Global and local flux jumps in MgB2 films: Magneto-optical imaging and theory

1. Global and local flux jumps in MgB2 films: Magneto-optical imaging and theory Daniel Shantsev, Yuri Galperin, Alexaner Bobyl, Tom Johansen Physics Department, University of Oslo, Norway Sung-Ik Lee Pohang University of Science and Technology, Korea

2. What determines the critical current density Jc ? Thermal Vortex Avalanches stable critical state described by critical currentJc thermo-magnetic instability (flux jumps) OR AND Jc due to depinning of vortices Jc due to thermal vortex avalanches > at least for MgB2 films for T<15 K

3. Mechanism of Thermo-Magnetic Instability • Flux motion releases heat • Temperature rise weakens flux pinning T0Jc Q T> T0 Positive feedback loop

4. Catastrophic flux jumps M(H) loop • DM ~ M • Critical state is destroyed • Temperature rises to ~Tc Muller & Andrikidis, PRB-94

5. Magneto-optical imaging Europhys. Lett. 59, 599-605 (2002) Dendritic flux jumps MgB2 film • DM ~ 0.01 M • Critical state is destroyed locally • Temperature rises to ~Tc locally Zhao et al, PRB 2002

6. 100 mm Microscopic flux jumps 5 mm MgB2 film fabricated by S.I. Lee (Pohang, Korea) MgB2 film Magneto-optical movie shows that flux penetration proceeds via small avalanches

7. 7.15 mT = MO image (7.165mT) — MO image (7.150mT) 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

8. 7mT 7.4mT 7.9mT Evolution of local flux density 5x5 mm2 Local B grows bysmall and repeated steps 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

9. 7,500F0 31,000F0 Flux density profiles Flux profiles before and after a flux jump have similar shapes x Microscopic flux jumps do not destroy the critical state film edge

10. Dendritic jumps Catastrophic jumps • DM ~ M • Critical state is destroyed • DM ~ 0.01 M : noisy M(H) • Critical state is destroyed locally • Global Jc is suppressed Microscopic jumps • DM ~ 10-5 M : invisible in M(H) • Critical state is preserved What determines Jc ?

11. Jc is determined by stability with respect to thermal avalanches Jc depends on thermal coupling to environment, specific heat, sample dimensions But we need to prove that the observed microscopic avalanches are indeed of thermal origin

12. Avalanche size distribution hints to the thermal mechanism The distribution has a peak at some typical size (self-organized criticality suggests a power-law)

13. Adiabatic critical state for a thin strip In the spirit of Swartz &Bean in 1968 Adiabatic : All energy released by flux motion is absorbed Critical state Biot-Savart for thin film Flux that has passed through “x” during avalanche

14. 7,500F0 31,000F0 B, T - profiles x film edge

15. T=0.1Tc Thermal origin of avalanches Flux jump size 0.3Tc • We fit • Bfj ~ 2 mT • Tth ~ 13 K • F(Ba) dependence • using only • one parameter:

16. Materials • Dendritic avalanches • seen by magneto-optics – • all kinds of MgB2 films (T<10K), • C-doped MgB2 • Nb, NbN, Nb3Sn, YBaCuO, Pb, YB2C2O • Peaked size distribution of avalanches • measured by Hall probes • Nb, Pb

17. Results • Small flux avalanches (~1000 F0) are observed in MgB2 films using magneto-optical imaging for T<15 K • Adiabatic model for the size of flux avalanches in a thin film is developed • Good agreement suggests the thermal mechanism of avalanches • Thermal avalanches can be microscopic • These avalanches can control formation of the critical state without destroying it • Jc is then determined by stability with respect to these thermal avalanches rather than by pinning • The avalanches are too small to be detected in M(H) loops Conclusions Phys. Rev. B 72, 024541 (2005) http://www.fys.uio.no/super/

19. H - T phase diagram the instability field for a thin strip: Dendritic jumps Microscopic flux jumps Tth temperature

20. Breakdown of critical state thermal avalanches (flux jumps) a new type of critical state with a new Jc at least for MgB2 films for T<15 K What determines the critical current density Jc ? Jc due to depairing of Cooper pairs Jc due to depinning of vortices Jc due to thermal vortex avalanches << < usually Vortex Pinning

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

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

23. Pierre G. de Gennes comments in his classic 1966 book Superconductivity of Metals and Alloys: ‘‘We can get some physical feeling for this critical state by thinking of a sand hill. If the slope of the sand hill exceeds some critical value, the sand starts flowing downwards (avalanche). The analogy is, in fact, rather good since it has been shown (by careful experiments with pickup coils) that, when the system becomes overcritical, the lines do not move as single units, but rather in the form of avalanches including typically 50 lines or more’’

24. Jc Motivation to study vortex avalanches • To understand something about vortices • To understand something about self-organization (local interactions between vortices lead to long-scales correlations) • To enhance Jc , i.e. the slope of the vortex pile • (for various applications of superconductors) Trapped field magnets up to 17 Tesla

25. Statistics of vortex avalanches From E. Altshuler and T. H. Johansen, Reviews of Modern Physics, 76, 471 (2004)

26. Using Magneto-optical Imaging to position the Hall probes

27. 100 mm Magneto-optical imagin to measure avalanches 5 mm MgB2 film

28. 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

29. Thermal effects 1) Flux motion releases heat 2) T rise weakens flux pinning T0Jc Q T > T0 The thermal instability is usually associated with catastrophic avalanches

30. Sometimes thermal avalanches are not complete, but they are limited only by sample dimensions, and obviously destroy the critical state DM ~ 0.2 M Nb disk, Goodman et al., Phys. Lett. 18, 236 (1965)

31. Are there small thermal avalanches ? Are there thermal avalanches that do not destroy the critical state? Can thermal avalanches stop before reaching the sample dimensions? Can we calculate the size of a thermal avalanche?

32. Adiabatic energy balance All energy released by flux motion is absorbed C dT = jE dt = jc dF the amount of flux that has passed through the given point during an avalanche

33. Adiabatic critical state for a thin strip is given by a set of equations: Biot-Savart Critical state

35. dH/dt~1G/s too small large E E > Ecdend 10 1000 avalanche size, F0 1,000,000 DB (r) 20 mm 1 mm 200 mm “Size” model “Shape” model 10 mm Number of avalanches

36. Conclusions Vortex Avalanches in MgB2 films Small: 50 - 50,000 vortices Round shape Big: ~5,000,000 vortices Dendritic shape 20 mm 1 mm “Shape” Model Maxwell + Thermal diffusion “uniform” shape dendritic shape • Criterion H(E,h0) • Dendrite width • Build-up time “Size” Model adiabatic critical state • Thermal effects control • dendritic avalanches • micro-avalanches down to 50 vortices More info: http://www.fys.uio.no/super

37. 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

38. 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)

39. vortex arrived vortex left DB (r) 1F0 1F0 4F0 Detecting vortex jumps B(r) Ba=4G Subtract subsequent images: DB(r) 90 % no motion

40. 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)

41. 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

42. 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

43. 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