Statistics of thermomagnetic breakdown in Nb superconducting films

[en] Superconductors are well known for their ability to screen out magnetic fields. In type-II superconductors, as the magnetic field pressure is progressively increased, magnetic flux accumulates at the periphery of the sample, very much like charges accumulate in a capacitor when voltage is increased. As for capacitors, exceeding certain threshold field causes the blocked magnetic flux to abruptly penetrate into the sample. This phenomenon, triggered by a thermomagnetic instability, is somewhat analogous to the dielectric breakdown of the capacitor and leaves behind a similar Lichtenberg imprinting. Even though electrical breakdown threshold has been extensively studied in dielectrics, little information is known about the statistical distribution of the thermomagnetic breakdown in superconductors. In this work, we address this problem by performing magneto-optical imaging experiments on a Nb film where nanometric heating elements are used to rapidly erase the magnetic history of the sample. We demonstrate that the size and shape distributions of avalanches permits to unambiguously identify the transition between two regimes where either thermal diffusivity or magnetic diffusivity dominate. Clear criteria for discriminating dynamic avalanches from thermally driven avalanches are introduced. This allows us to provide the first precise determination of the threshold field of the thermomagnetic breakdown and unveil the details of the transition from finger-like magnetic burst to dendritic branching morphology. These findings open a new avenue in the interdisciplinary exploration of catastrophic avalanches through non destructive repeatable experiments.

Disciplines :

Physics

Author, co-author :

Blanco Alvarez, Sylvain ; Université de Liège - ULiège > Département de physique > Physique expérimentale des matériaux nanostructurés

Brisbois, Jérémy ; Université de Liège - ULiège > Département de physique > CSL (Centre Spatial de Liège)

Melinte, Sorin; Université Catholique de Louvain - UCL

Kramer, Roman; Institut Néel, CNRS, Université Grenoble Alpes, 38042, Grenoble, France

Silhanek, Alejandro ; Université de Liège - ULiège > Département de physique > Physique expérimentale des matériaux nanostructurés

Language :

English

Title :

Statistics of thermomagnetic breakdown in Nb superconducting films

Publication date :

March 2019

Journal title :

Scientific Reports

eISSN :

2045-2322

Publisher :

Nature Publishing Group, London, United Kingdom

Peer reviewed :

Peer Reviewed verified by ORBi

Name of the research project :

PDR T.0106.16

Funders :

F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]

Available on ORBi :

