Scholar
  199. 199.
    C. Hilbert and J. Clarke,J. Low Temp. Phys. 61, 263 (1985).Google Scholar
  200. 200.
    R. S. Germain, M. L. Roukes, M. R. Freeman, R. C. Richardson, and M. B. Ketchen, inProceedings of the 17th International Conference on Low Temperature Physics LT-17, U. Eckern, A. Schmid, W. Weber, and H. Wühl, eds. (North-Holland, Amsterdam, 1984), p. 203.Google Scholar
  201. 201.
    J. M. Martinis and J. Clarke,J. Low Temp. Phys. 65, 459 (1986).Google Scholar
  202. 202.
    T. Ryhänen and H. Seppä, (1989), to be published.Google Scholar
  203. 203.
    R. Ilmoniemi, R. Hari, and K. Reinikainen,Electroenceph. Clin. Neurophysiol. 58, 467 (1984).Google Scholar
  204. 204.
    H. J. Paik, R. H. Mathews, and M. G. Castellano,IEEE Trans. Magn. MAG-17, 404 (1981).Google Scholar
  205. 205.
    K. Enpuku, T. Muta, K. Yoshida, and F. Irie,J. Appl. Phys. 58, 1916 (1985).Google Scholar
  206. 206.
    K. Enpuku and K. Yoshida,J. Appl. Phys. 59, 1714 (1986).Google Scholar
  207. 207.
    K. Enpuku, K. Yoshida, and S. Kohjiro,J. Appl. Phys. 60, 4218 (1986).Google Scholar
  208. 208.
    H. Koch, inSQUID '85, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1985), p. 773.Google Scholar
  209. 209.
    P. Carelli and V. Foglietti,IEEE Trans. Magn. MAG-19, 299 (1983).Google Scholar
  210. 210.
    P. Carelli and V. Foglietti,IEEE Trans. Magn. MAG-21, 424 (1985).Google Scholar
  211. 211.
    B. Muhlfelder, W. Johnson, and M. W. Cromar,IEEE Trans. Magn. MAG-19, 303 (1983).Google Scholar
  212. 212.
    R. F. Broom, S. I. Raider, A. Oosenbrug, R. E. Drake, and W. Walter,IEEE Trans. Electron Dev. ED-27, 1998 (1980).Google Scholar
  213. 213.
    S. I. Raider,IEEE Trans. Magn. MAG-21, 110 (1985).Google Scholar
  214. 214.
    G. Hawkins and J. Clarke,J. Appl. Phys. 47, 1616 (1976).Google Scholar
  215. 215.
    E. E. Latta and M. Gasser,J. Appl. Phys. 54, 1115 (1983).Google Scholar
  216. 216.
    R. J. P. Bain and G. B. Donaldson,IEEE Trans. Magn. MAG-21, 543 (1985).Google Scholar
  217. 217.
    A. I. Braginski, inExtended Abstracts of the 1987 International Superconductivity Electronics Conference ISEC'87 (Japan Society of Applied Physics, Tokyo, 1987), p. 63.Google Scholar
  218. 218.
    M. K. Wu, J. R. Ashburn, C. J. Torng, P. H. Hor, R. L. Meng, L. Gao, Z. J. Huang, Y. Q. Wang, and C. W. Chu,Phys. Rev. Lett. 58, 908 (1987).Google Scholar
  219. 219.
    H. Maeda, Y. Tanaka, M. Fukutomi, and T. Asano,Jpn. J. Appl. Phys. 27, L209 (1988).Google Scholar
  220. 220.
    S. S. P. Parkin, V. Y. Lee, E. M. Engler, A. I. Nazzal, T. C. Huang, G. Gornam, R. Savoy, and R. Beyers,Phys. Rev. Lett. 60, 2539 (1988).Google Scholar
  221. 221.
    C. C. Torardi, M. A. Subramanian, J. C. Calabrese, J. Gopalakrishnan, K. J. Morrissey, T. R. Flippen, U. Chowdhry, and A. W. Sleight,Science 240, 631 (1988).Google Scholar
  222. 222.
    D. Estève, J. M. Martinis, C. Urbina, M. H. Devoret, G. Collin, P. Monod, M. Ribault, and A. Revcolevschi,Europhys. Lett. 3, 1237 (1987).Google Scholar
  223. 223.
    A. Inoue, K. Takeuchi, H. Ito, A. Nakayama, and S. Naito,Jpn. J. Appl. Phys. 26, L1211 (1987).Google Scholar
  224. 224.
    Y. Higashino, T. Takahashi, T. Kawai, and S. Naito,Jpn. J. Appl. Phys. 26, L1211 (1987).Google Scholar
  225. 225.
    H. Tanabe, S. Kita, and T. Kobayashi, inExtended Abstracts of the 1987 International Superconductivity Electronics Conference ISEC '87 (Japan Society of Applied Physics, Tokyo, 1987), p. 397.Google Scholar
  226. 226.
    P. H. Wu, Q. H. Cheng, S. Z. Yang, J. Chen, Y. Li, Z. M. Ji, J. M. Song, H. X. Lu, X. K. Gao, J. Wu, and X. Y. Zhang, inExtended Abstracts of the 1987 International Superconductivity Electronics Conference ISEC '87 (Japan Society of Applied Physics, Tokyo, 1987), p. 392.Google Scholar
  227. 227.
