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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 What determines the critical current density Jc ? Thermal Vortex Avalanches stable critical state described by critical current Jc Jc due to depinning of vortices OR AND > thermo-magnetic instability (flux jumps) Jc due to thermal vortex avalanches at least for MgB2 films for T<15 K Mechanism of Thermo-Magnetic Instability Flux motion releases heat Temperature rise weakens flux pinning T0 Jc Q T > T0 Positive feedback loop Catastrophic flux jumps M(H) loop M ~ M Critical state is destroyed Temperature rises to ~Tc Muller & Andrikidis, PRB-94 Dendritic flux jumps M ~ 0.01 M Critical state is destroyed locally Temperature rises to ~Tc locally MgB2 film Magneto-optical imaging Zhao et al, PRB 2002 Europhys. Lett. 59, 599-605 (2002) Microscopic flux jumps 5 mm MgB2 film fabricated by S.I. Lee (Pohang, Korea) MgB2 film 100 mm Magneto-optical movie shows that flux penetration proceeds via small avalanches Analyzing difference images 7.15 mT = — MO image (7.150mT) local increase of flux density - linear ramp of Ba 15 MO images MO image (7.165mT) avalanche 23000 T=3.6K 11000 7.40 mT 2500 number of vortices 50 - 50000 Evolution of local flux density 5x5 mm2 local B (m T) 30 Local B grows by small and repeated steps 20 10 7.4mT 7.9mT 7mT 0 6.8 7.2 7.6 8.0 8.4 B a (mT) 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 Flux density profiles before jump after jump Flux density B (mT) 50 Flux profiles before and after a flux jump have similar shapes 40 7,5000 30 20 31,0000 Ba=11.6mT 10 Ba=5.6mT edge 0 -100 0 100 200 distance (mm) x Microscopic flux jumps do not destroy the critical state film edge Catastrophic jumps M ~ M Critical state is destroyed Dendritic jumps M ~ 0.01 M : noisy M(H) Critical state is destroyed locally Global Jc is suppressed Microscopic jumps M ~ 10-5 M : invisible in M(H) Critical state is preserved What determines Jc ? 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 Avalanche size distribution hints to the thermal mechanism 4mT 3 Number of Jumps 10 10mT 2 10 40mT 1 10 10 2 10 3 10 4 10 5 10 6 10 7 Jump size (0) The distribution has a peak at some typical size (self-organized criticality suggests a power-law) 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 B, T - profiles before jump after jump 1.2 0.8 Ba = 2Bc 0.4 0.2 Ba = Bc 0.0 -1.5 -1.0 -0.5 0.0 x/w 0.3 40 7,5000 30 20 31,0000 Ba=11.6mT 10 Ba=5.6mT edge 0 Ba = 2Bc T / Tc before jump after jump 50 0.6 Flux density B (mT) B / m0 jcd 1.0 -100 0 100 200 distance (mm) Ba = Bc 0.2 0.1 -1.5 x -1.0 -0.5 0.0 x/w film edge Flux jump size 0.1Tc 0.1 0.2Tc 0.01 Bfj 1E-3 0.3Tc Flux jump size (0) Jump Size, / m0 jc0 dw 10 6 T=0.1Tc 10 5 10 4 10 3 10 2 1E-4 1 4 Applied field, Ba / Bc(T0) 8 12 Ba (mT) We fit • Bfj ~ 2 mT • Tth ~ 13 K • (Ba) dependence using only one parameter: Thermal origin of avalanches 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 Results • Small flux avalanches (~1000 0) 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 Conclusions 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 Phys. Rev. B 72, 024541 (2005) http://www.fys.uio.no/super/ H-T phase diagram the instability field for a thin strip: Dendritic jumps Microscopic flux jumps Tth temperature 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 Breakdown of critical state thermal avalanches (flux jumps) a new type of critical state with a new Jc usually Vortex Pinning at least for MgB2 films for T<15 K Critical state Vortices : • driven inside due to applied field • get pinned by tiny inhomogeneities => Metastable critical state Sandpile Critical state in a superconductor Distribution of flux density YBaCuO film, picture from R.Wijngarden picture from E.Altshuler Critical current Critical angle 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’’ 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 Jc Statistics of vortex avalanches From E. Altshuler and T. H. Johansen, Reviews of Modern Physics, 76, 471 (2004) Using Magneto-optical Imaging to position the Hall probes Magneto-optical imagin to measure avalanches 5 mm MgB2 film 100 mm Irreproducibility T=3.6K Ba = 13.6 mT B(r) the flux pattern almost repeats itself MOI(8.7mT) - MOI(8.5mT) B(r) B(r) is irreproducible! The final pattern is the same but the sequences of avalanches are different 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 Sometimes thermal avalanches are not complete, but they are limited only by sample dimensions, and obviously destroy the critical state M ~ 0.2 M Nb disk, Goodman et al., Phys. Lett. 18, 236 (1965) 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? Adiabatic energy balance All energy released by flux motion is absorbed C dT = jE dt = jc d the amount of flux that has passed through the given point during an avalanche Adiabatic critical state for a thin strip is given by a set of equations: Biot-Savart Critical state Number of avalanches dH/dt~1G/s too small large E 10 B (r) 10 mm E > Ecdend 1000 1,000,000 20 mm 200 mm “Size” model avalanche size, 0 1 mm “Shape” model Conclusions Small: 50 - 50,000 vortices Round shape 20 mm Vortex Avalanches in MgB2 films Big: ~5,000,000 vortices Dendritic shape 1 mm “Shape” Model “uniform” shape “Size” Model Jump Size, / m0 jc0 dw adiabatic critical state Maxwell + Thermal diffusion dendritic shape • Criterion H(E,h0) • Dendrite width • Build-up time 0.1Tc 0.1 0.2Tc 0.01 Bfj 1E-3 1E-4 1 Applied field, Ba / Bc(T0) Thermal effects control • dendritic avalanches • micro-avalanches down to 50 vortices More info: http://www.fys.uio.no/super Magneto-optical Imaging image q F(H) Faraday-active crystal A small Linearly polarized light large Faraday rotation polarizer P H Magnetic field light source MO indicator mirror Square YBaCuO film N S small normal core x The vortex core interacts with tiny inhomogeneities (x ~ nanometers) J => B(r) l Flux quantum: B dA = h/2e = 0 vortices get pinned (don’t want to move) Detecting vortex jumps B (r) Ba=4G Subtract subsequent images: B(r) vortex arrived B (r) vortex left 10 90 % no motion 40 10 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) Evolution of local flux density 5x5 mm2 No long-range correlation between the jumps local B (m T) 30 20 Frequent jumps at the same place 10 7.4mT 7.9mT 7mT 0 6.8 7.2 7.6 8.0 8.4 B a (mT) 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 Number of Jumps Why small and big jumps ? 40mT 1 10 10 3 10 4 10 5 10 6 10 7 Jump size (0) Both types of jumps have the same threshold T=10K Nb films: also 2 types of jumps, big and small: the same mechanism James et al., Phys.C 2000 Nowak et al, PRB 1997 Distribution functions of jump sizes 10% 50% 4mT 10mT 10 10 resolution limit Some flux penetrates into the sample via very small jumps or without jumps at all Number of Jumps 10 3 2 1 10 Fraction of flux arrived via jumps: 0 10 1 90% 40mT 10 2 10 3 4 10 10 Jump size (0) Sall jumps i final - initial = ? 5 10 6 10 7 Dendritic < 100%