since 01 March 2019

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Bibliography

Niemeyer, L., Pietronero, L. & Wiesmann, H. J. Fractal dimension of dielectric breakdown. Phys. Rev. Lett. 52, 1033–1036, 10.1103/PhysRevLett.52.1033 (1984).
Baumans, X. D. A. et al. Statistics of localized phase slips in tunable width planar point contacts. Sci. Rep. 7, 44569, 10.1038/srep44569 (2017).
Denisov, D. V., Villanueva, Y., Lőrincz, K. A., May, S. & Wijngaarden, R. J. Relation between self-organized criticality and grain aspect ratio in granular piles. Phys. Rev. E 85, https://doi.org/10.1103/PhysRevE.85.051309 (2012).
Virot, E. & Ponomarenko, A. Popcorn: critical temperature, jump and sound. J. Royal Soc. Interface 12, 20141247, 10.1098/rsif.2014.1247 (2015).
Bak, P., Tang, C. & Wiesenfeld, K. Self-organized criticality: An explanation of the 1/f noise. Phys. Rev. Lett. 59, 381–384, 10.1103/PhysRevLett.59.381 (1987).
Wijngaarden, R. J., Welling, M. S., Aegerter, C. M. & Menghini, M. Avalanches and self-organized criticality in superconductors. Eur. Phys. J. B 50, 117–122, 10.1140/epjb/e2006-00063-7 (2006).
Wiesmann, H. J. & Zeller, H. R. A fractal model of dielectric breakdown and prebreakdown in solid dielectrics. J. Appl. Phys. 60, 1770–1773, 10.1063/1.337219 (1986).
Altshuler, E. & Johansen, T. H. Colloquium: Experiments in vortex avalanches. Rev. Mod. Phys. 76, 471–487, 10.1103/RevModPhys.76.471 (2004).
Jing, Z., Yong, H. & Zhou, Y. Influences of non-uniformities and anisotropies on the flux avalanche behaviors of type-II superconducting films. Supercond. Sci. Technol. 29, 105001, 10.1088/0953-2048/29/10/105001 (2016).
Vestgården, J. I., Galperin, Y. M. & Johansen, T. H. Oscillatory regimes of the thermomagnetic instability in superconducting films. Phys. Rev. B 93, 174511, 10.1103/PhysRevB.93.174511 (2016).
Brisbois, J. et al. Magnetic flux penetration in Nb superconducting films with lithographically defined microindentations. Phys. Rev. B 93, 054521, 10.1103/PhysRevB.93.054521 (2016).
Wertheimer, M. & Gilchrist, J. le G. Flux jumps in type ii superconductors. J. Phys. Chem. Solids 28, 2509–2524, 10.1016/0022-3697(67)90038-8 (1967).
Durán, C. A., Gammel, P. L., Miller, R. E. & Bishop, D. J. Observation of magnetic-field penetration via dendritic growth in superconducting niobium films. Phys. Rev. B 52, 75–78, 10.1103/PhysRevB.52.75 (1995).
Nowak, E. R., Taylor, O. W., Liu, L., Jaeger, H. M. & Selinder, T. I. Magnetic flux instabilities in superconducting niobium rings: Tuning the avalanche behavior. Phys. Rev. B 55, 11702–11705, 10.1103/PhysRevB.55.11702 (1997).
Behnia, K., Capan, C., Mailly, D. & Etienne, B. Internal avalanches in a pile of superconducting vortices. Phys. Rev. B 61, R3815–R3818, 10.1103/PhysRevB.61.R3815 (2000).
Motta, M. et al. Enhanced pinning in superconducting thin films with graded pinning landscapes. Appl. Phys. Lett. 102, 212601, 10.1063/1.4807848 (2013).
Brisbois, J. et al. Imprinting superconducting vortex footsteps in a magnetic layer. Sci. Rep. 6, 27159, 10.1038/srep27159 (2016).
Lombardo, J. et al. In situ tailoring of superconducting junctions via electro-annealing. Nanoscale 10, 1987–1996, 10.1039/C7NR08571K (2018).
Flubacher, P., Leadbetter, A. J. & Morrison, J. A. The heat capacity of pure silicon and germanium and properties of their vibrational frequency spectra. The Philos. Mag. A J. Theor. Exp. Appl. Phys. 4, 273–294, 10.1080/14786435908233340 (1959).
Glassbrenner, C. J. & Slack, G. A. Thermal conductivity of silicon and germanium from 3 °K to the melting point. Phys. Rev. 134, A1058–A1069, 10.1103/PhysRev.134.A1058 (1964).
Koblischka, M. R. & Wijngaarden, R. J. Magneto-optical investigations of superconductors. Supercond. Sci. Technol. 8, 199–213 (1995).
Shaw, G. et al. Quantitative magneto-optical investigation of superconductor/ferromagnet hybrid structures. Rev. Sci. Instrum. 89, 023705, 10.1063/1.5016293 (2018).
Colauto, F. et al. Mapping flux avalanches in MgB films—equivalence between magneto-optical imaging and magnetic measurements. Supercond. Sci. Technol. 20, L48–L50, 10.1088/0953-2048/20/8/L02 (2007).
Bean, C. P. Magnetization of hard superconductors. Phys. Rev. Lett. 8, 250–253, 10.1103/PhysRevLett.8.250 (1962).
Mints, R. G. & Rakhmanov, A. L. Critical state stability in type-II superconductors and superconductingnormal-metal composites. Rev. Mod. Phys. 53, 551–592, 10.1103/RevModPhys.53.551 (1981).
Treiber, S., Stahl, C., Schütz, G. & Albrecht, J. Unusual flux jumps above 12 K in non-homogeneous MgB2 thin films. Supercond. Sci. Technol. 25, 065010, 10.1088/0953-2048/25/6/065010 (2012).
Altshuler, E. et al. Vortex avalanches with robust statistics observed in superconducting niobium. Phys. Rev. B 70, 140505, 10.1103/PhysRevB.70.140505 (2004).
Treiber, S., Stahl, C., Schütz, G. & Albrecht, J. Stability of the current-carrying state in nonhomogeneous MgB films. Phys. Rev. B 84, 094533, 10.1103/PhysRevB.84.094533 (2011).
Johansen, T. H. et al. Reproducible nucleation sites for flux dendrites in MgB. Surf. Sci. 601, 5712–5714, 10.1016/j.susc.2007.06.068 (2007).
McPherson, J. W. Reliability Physics and Engineering (Springer, New York, 2010).
Gumbel, E. J. Statistical theory of extreme values and some practical applications. technical report, National Bureau of Standards, Washington D. C., Applied mathematics Div. Applied mathematics series (1954).
Baumans, X. D. A. et al. Healing effect of controlled anti-electromigration on conventional and high-Tc superconducting nanowires. Small 13, 1700384, 10.1002/smll.201700384 (2017).
Li, P. et al. Switching currents limited by single phase slips in one-dimensional superconducting Al nanowires. Phys. Rev. Lett. 107, 137004, 10.1103/PhysRevLett.107.137004 (2011).
Aref, T., Levchenko, A., Vakaryuk, V. & Bezryadin, A. Quantitative analysis of quantum phase slips in superconducting Mo76 Ge24 nanowires revealed by switching-current statistics. Phys. Rev. B 86, 024507, 10.1103/PhysRevB.86.024507 (2012).
Lee, J.-Y. et al. Microscopic flux density of small and dendritic flux jumps in MgB thin films. Supercond. Sci. Technol. 21, 105021, 10.1088/0953-2048/21/10/105021 (2008).
Mints, R. G. & Brandt, E. H. Flux jumping in thin films. Phys. Rev. B 54, 12421–12426, 10.1103/PhysRevB.54.12421 (1996).
Johansen, T. H. et al. Dendritic magnetic instability in superconducting MgB2 films. Eur. Lett 59, 599–605, 10.1209/epl/i2002-00146-1 (2002).
Vestgården, J. I., Shantsev, D. V., Galperin, Y. M. & Johansen, T. H. The diversity of flux avalanche patterns in superconducting films. Supercond. Sci. Technol. 26, 055012, 10.1088/0953-2048/26/5/055012 (2013).
Baruch-El, E. et al. Dendritic flux instability in MgB2 films above liquid hydrogen temperature. Supercond. Sci. Technol. 31, 025005, 10.1088/1361-6668/aa9f41 (2018).
Qureishy, T. et al. Dendritic flux avalanches in a superconducting MgB2 tape. Supercond. Sci. Technol. 30, 125005, 10.1088/1361-6668/aa9244 (2017).
Motta, M. et al. Controllable morphology of flux avalanches in microstructured superconductors. Phys. Rev. B 89, 134508, 10.1103/PhysRevB.89.134508 (2014).
Vestgården, J. I., Shantsev, D. V., Galperin, Y. M. & Johansen, T. H. Lightning in superconductors. Sci. Rep. 2, 886, 10.1038/srep00886 (2012).