    M. Murakami, E. Alessandrini, and K. Kim,J. Appl. Phys. 56, 2068 (1984).Google Scholar
  228. 228.
    M. Murakami, E. Alessandrini, and K. Kim,J. Appl. Phys. 56, 2076 (1984).Google Scholar
  229. 229.
    H. Yamada and A. Ishida,J. Vac. Sci. Technol. 16, 875 (1979).Google Scholar
  230. 230.
    S. Kosaka, A. Shoji, M. Ayoagi, Y. Sakamoto, F. Shinoki, and H. Hayakawa,IEEE Trans. Magn. MAG-23, 1389 (1987).Google Scholar
  231. 231.
    S. A. Reible,IEEE Trans. Magn. MAG-17, 303 (1981).Google Scholar
  232. 232.
    M. Chen and R. Wang,J. Vac. Sci. Technol. A1, 708 (1983).Google Scholar
  233. 233.
    R. E. Lee,J. Vac. Sci. Technol. 16, 164 (1979).Google Scholar
  234. 234.
    M. Gurvitch, M. A. Washington, and H. A. Huggins,Appl. Phys. Lett. 42, 472 (1983).Google Scholar
  235. 235.
    A. Shoji, F. Shinoki, S. Kosaka, M. Ayoagi, and H. Hayakawa,Appl. Phys. Lett. 41, 1097 (1982).Google Scholar
  236. 236.
    S. Morohashi, S. Hasuo, and T. Yamaoka,Appl. Phys. Lett. 48, 254 (1986).Google Scholar
  237. 237.
    H. Kroger, L. Smith, and D. Jillie,Appl. Phys. Lett. 39, 280 (1981).Google Scholar
  238. 238.
    J. C. Villegier, L. Vieux-Rochaz, M. Goniche, P. Renard, and M. Vabre,IEEE Trans. Magn. MAG-21, 498 (1985).Google Scholar
  239. 239.
    M. Yuda, K. Kuroda, and J. Nakano,Jpn. J. Appl. Phys. 26, L166 (1987).Google Scholar
  240. 240.
    L. Yu, C. Berry, R. Drake, K. Li, R. Patt, M. Radparvar, S. Whiteley, and S. Faris,IEEE Trans. Magn. MAG-23, 1476 (1987).Google Scholar
  241. 241.
    J. H. Magerlein,IEEE Trans. Magn. MAG-17, 286 (1981).Google Scholar
  242. 242.
    L. Young,Anodic Oxide Films (Academic Press, New York, 1971).Google Scholar
  243. 243.
    R. F. Broom, A. Oosenbrug, and W. Walter,Appl. Phys. Lett. 37, 237 (1980).Google Scholar
  244. 244.
    A. W. Kleinsasser and R. A. Buhrman,Appl. Phys. Lett. 37, 841 (1980).Google Scholar
  245. 245.
    A. Tugwell, C. M. Pegrum, G. B. Donaldson, and M. Wicks,IEEE Trans. Magn. MAG-23, 676 (1987).Google Scholar
  246. 246.
    H. Koch, inExtended Abstracts of the 1987 International Superconductivity Electronics Conference ISEC '87 (Japan Society of Applied Physics, Tokyo, 1987), p. 281.Google Scholar
  247. 247.
    I. Ishida, S. Tahara, and Y. Wada,Appl. Phys. Lett. 53, 316 (1988).Google Scholar
  248. 248.
    S. Nagasawa, H. Tsuge, and Y. Wada,IEEE Electron. Dev. Lett. 9, 414 (1988).Google Scholar
  249. 249.
    P. Chaudhari, J. Mannhart, D. Dimos, C. C. Tsuei, J. Chi, M. M. Oprysko, and M. Scheuermann,Phys. Rev. Lett. 60, 1653 (1988).Google Scholar
  250. 250.
    J. H. Greiner,J. Appl. Phys. 42, 5151 (1971).Google Scholar
  251. 251.
    W. Schroen,J. Appl. Phys. 39, 2671 (1968).Google Scholar
  252. 252.
    J. Salmi, J. Knuutila, H. Seppä, and P. Immonen,Thin Solid Films 126, 77 (1985).Google Scholar
  253. 253.
    R. Herwig, in Proceedings of the 17th International Conference on Low Temperature Physics, U. Eckern, A. Schmid, W. Weber, and H. Wühl, Eds. (North-Holland, Amsterdam, 1984), p. 209.Google Scholar
  254. 254.
    S. S. Pei and R. B. van Dover,Appl. Phys. Lett. 44, 703 (1984).Google Scholar
  255. 255.
    A. W. Kleinsasser,J. Appl. Phys. 57, 2575 (1985).Google Scholar
  256. 256.
    J. Salmi, J. Knuutila, and R. Mutikainen, inErosion and Growth of Solids Stimulated by Atom and Ion Beams, G. Kiriakidis, G. Carter, and J. L. Whitton, eds. (Martinus Nijhoff Publishers, Dordrecht, 1986), p. 366.Google Scholar
  257. 257.
    J. C. Villegier and G. Matheron, inSQUID '80, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1980), p. 381.Google Scholar
  258. 258.
    W. J. Gallagher, S. I. Raider, and R. E. Drake,IEEE Trans. Magn. MAG-19, 807 (1983).Google Scholar
  259. 259.
