Skip to main content
SpringerLink
Log in

The Thermomagnetic Instability in Superconducting Films with Adjacent Metal Layer

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

Dendritic flux avalanches is a frequently encountered consequence of the thermomagnetic instability in type-II superconducting films. The avalanches, which are potentially harmful for superconductor-based devices, can be suppressed by an adjacent normal metal layer, even when the two layers are not in thermal contact. The suppression of the avalanches in this case is due to so-called magnetic braking, caused by eddy currents generated in the metal layer by propagating magnetic flux. We develop a theory of magnetic braking by analyzing coupled electrodynamics and heat flow in a superconductor-normal metal bilayer. The equations are solved by linearization and by numerical simulation of the avalanche dynamics. We find that in an uncoated superconductor, even a uniform thermomagnetic instability can develop into a dendritic flux avalanche. The mechanism is that a small non-uniformity caused by the electromagnetic non-locality induces a flux-flow hot spot at a random position. The hot spot quickly develops into a finger, which at high speeds penetrates into the superconductor, forming a branching structure. Magnetic braking slows the avalanches, and if the normal metal conductivity is sufficiently high, it can suppress the formation of the dendritic structure. During avalanches, the braking by the normal metal layer prevents the temperature from exceeding the transition temperature of the superconductor. Analytical criteria for the instability threshold are developed using the linear stability analysis. The criteria are found to match quantitatively the instability onsets obtained in simulations.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. C.P. Bean, Rev. Mod. Phys. 36, 31 (1964)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. E.H. Brandt, Rep. Prog. Phys. 58, 1465 (1995)

    Article  ADS  Google Scholar 

  4. S.L. Wipf, Phys. Rev. 161, 404 (1967)

    Article  ADS  Google Scholar 

  5. P.S. Swartz, C.P. Bean, J. Appl. Phys. 39, 4991 (1968)

    Article  ADS  Google Scholar 

  6. R.G. Mints, A.L. Rakhmanov, Rev. Mod. Phys. 53, 551 (1981)

    Article  ADS  Google Scholar 

  7. S.L. Wipf, Cryogenics 31, 936 (1991)

    Article  ADS  Google Scholar 

  8. Y.B. Kim, C.F. Hempstead, A.R. Strnad, Phys. Rev. 129, 528 (1963). doi:10.1103/PhysRev.129.528

    Article  ADS  Google Scholar 

  9. I.L. Maksimov, Physica C 235–240, 3017 (1994). doi:10.1016/0921-4534(94)91035-9

    Article  Google Scholar 

  10. P. Leiderer, J. Boneberg, P. Brüll, V. Bujok, S. Herminghaus, Phys. Rev. Lett. 71(16), 2646 (1993). doi:10.1103/PhysRevLett.71.2646

