Vortex avalanches in superconductors: Size distribution and Mechanism

1. Vortex avalanches in superconductors: Size distribution and Mechanism Daniel Shantsev Tom Johansen and Yuri Galperin AMCS group Department of Physics, University of Oslo A. V. Bobyl A. F. Ioffe Institute, St. Petersburg, Russia

2. Vortex lattice • A. Abrikosov • (published 1957) Hc2 Normal state Mixed state (vortex matter) Type II 2003 Hc1 Meissner state Temperature Tc Vortices in Superconductors

3. Critical state • Vortices : • driven inside due to applied field • get pinned by tiny inhomogeneities • => Metastable critical state

4. Sandpile Critical state in a superconductor Distribution of flux density YBaCuO film, picture from R.Wijngarden picture from E.Altshuler Critical current Critical angle Avalanches ???

5. Trapped field magnets High-current cables Jc Record trapped field: 17 Tesla ~100 times better than Cu wire Motivation to study vortex avalanches The slope of the vortex pile - the critical current density Jc – is the key parameter for many applications of superconductors

6. Size distribution H SOC or YBCO Hall probe Measuring avalanches

7. Reference Geometry Material Sensor Avalanche type Avalanche distribution Heiden & Rochlin PRL (1968) Hollow cylinder Pb-In Coil Off the edge Exponential Field et al PRL (1995) Hollow cylinder Nb-Ti Coil Off the edge Power law (slow ramps) Zieve et al PRB (1996) Planar YBCO crystal 1 Hall probe Internal Peaked Nowak et al PRB (1997) Ring Nb film 2 Hall probes Off the edge & internal Peaked or Power law (dep. on T) Aegerter PRE (1998) Planar BSCCO crystal SQUID Off the edge Exp or Power law (dep. on T & t) Behnia et al PRB (2000) Planar Nb film Hall probe arrang. Internal Peaked or Power Law (dep. on H & T) Statistics of vortex avalanches Why peaked?

8. The thermal instability can lead to catastrophic avalanches with thermal runaways (flux jumps) and sometimes remarkable flux patterns Magneto-optical movie of flux penetration in MgB2 film 1 mm Thermal effects 1) Flux motion releases heat 2) T rise weakens flux pinning Can it also affect the statistics of small avalanches? and in what way? T0Jc Q T > T0

9. q (H) F image Faraday-activecrystal A small large small Faraday Linearly polarized light rotation polarizer P H Magnetic field light source MO indicator mirror N Square YBaCuO film S Magneto-optical Imaging

10. Ba rise 100 mm Down to small scales... • Flux penetration • on small scales : • in space: • highly non-uniform • in time: • gradual or abrupt??? 5 mm MgB2 film

11. 7.15 mT = MO image (7.165mT) — MO image (7.150mT) DBa= 0.015mT, Dt=2.5 sec local increase of flux density - linear ramp of Ba 15 MO images avalanche 2300F0 T=3.6K 1100F0 250F0 7.40 mT Analyzing difference images number of vortices 50 - 50000

12. Avalanche size • Typical size exists • It grows with Ba 2.500.000F0 20F0

13. MOI(8.7mT) - MOI(8.5mT) DB(r) DB(r) is irreproducible! The final pattern is the same but the sequences of avalanches are different Irreproducibility T=3.6K Ba = 13.6 mT B(r) the flux pattern almost repeats itself

14. Adiabatic approach Heat stays where it has been released OK if thermal diffusion is much slower than flux diffusion DT<<DM Originally used by Swartz &Bean in 1968

15. Adiabatic critical state for a thin strip is given by a set of equations: Adiabatic : All energy released by flux motion is absorbed Critical state Flux that has passed through “x” during avalanche Biot-Savart

16. Intermediate result: the adiabatic instability field for a thin strip Demonstrates existence of a threshold T (above which jumps do not occur no matter how large field is applied) Tth temperature

17. 7,500F0 31,000F0 B, T - profiles x film edge

18. T=0.1Tc Thermal origin of avalanches 0.3Tc • We fit • Bfj ~ 2 mT • Tth ~ 10 K • F(Ba) dependence • using only • one parameter:

19. Conclusions Trivial conclusions: • Flux avalanches are observed in superconducting films using magneto-optical imaging • They have a charactristic size (~1000 F0) that grows with Ba • Adiabatic model for the size of thermal flux avalanche in a thin film is developed • Agreement with experiment (the thershold Ba, threshold T, size(Ba)-dependence) • Thermal mechanism can be responsible for • microscopic avalanches (not only catastrophic jumps) • and leads to a peaked size distribution • Thermal effects contribute to formation of the critical state (and modify Jc ) without destroying it Deep conclusions: Phys. Rev. B 72, 024541 (2005) http://www.fys.uio.no/super/

21. normal core x J B(r) l B dA = h/2e = 0 Flux quantum: The vortex core interacts with tiny inhomogeneities (x ~ nanometers) => vortices get pinned (don’t want to move)

22. We want to understand how the critical state is formed because: • it determines the critical current density Jc – the key parameter for most applications of superconductors (high-current cables, trapped-field magnets) • to test models, e.g. self-organized criticality, for applicability to vortices (that move in a disordered landscape and don’t have inertia)

23. 7mT 7.4mT 7.9mT Evolution of local flux density 5x5 mm2 No long-range correlation between the jumps Frequent jumps at the same place linear ramp 6 mT/s local flux density calculated from local intensity of MO image; each point on the curve corresponds to one MO image

24. Why small and big jumps ? Both types of jumps have the same threshold T=10K the same mechanism Nb films: also 2 types of jumps, big and small: James et al., Phys.C 2000 Nowak et al, PRB 1997

25. Some flux penetrates into the sample via very small jumps or without jumps at all 10% 50% resolution limit 90% Sall jumps Fi = ? < 100% Fraction of flux arrived via jumps: Ffinal - Finitial Distribution functions of jump sizes Dendritic