    S. I. Raider and R. E. Drake,IEEE Trans. Magn. MAG-17, 299 (1981).Google Scholar
  260. 260.
    S. I. Raider, R. W. Johnson, T. S. Kuan, R. E. Drake, and R. A. Pollak,IEEE Trans. Magn. MAG-19, 803 (1983).Google Scholar
  261. 261.
    T. S. Kuan, S. I. Raider, and R. E. Drake,J. Appl. Phys. 53, 7464 (1982).Google Scholar
  262. 262.
    T. Imamura, H. Hoko, and S. Hasuo, inExtended Abstracts of the 1987 International Superconductivity Electronics Conference ISEC '87 (Japan Society of Applied Physics, Tokyo, 1987), p. 57.Google Scholar
  263. 263.
    A. Nakayama, A. Inoue, and Y. Okabe, inExtended Abstracts of the 1987 International Superconductivity Electronics Conference ISEC '87 (Japan Society of Applied Physics, Tokyo, 1987), p. 301.Google Scholar
  264. 264.
    J. M. Rowell, M. Gurvitch, and J. Geerk,Phys. Rev. B 24, 2278 (1981).Google Scholar
  265. 265.
    J. Talvacchio, J. R. Gavaler, A. I. Braginski, and M. A. Janocko,J. Appl. Phys. 58, 4638 (1985).Google Scholar
  266. 266.
    J. Talvacchio and A. I. Braginski, inExtended Abstracts of the 1987 International Superconductivity Electronics Conference ISEC '87 (Japan Society of Applied Physics, Tokyo, 1987), p. 309.Google Scholar
  267. 267.
    H. Asano, K. Tanabe, O. Michikami, M. Igarashi, and M. Beasley,Jpn. J. Appl. Phys. 24, 289 (1985).Google Scholar
  268. 268.
    A. Shoji, M. Aoyagi, S. Kosaka, F. Shinoki, and H. Hayakawa,Appl. Phys. Lett. 46, 1098 (1985).Google Scholar
  269. 269.
    J. B. Barner and S. T. Ruggiero,IEEE Trans. Magn. MAG-23, 854 (1987).Google Scholar
  270. 270.
    M. Radparvar, M. Berry, R. Drake, S. Faris, S. Whiteley, and L. Yu,IEEE Trans. Magn. MAG-23, 1480 (1987).Google Scholar
  271. 271.
    J. Talvacchio and A. I. Braginski,IEEE Trans. Magn. MAG-23, 859 (1987).Google Scholar
  272. 272.
    E. J. Cukauskas, M. Nisenoff, D. W. Jillie, H. Kroger, and L. N. Smith,IEEE Trans. Magn. MAG-19, 831 (1983).Google Scholar
  273. 273.
    E. J. Cukauskas, W. L. Carter, and M. Nisenoff, inExtended Abstracts of the 1987 International Superconductivity Electronics Conference ISEC '87 (Japan Society of Applied Physics, Tokyo, 1987), p. 314.Google Scholar
  274. 274.
    C. T. Rogers, R. A. Buhrman, W. J. Gallagher, S. Raider, A. W. Kleinsasser, and R. L. Sandstrom,IEEE Trans. Magn. MAG-23, 1658 (1987).Google Scholar
  275. 275.
    B. Savo, F. C. Wellstood, and J. Clarke,Appl. Phys. Lett. 50, 1757 (1987).Google Scholar
  276. 276.
    R. H. Koch, C. P. Umbach, G. J. Clark, P. Chaudhari, and R. B. Laibowitz,Appl. Phys. Lett. 51, 200 (1987).Google Scholar
  277. 277.
    H. Nakane, T. Nishino, M. Hirano, K. Takagi, and U. Kawabe, inExtended Abstracts of the 1987 International Superconductivity Electronics Conference ISEC '87 (Japan Society of Applied Physics, Tokyo, 1987), p. 411.Google Scholar
  278. 278.
    I. Iguchi, A. Sugishita, and M. Yanagisawa,Jpn. J. Appl. Phys. 26, L1021 (1987).Google Scholar
  279. 279.
    J. E. Zimmerman, J. A. Beall, M. W. Cromar, and R. H. Ono,Appl. Phys. Lett. 51, 617 (1987).Google Scholar
  280. 280.
    C. M. Pegrum, G. B. Donaldson, A. H. Carr, and A. Hendry,Appl. Phys. Lett. 51, 1364 (1987).Google Scholar
  281. 281.
    R. H. Koch and A. P. Malozemoff, inProceedings of a Conference on High Performance SQUID Systems (Stanford University, Stanford, 1988).Google Scholar
  282. 282.
    R. H. Koch, C. P. Umbach, M. M. Oprysko, J. D. Mannhart, B. Bumble, G. J. Clark, W. J. Gallagher, A. Gupta, A. Kleinsasser, R. B. Laibowitz, R. B. Sandstrom, and M. R. Scheuermann,Physica C 153–155, 1685 (1988).Google Scholar
  283. 283.
    M. J. Ferrari, M. Johnson, F. C. Wellstood, J. Clarke, P. A. Rosenthal, R. H. Hammond, and M. R. Beasley,Appl. Phys. Lett. 53, 695 (1988).Google Scholar
  284. 284.