    Article  ADS  Google Scholar 

  11. C.A. Durán, P.L. Gammel, R.E. Miller, D.J. Bishop, Phys. Rev. B 52, 75 (1995)

    Article  ADS  Google Scholar 

  12. V. Vlasko-Vlasov, U. Welp, V. Metlushko, G.W. Crabtree, Physica C 341, 1281 (2000)

    Article  Google Scholar 

  13. I. Aranson, A. Gurevich, V. Vinokur, Phys. Rev. Lett. 87, 067003 (2001)

    Article  ADS  Google Scholar 

  14. A. Gurevich, R.G. Mints, Rev. Mod. Phys. 59, 941 (1987). doi:10.1103/RevModPhys.59.941

    Article  ADS  Google Scholar 

  15. K.H. Müller, C. Andrikidis, Phys. Rev. B 49, 1294 (1994). doi:10.1103/PhysRevB.49.1294

    Article  ADS  Google Scholar 

  16. M.N. Wilson, C.R. Walters, J.D. Lewin, P.F. Smith, J. Phys. D 3, 1571 (1970)

    Google Scholar 

  17. M.G. Kremlev, Pis’ma Zh. Eksp. Teor. Fiz. 17, 312 (1973)

    Google Scholar 

  18. R.G. Mints, A.L. Rakhmanov, J. Phys. D 8, 1769 (1975)

    Article  ADS  Google Scholar 

  19. A.L. Rakhmanov, D.V. Shantsev, Y.M. Galperin, T.H. Johansen, Phys. Rev. B 70, 224502 (2004)

    Article  ADS  Google Scholar 

  20. L. Legrand, I. Rosenman, C. Simon, G. Collin, Physica C 211, 239 (1993)

    Article  ADS  Google Scholar 

  21. R.G. Mints, Phys. Rev. B 53, 12311 (1996). doi:10.1103/PhysRevB.53.12311

    Article  ADS  Google Scholar 

  22. E.H. Brandt, M. Indenbom, Phys. Rev. B 48(17), 12893 (1993)

    Article  ADS  Google Scholar 

  23. E. Zeldov, J.R. Clem, M. McElfresh, M. Darwin, Phys. Rev. B 49(14), 9802 (1994). doi:10.1103/PhysRevB.49.9802

    Article  ADS  Google Scholar 

  24. V.M. Vinokur, M.V. Feigel’man, V.B. Geshkenbein, Phys. Rev. Lett. 67, 915 (1991)

    Article  ADS  Google Scholar 

  25. E.H. Brandt, Phys. Rev. Lett. 76(21), 4030 (1996)

    Article  ADS  Google Scholar 

  26. D.V. Denisov, A.L. Rakhmanov, D.V. Shantsev, Y.M. Galperin, T.H. Johansen, Phys. Rev. B 73(1), 014512 (2006). doi:10.1103/PhysRevB.73.014512

    Article  ADS  Google Scholar 

  27. D.V. Denisov, D.V. Shantsev, Y.M. Galperin, E.M. Choi, H.S. Lee, S.I. Lee, A.V. Bobyl, P.E. Goa, A.A.F. Olsen, T.H. Johansen, Phys. Rev. Lett. 97, 077002 (2006)

    Article  ADS  Google Scholar 

  28. I.S. Aranson, A. Gurevich, M.S. Welling, R.J. Wijngaarden, V.K. Vlasko-Vlasov, V.M. Vinokur, U. Welp, Phys. Rev. Lett. 94(3), 037002 (2005). doi:10.1103/PhysRevLett.94.037002

    Article  ADS  Google Scholar 

  29. R.G. Mints, E.H. Brandt, Phys. Rev. B 54(17), 12421 (1996)

    Article  ADS  Google Scholar 

  30. A. Gurevich, Appl. Phys. Lett. 78(13), 1891 (2001)

    Article  ADS  Google Scholar 

  31. J.I. Vestgården, D.V. Shantsev, Y.M. Galperin, T.H. Johansen, Phys. Rev. B 84, 054537 (2011)

    Article  ADS  Google Scholar 

  32. J.I. Vestgården, D.V. Shantsev, Y.M. Galperin, T.H. Johansen, Sci. Rep. 2, 886 (2012)

    Article  ADS  Google Scholar 

  33. J.I. Vestgården, D.V. Shantsev, Y.M. Galperin, T.H. Johansen, Supercond. Sci. Technol. 26, 055012 (2013). doi:10.1088/0953-2048/26/5/055012

    Article  ADS  Google Scholar 

  34. T.H. Johansen, M. Baziljevich, D.V. Shantsev, P.E. Goa, Y.M. Galperin, W.N. Kang, H.J. Kim, E.M. Choi, M.-S. Kim, I. Lee, Europhys. Lett. 59, 599 (2002)