    R. L. Sandstrom, W. J. Gallagher, T. R. Dinger, R. H. Koch, R. B. Laibowitz, A. W. Kleinsasser, R. J. Gambino, B. Bumble, and M. F. Chisholm,Appl. Phys. Lett. 53, 444 (1988).Google Scholar
  285. 285.
    R. H. Koch and P. Chaudhari,Nature 332, 682 (1988).Google Scholar
  286. 286.
    J. Clarke and R. H. Koch,Science 242, 217 (1988).Google Scholar
  287. 287.
    E. Tjukanov, R. W. Cline, R. Krahn, M. Hayden, M. W. Reynolds, W. N. Hardy, J. F. Carolan, and R. C. Thompson,Phys. Rev. B 36, 7244 (1987).Google Scholar
  288. 288.
    J. C. Gallop, C. D. Langham, W. J. Radcliffe, and W. B. Roys,Phys. Lett. 128A, 222 (1988).Google Scholar
  289. 289.
    Y. Yeshurun and A. P. Malozemoff,Phys. Rev. Lett. 60, 2202 (1988).Google Scholar
  290. 290.
    M. J. Ferrari, M. Johnson, F. C. Wellstood, J. Clarke, P. A. Rosenthal, R. H. Hammond, and M. R. Beasley,IEEE Trans. Magn. MAG-25, 806 (1989).Google Scholar
  291. 291.
    P. Rosenthal, R. H. Hammond, M. R. Beasley, R. Leoni, Ph. Lerch, and J. Clarke, IEEE Trans. Magn.MAG-25, 973 (1989).Google Scholar
  292. 292.
    J. Mannhart, P. Chaudhari, D. Dimos, C. C. Tsuei, and T. R. McGuire,Phys. Rev. Lett. 61, 2476 (1988).Google Scholar
  293. 293.
    P. W. Anderson,Phys. Rev. Lett. 9, 309 (1962).Google Scholar
  294. 294.
    Y. B. Kim,Rev. Mod. Phys. 36, 39 (1964).Google Scholar
  295. 295.
    M. Tinkham,Helv. Phys. Acta 61, 443 (1988).Google Scholar
  296. 296.
    J. Kuzník, M. Odehnal, S. Šafrata and J. Endal,J. Low Temp. Phys. 69, 313 (1987).Google Scholar
  297. 297.
    R. Tichý, M. Odehnal, V. Petříček, S. Šafrata, E. Pollert, J. Kamarád, J. Hejtmánek, O. Smrčková, and D. Sýkorová,J. Low Temp. Phys. 70, 187 (1988).Google Scholar
  298. 298.
    N. García, S. Vieira, A. M. Baro, J. Tornero, M. Pazos, L. Vázquez, J. Gómez, A. Aguiló, S. Bourgeal, A. Buendía, M. Hortal, M. A. López de la Torre, M. A. Ramos, R. Villar, K. V. Rao, D.-X. Chen, J. Nogues, and N. Karpe,Z. Phys. B 70, 9 (1988).Google Scholar
  299. 299.
    R. L. Forgacs and A. Warnick,IEEE Trans. Instrum. Meas. IM-15, 113 (1966).Google Scholar
  300. 300.
    R. L. Forgacs and A. Warnick,Rev. Sci. Instrum. 38, 214 (1967).Google Scholar
  301. 301.
    R. P. Giffard, inSQUID '80, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1980), p. 445.Google Scholar
  302. 302.
    C. Rillo, D. Veldhuis, and J. Flokstra,IEEE Trans. Instrum. Meas. IM-36, 770 (1987).Google Scholar
  303. 303.
    G. J. Ehnolm, J. P. Ekström, M. T. Loponen, and J. K. Soini,Cryogenics 19, 673 (1979).Google Scholar
  304. 304.
    K. H. G. Duh, M. W. Pospieszalski, W. F. Kopp, P. Ho, A. A. Jabra, P.-C. Chao, P. M. Smith, L. F. Lester, J. M. Ballingall, and S. Weinreb,IEEE Trans. Electron Dev. ED-35, 249 (1988).Google Scholar
  305. 305.
    M. W. Pospieszalski, S. Weinreb, R. D. Norrod, and R. Harris,IEEE Trans. Microwave Theory Tech. MMT-36, 552 (1988).Google Scholar
  306. 306.
    J. Clarke, W. M. Goubau, and M. B. Ketchen,Appl. Phys. Lett. 27, 155 (1975).Google Scholar
  307. 307.
    V. V. Danilov, K. K. Likharev, D. V. Sniguiriev, and E. S. Soldatov,IEEE Trans. Magn. MAG-13, 240 (1977).Google Scholar
  308. 308.
    F. C. Wellstood, C. Heiden, and J. Clarke,Rev. Sci. Instrum. 55, 952 (1984).Google Scholar
  309. 309.
    Biomagnetic Technologies, Inc., 4174 Sorrento Valley Boulevard, San Diego, CA 92121.Google Scholar
  310. 310.
    R. H. Koch, J. Clarke, W. M. Goubau, J. M. Martinis, C. M. Pegrum, and D. J. Van Harlingen,J. Low Temp. Phys. 51, 207 (1983).Google Scholar
  311. 311.
    V. Foglietti, W. J. Gallagher, M. B. Ketchen, A. W. Kleinsasser, R. H. Koch, S. I. Raider, and R. L. Sandstrom,Appl. Phys. Lett. 49, 1393 (1986).Google Scholar
  312. 312.
    D. Drung, E. Crocoll, R. Herwig, M. Neuhaus, and W. Jutzi,IEEE Trans. Magn. MAG-25, 1034 (1989).Google Scholar
  313. 313.
    H. Furukawa, M. Katayama, H. Emoto, and K. Shirae, inProceedings of the 6th Sensor Symposium, S. Kataoka, ed. (Institute of Electrical Engineers of Japan, Tsukuba, 1986), p. 319.Google Scholar
  314. 314.
    K. Shirae, H. Furukawa, M. Katayama, and T. Katayama, inBiomagnetism '87, K. Atsumi, M. Kotani, S. Ueno, T. Katila, and S. J. Williamson, eds. (Tokyo Denki University Press, Tokyo, 1987).Google Scholar
  315. 315.
    D. Drung,Cryogenics 26, 623 (1986).Google Scholar
  316. 316.
    N. Fujimaki, H. Tamura, T. Imamura, and S. Hasuo,IEEE Trans. Electron Dev. ED-35, 2412 (1988).Google Scholar
  317. 317.
    A. Widom,J. Low Temp. Phys. 37, 449 (1979).Google Scholar
  318. 318.
    A. Widom, T. D. Clark, and G. Megaloudis,Phys. Lett. 76A, 163 (1980).Google Scholar
  319. 319.
    R. F. Voss,Appl. Phys. Lett. 38, 182 (1981).Google Scholar
  320. 320.
    T. A. Fulton and L. N. Dunkleberger,Phys. Rev. B 9, 4760 (1974).Google Scholar
  321. 321.
    P. Dutta and P. M. Horn,Rev. Mod. Phys. 53, 497 (1981).Google Scholar
  322. 322.
    M. B. Weissman,Rev. Mod. Phys. 60, 537 (1988).Google Scholar
  323. 323.
    R. H. Koch, J. Clarke, J. M. Martinis, W. M. Goubau, C. M. Pegrum, and D. J. Van Harlingen,IEEE Trans. Magn. MAG-19, 449 (1983).Google Scholar
  324. 324.
    R. H. Koch, inNoise in Physical Systems and 1/f Noise, M. Savelli, G. Lecoy, and J.-P. Nougier, eds., (Elsevier, New York, 1983), p. 377.Google Scholar
  325. 325.
    C. T. Rogers and R. A. Buhrman,IEEE Trans. Magn. MAG-21, 126 (1985).Google Scholar
  326. 326.
    C. T. Rogers and R. A. Buhrman,Phys. Rev. Lett. 55, 859 (1985).Google Scholar
  327. 327.
    J. Bernamont,Ann. Phys. (Leipzig)7, 71 (1937).Google Scholar
  328. 328.
    A. L. McWhorter, inSemiconductor Surface Physics, R. H. Kingston, ed., (University of Pennsylvania Press, Philadelphia, 1957), p. 207.Google Scholar
  329. 329.
    P. Dutta, P. Dimon, and P. M. Horn,Phys. Rev. Lett. 43, 646 (1979).Google Scholar
  330. 330.
    R. F. Voss and J. Clarke,Phys. Rev. B 13, 556 (1976).Google Scholar
  331. 331.
    H. Seppä, T. Ryhänen, and J. Kurkijärvi,Phys. Rev. B, to be published.Google Scholar
  332. 332.
    S. Hashiguchi, inProceedings of the Ninth International Conference on Noise in Physical Systems, C. M. Van Vliet, ed. (World Scientific, Toronto, 1987), p. 315.Google Scholar
  333. 333.
    K. Atsumi, M. Kotani, S. Ueno, T. Katila, and S. J. Williamson, eds.,Biomagnetism '87 (Tokyo Denki University Press, Tokyo, 1988).Google Scholar
  334. 334.
    S. J. Williamson, G. L. Romani, L. Kaufman, and I. Modena, eds.,Biomagnetism: An Interdisciplinary Approach, Vol. 66 of NATO Advanced Science Institutes Series. Series A: Life Sciences (Plenum, New York, 1983).Google Scholar
  335. 335.
    D. Cohen,Science 180, 745 (1973).Google Scholar
  336. 336.
    D. N. Paulson, R. Toussaint, R. L. Fagaly, and S. E. Robinson,IEEE Trans. Magn. MAG-23, 1315 (1987).Google Scholar
  337. 337.
    R. J. Ilmoniemi, S. J. Williamson, and W. E. Hostetler, in K. Atsumi, M. Kotani, S. Ueno, T. Katila, and S. J. Williamson, eds.,Biomagnetism '87, (Tokyo Denki University Press, Tokyo, 1988), p. 182.Google Scholar
  338. 338.
    K. Kalliomäki, P.-L. Kalliomäki, K. Aittoniemi, and M. Moilanen, inBiomagnetism: An Interdisciplinary Approach S. J. Williamson, G.-L. Romaini, L. Kaufman, and I. Modena, eds. (Plenum, New York, 1983), p. 545.Google Scholar
  339. 339.
    G. M. Brittenham, D. E. Farrell, J. W. Harris, E. S. Feldman, E. H. Danish, W. A. Muir, J. H. Tripp, and E. M. Bellon,New Engl. J. Med. 307, 1671 (1982).Google Scholar
  340. 340.