    Article  ADS  Google Scholar 

  35. U. Bolz, B. Biehler, D. Schmidt, B. Runge, P. Leiderer, Europhys. Lett. 64, 517 (2003)

    Article  ADS  Google Scholar 

  36. J. Albrecht, A.T. Matveev, J. Strempfer, H.U. Habermeier, D.V. Shantsev, Y.M. Galperin, T.H. Johansen, Phys. Rev. Lett. 98(11), 117001 (2007). doi:10.1103/PhysRevLett.98.117001

    Article  ADS  Google Scholar 

  37. M.N. Wilson, Superconducting Magnets (Clarendon Press, Oxford, 1983)

    Google Scholar 

  38. M. Baziljevich, A.V. Bobyl, D.V. Shantsev, E. Altshuler, T.H. Johansen, S.I. Lee, Physica C 369, 93 (2002)

    Article  ADS  Google Scholar 

  39. C. Stahl, S. Treiber, G. Schütz, J. Albrecht, Supercond. Sci. Technol. 26, 015007 (2013)

    Article  ADS  Google Scholar 

  40. E.-M. Choi, H.-S. Lee, H.-J. Kim, S.-I. Lee, H.-J. Kim, W.N. Kang, Appl. Phys. Lett. 84, 82 (2004). doi:10.1063/1.1637944

    Article  ADS  Google Scholar 

  41. E.-M. Choi, H.-S. Lee, H.J. Kim, B. Kang, S. Lee, Å.A.F. Olsen, D.V. Shantsev, T.H. Johansen, Appl. Phys. Lett. 87, 152501 (2005)

    Article  ADS  Google Scholar 

  42. J. Albrecht, A.T. Matveev, M. Djupmyr, G. Schütz, B. Stuhlhofer, H. Habermeier, Appl. Phys. Lett. 87, 182501 (2005)

    Article  ADS  Google Scholar 

  43. E.-M. Choi, V.V. Yurchenko, T.H. Johansen, H.-S. Lee, J.Y. Lee, W.N. Kang, S.-I. Lee, Supercond. Sci. Technol. 22 (2009)

  44. S. Treiber, J. Albrecht, New J. Phys. 12, 093043 (2010)

    Article  ADS  Google Scholar 

  45. F. Colauto, E. Choi, J.Y. Lee, S.I. Lee, E.J. Patiño, M.G. Blamire, T.H. Johansen, W.A. Ortiz, Appl. Phys. Lett. 96, 092512 (2010)

    Article  ADS  Google Scholar 

  46. P. Mikheenko, A.J. Qviller, J.I. Vestgården, S. Chaudhuri, I.J. Maasilta, Y.M. Galperin, T.H. Johansen, Appl. Phys. Lett. 102, 022601 (2013). doi:10.1063/1.4775693

    Article  ADS  Google Scholar 

  47. E.H. Brandt, Phys. Rev. B 52(21), 15442 (1995)

    Article  ADS  Google Scholar 

  48. B.J. Roth, N.G. Sepulveda, J.P. Wikswo Jr., J. Appl. Phys. 65(1), 361 (1989)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was financially supported by the Research Council of Norway.

Author information

Authors and Affiliations

  1. Department of Physics, University of Oslo, P.O. box 1048, Blindern, 0316, Oslo, Norway

    J. I. Vestgården, Y. M. Galperin & T. H. Johansen

  2. Ioffe Physical Technical Institute, 26 Polytekhnicheskaya, St Petersburg, 194021, Russian Federation

    Y. M. Galperin

  3. Institute for Superconducting and Electronic Materials, University of Wollongong, Northfields Avenue, Wollongong, NSW, 2522, Australia

    T. H. Johansen

Authors
  1. J. I. Vestgården
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. M. Galperin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. H. Johansen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. I. Vestgården.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vestgården, J.I., Galperin, Y.M. & Johansen, T.H. The Thermomagnetic Instability in Superconducting Films with Adjacent Metal Layer. J Low Temp Phys 173, 303–326 (2013). https://doi.org/10.1007/s10909-013-0899-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10909-013-0899-1

Keywords

Search

Navigation