    R. Hari and R. J. Ilmoniemi,CRC Critical Rev. in Biomed. Eng. 14, 93 (1986).Google Scholar
  341. 341.
    G.-L. Romani and L. Narici,Med. Progr. Technol. 11, 123 (1986).Google Scholar
  342. 342.
    S. J. Williamson, L. Kaufman, and D. Brenner,J. Appl. Phys. 50, 2418 (1979).Google Scholar
  343. 343.
    D. Cohen,Science 175, 664 (1972).Google Scholar
  344. 344.
    J. Knuutila, S. Ahlfors, A. Ahonen, J. Hällström, M. Kajola, O. V. Lounasmaa, V. Vilkman, and C. Tesche,Rev. Sci. Instrum. 58, 2145 (1987).Google Scholar
  345. 345.
    S.-L. Joutsiniemi,Acta. Neurol. Scand. 78, 337 (1989).Google Scholar
  346. 346.
    S. N. Erné,Med. Biol. Eng. Comput. 23 (S2, 1447 (1985).Google Scholar
  347. 347.
    T. Katila, R. Maniewski, M. Mäkijärvi, J. Nenonen, and P. Siltanen,Phys. Med. Biol. 32, 125 (1987).Google Scholar
  348. 348.
    B. M. Horacek,IEEE Trans. Magn. MAG-9, 440 (1973).Google Scholar
  349. 349.
    B. N. Cuffin and D. B. Geselowitz,IEEE Trans. Biomed. Eng. BME-24, 242 (1977).Google Scholar
  350. 350.
    W. T. Miller, III and D. B. Geselowitz,Circulation Res. 43, 301 (1978).Google Scholar
  351. 351.
    B. W. Petley, inQuantum Metrology and Fundamental Physical Constants, P. H. Cutler and A. A. Lucas, eds (Plenum, New York, 1983), p. 293.Google Scholar
  352. 352.
    A. Davidson,Appl. Phys. Lett. 38, 721 (1981).Google Scholar
  353. 353.
    J. A. Rowlands and S. B. Woods,Rev. Sci. Instrum. 47, 795 (1976).Google Scholar
  354. 354.
    D. J. Van Harlingen, D. F. Heidel, and J. C. Garland,Phys. Rev. B 21, 1842 (1980).Google Scholar
  355. 355.
    G. Pickett,Phys. Rev. Lett. 47, 134 (1981).Google Scholar
  356. 356.
    J.-S. Tsai, A. K. Jain, and J. E. Lukens,Phys. Rev. Lett. 51, 316 (1983).Google Scholar
  357. 357.
    D. B. Sullivan,Rev. Sci. Instrum. 43, 499 (1972).Google Scholar
  358. 358.
    I. K. Harvey,Metrologia 12, 47 (1976).Google Scholar
  359. 359.
    R. F. Dziuba, B. F. Field, and T. F. Finnegan,IEEE Trans. Instrum. Meas. IM-23, 264 (1974).Google Scholar
  360. 360.
    V. Kose, F. Melcert, W. Engelland, H. Fack, B. Fuhrmann, P. Gutmann, and P. Warnecke,IEEE Trans. Instrum. Meas. IM-23, 271 (1974).Google Scholar
  361. 361.
    J. C. Gallop and B. W. Petley,IEEE Trans. Instrum. Meas. IM-23, 267 (1974).Google Scholar
  362. 362.
    D. Andreone, E. Arri, G. Boella, and G. C. Marullo,IEEE Trans. Instrum. Meas. IM-25, 512 (1976).Google Scholar
  363. 363.
    I. K. Harvey,Rev. Sci. Instrum. 43, 1626 (1972).Google Scholar
  364. 364.
    I. K. Harvey and H. C. Collins,Rev. Sci. Instrum. 44, 1700 (1973).Google Scholar
  365. 356.
    D. B. Sullivan and R. F. Dziuba,Rev. Sci. Instrum. 45, 517 (1974).Google Scholar
  366. 366.
    K. Grohmann, H. D. Hahlbohm, H. Lübbig, and H. Ramin,IEEE Trans. Instrum. Meas. IM-23, 261 (1974).Google Scholar
  367. 367.
    K. von Klitzing, G. Dorda, and M. Pepper,Phys. Rev. Lett. 45, 494 (1980).Google Scholar
  368. 368.
    F. Delahaye,IEEE Trans. Instrum. Meas. IM-27, 426 (1978).Google Scholar
  369. 369.
    H. Seppä, IEEE Cat. 80 CH 1497-7 IM, CPEM Dig., p. 172 (1980).Google Scholar
  370. 370.
    A. Hartland, inProceedings of the Precision Measurement and Fundamental Constants II, Vol. 617 (National Bureau of Standards, Washington D.C., 1982), p. 543.Google Scholar
  371. 371.
    F. Delahaye and D. Reymann,IEEE Trans. Instrum. Meas. IM-34, 316 (1985).Google Scholar
  372. 372.
    K. Grohmann and D. Hechftischer,IEEE Trans. Instrum. Meas. IM-33, 91 (1984).Google Scholar
  373. 373.
    K. Grohmann, D. Hechtfischer, and J. Jakschik, inSQUID '76, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1977), p. 311.Google Scholar
  374. 374.
    S. N. Erné and H. Luther,IEEE Trans. Instrum. Meas. IM-24, 345 (1975).Google Scholar
  375. 375.
    K. Weyand,IEEE Trans. Instrum. Meas. IM-29, 324 (1980).Google Scholar
  376. 376.
    R. L. Kautz,Appl. Phys. Lett. 36, 386 (1980).Google Scholar
  377. 377.
    R. L. Kautz and G. Costabile,IEEE Trans. Magn. MAG-17, 780 (1981).Google Scholar
  378. 378.
    J. Niemeyer, J. H. Hinken, and W. Meier,IEEE Trans. Instrum. Meas. IM-33, 311 (1984).Google Scholar
  379. 379.
    R. E. Harris and C. A. Hamilton, inAIP Conference Proceedings, Vol. 44, B. Deaver, ed. (1978), p. 448.Google Scholar
  380. 380.
    D. B. Sullivan and N. V. Frederick,IEEE Trans. Magn. MAG-13, 396 (1977).Google Scholar
  381. 381.
    J. C. Gallop, inSQUID '76, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1977), p. 267.Google Scholar
  382. 382.
    J. C. Gallop,J. Phys. B 11, L93 (1978).Google Scholar
  383. 383.
    F. Shiota and K. Hara,IEEE Trans. Instrum. Meas. IM-36, 271 (1987).Google Scholar
  384. 384.
    R. Meservey,J. Appl. Phys. 39, 2598 (1968).Google Scholar
  385. 385.
    E. R. Williams and P. T. Olsen,IEEE Trans. Instrum. Meas. IM-27, 467 (1978).Google Scholar
  386. 386.
    B. N. Taylor, W. H. Parker, and D. N. Langenberger,Rev. Mod. Phys. 41, 375 (1969).Google Scholar
  387. 387.
    B. Cabrera, S. Benjamin, and J. T. Anderson,Physica 107B, 19 (1981).Google Scholar
  388. 388.
    S. B. Felch, B. Cabrera, J. Tate, and J. T. Anderson, inProceedings of the 17th International Conference on Low Temperature Physics LT-17, U. Eckern, A. Schmid, W. Weber, and H. Wühl, eds. (North-Holland, Amsterdam, 1984), p. 923.Google Scholar
  389. 389.
    T. D. Gamble, W. M. Goubau, and J. Clarke,Geophysics 44, 959 (1979).Google Scholar
  390. 390.
    M. Wilt, N. E. Goldstein, M. Stark, J. R. Haught, and H. F. Morrison,Geophysics 48, 1090 (1983).Google Scholar
  391. 391.
    J. Clarke,IEEE Trans. Magn. MAG-19, 288 (1983).Google Scholar
  392. 392.
    P. V. Czipott, and W. N. Podney,IEEE Trans. Magn. MAG-23, 465 (1987).Google Scholar
  393. 393.
    Z. Janu, M. Odehnal, V. Petříček, and R. Tichý, inSQUID '85, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1985), p. 885.Google Scholar
  394. 394.
    H. J. Paik,J. Appl. Phys. 47, 1168 (1976).Google Scholar
  395. 395.
    H. J. Paik, E. R. Mapoles, and K. Y. Wang, inFuture Trends in Superconductive Electronics, B. S. Deaver, Jr., C. M. Falco, J. H. Harris, and S. A. Wolf, eds. (American Institute of Physics, New York), 1978), p. 166.Google Scholar
  396. 396.
    A. B. Colquhoun, N. A. Lockerbie, and G. B. Donaldson, inSQUID '85, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1985), p. 1191.Google Scholar
  397. 397.
    J. F. Kos, R. Barton, and B. Ramadan,J. Appl. Phys. 48, 3193 (1977).Google Scholar
  398. 398.
    M. S. McAshan, W. M. Fairbank, P. F. Michelson, and R. C. Taber,Physica 107B, 23 (1981).Google Scholar
  399. 399.
    E. Ikonen, P. Karp, T. Katila, and K. Riski,J. Phys. E 16, 875 (1983).Google Scholar
  400. 400.
    J. F. Kos,J. Appl. Phys. 49, 955 (1978).Google Scholar
  401. 401.
    C. Cosmelli, P. Carelli, M. G. Castellano, and V. Foglietti,IEEE Trans. Magn. MAG-23, 454 (1987).Google Scholar
  402. 402.
    B. Cabrera,Phys. Rev. Lett. 48, 1378 (1982).Google Scholar
  403. 403.
    B. Cabrera, M. Taber, R. Gardner, and J. Bourg,Phys. Rev. Lett. 51, 1933 (1983).Google Scholar
  404. 404.
    C. D. Tesche, C. C. Chi, C. C. Tsuei, and P. Chaudhari,Appl. Phys. Lett. 43, 384 (1983).Google Scholar
  405. 405.
    J. Incandela, M. Campbell, H. Frisch, S. Somalwar, M. Kuchnir, and H. R. Gustafson,Phys. Rev. Lett. 53, 2067 (1984).Google Scholar
  406. 406.
    C. C. Chi, C. D. Tesche, C. C. Tsuei, P. Chaudhari, and S. Bermon, inMonopole '83, J. L. Stone, ed. (Plenum, New York, 1984), p. 451.Google Scholar
  407. 407.
    S. Bermon, P. Chaudhari, C. C. Chi, C. D. Tesche, and C. C. Tsuei,Phys. Rev. Lett. 55, 1850 (1985).Google Scholar
  408. 408.
    S. Bermon,IEEE Trans. Magn. MAG-23, 441 (1987).Google Scholar
  409. 409.
    M. E. Huber, B. Cabrera, M. A. Taber, and R. D. Gardner,Jpn. J. Appl. Phys. 26–3, 1687 (1987).Google Scholar
  410. 410.
    M. S. Turner, E. N. Parker, and T. J. Bogdan,Phys. Rev. D 26, 1296 (1982).Google Scholar
  411. 411.
    B. Cabrera, inFuture Trends in Superconductive Electronics, B. S. Deaver, Jr., C. M. Falco, J. H. Harris, and S. A. Wolf, eds. (American Institute of Physics, New York), p. 73 (1978).Google Scholar
  412. 412.
    W. M. Fairbank,Physica 109 & 110B, 1404 (1982).Google Scholar
  413. 413.
    M. Odehnal,Sov. J. Low Temp. Phys. 11, 1 (1985).Google Scholar
  414. 414.
    R. A. Webb,Rev. Sci. Instrum. 48, 1585 (1977).Google Scholar
  415. 415.
    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
  416. 416.
    M. Kohl, M. Odehnal, V. Petříček, and R. Tichý, inSQUID '85, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1985), p. 879.Google Scholar
  417. 417.
    M. Kohl, M. Odehnal, V. Petříček, R. Tichý, and S. Šafrata,J. Low Temp. Phys. 72, 319 (1988).Google Scholar
  418. 418.
    A. K. M. Wennberg, L. J. Friedman, and H. M. Bozler, inProceedings of the 17th International Conference on Low Temperature Physics LT-17, U. Eckern, A. Schmid, W. Weber, and H. Wühl, eds. (North-Holland, Amsterdam, 1984), p. 265.Google Scholar
  419. 419.
    M. R. Freeman, R. S. Germain, R. C. Richardson, M. L. Roukes, W. J. Gallagher, and M. B. Ketchen,Appl. Phys. Lett. 48, 300 (1986).Google Scholar
  420. 420.
    T. Sleator, E. L. Hahn, C. Hilbert, and J. Clarke,Phys. Rev. Lett. 55, 1742 (1985).Google Scholar
  421. 421.
    T. Sleator, E. L. Hahn, M. B. Heaney, C. Hilbert, and J. Clarke,Phys. Rev. Lett. 57, 2756 (1986).Google Scholar
  422. 422.
    C. Hilbert, J. Clarke, T. Sleator, and E. L. Hahn,Appl. Phys. Lett. 47, 637 (1985).Google Scholar
  423. 423.
    R. Adams, S. P. Potts, J. C. Gallop, and W. J. Radcliffe, inSQUID '80, Superconducting Quantum Interference Devices and Their Applications, H. D. Hahlbohm and H. Lübbig, eds. (Walter de Gruyter, Berlin, 1980), p. 509.Google Scholar
  424. 424.
    C. W. F. Everitt, W. M. Fairbank, and W. O. Hamilton, inRelativity, M. Carmeli, S. I. Fickler, and L. Witten, eds. (Plenum, New York, 1970), p. 145.Google Scholar
  425. 425.
    C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (Freeman, San Francisco, 1973), p. 1117.Google Scholar
  426. 426.
    J. P. Turneaure, C. W. F. Everitt, B. W. Parkinson, J. T. Anderson, D. Bardas, W. S. Cheung, D. B. DeBra, W. M. Fairbank, R. A. Farnsworth, D. Gill, R. Hacker, G. M. Keiser, J. A. Lipa, J. M. Lockhart, R. A. Van Pattern, R. Parmely, R. H. Vassar, and L. S. Young, inProceedings of the Fourth Marcel Grossman Meeting On General Relativity, R. Ruffini, ed. (North-Holland, Amsterdam, 1986), p. 411.Google Scholar
  427. 427.
    J. P. Turneaure, C. W. F. Everitt, B. W. Parkinson, D. Bardas, J. V. Breakwell, S. Buchman, W. S. Cheung, D. E. Davidson, D. B. DeBra, W. M. Fairbank, S. Feteih, D. Gill, R. Hacker, G. M. Keiser, J. M. Lockhart, B. Muhlfelder, R. Parmley, X. Qin, M. Taber, R. A. Van Pattern, Y. M. Xiao, and P. Zhou, inProceedings of the XXVII COSPAR Symposium on Relativistic Gravitation, Espoo, July 18–29, 1988, in press.Google Scholar
  428. 428.
    H. Koch, inSensors—A Comprehensive Book Series in Eight Volumes, W. Göbel, J. Hesse, and J. N. Zemel, eds. (VCH Verlagsgesellschaft, Weinheim, 1989); inMagnetic Sensors, R. Boll and K. J. Overshott, eds. (VCH Verlagsgesellschaft, Weinheim, 1989), chap. 9.Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • Tapani Ryhänen
    • 1
  • Heikki Seppä
    • 1
  • Risto Ilmoniemi
    • 2
  • Jukka Knuutila
    • 2
  1. 1.Metrology Research InstituteHelsinki University of Technology and Technical Research Centre of FinlandEspooFinland
  2. 2.Low Temperature LaboratoryHelsinki University of TechnologyEspooFinland

Personalised recommendations