Critical state controlled by microscopic flux jumps in superconductors

1. Critical state controlled by microscopic flux jumps in superconductors Daniel Shantsev Physics Department, University of Oslo, Norway in collaboration with Vitali Yurchenko, Alexander Bobyl, Yuri Galperin, Tom Johansen Physics Department, University of Oslo, Norway Eun-Mi Choi, Sung-Ik Lee Pohang University of Science and Technology, Korea

2. What determines the maximal current a superconductor can carry?

3. 1. Solsby Rule H Magnetic field created by current, should not exceed the critical magnetic field H = I/2p R < Hc R Jc(1) = 2Hc / R I

4. 2. Depairing current density Ginsburg-Landau equations have a solution only if R J < Jc(2) Hc / l For J>Jc the kinetic energy of Cooper pairs exceeds the superconducting energy gap I

5. normal core x~10 Å J B(r) l B dA = h/2e = 0 Flux quantum: Meissner effect Vortex lattice

6. Vortices get pinned by tiny defects and start moving only ifLorentz force > Pinning force Ba Lorentzforce J pinningforce Vortices are driven by Lorentz force and their motion creates electric field E ~ dB/dt Lorentz force F = j F0 current

7. 3. Depinning current density Superconductor remains in the non-resistive state only if Lorentz force < Pinning force, i.e. if U(r) J < Jc(3) = U / F0 Ideal pinning center is a non-SC column of radius ~ xso that U ~ Hc2x2 and similar to the depairing Jc Jc(3)~ Hc / l

8. Local Temperature Increases It is easier for vortices to overcome pinning barriers +kT Vortices move faster E ~ dB/dt Vortex motion dissipates energy, J*E velocity positive feedback current

9. dQM =Jc(T) dF = H2/2JcdJc/dT dT dQT = C(T) dT dQM > dQT - instability starts H > Hfj = (2C Jc [dJc/dT]-1)1/2 Jc(4) = (2C Jc(3) [dJc(3) /dT]-1)1/2/2w d<<w j H Hfj Hfjslab (d/w)1/2 dF x 2w D. S. et al. PRB 2005 Thermal instability criterion ~ Swartz &Bean, JAP 1968 j H dF x 0

10. We need to know which Jc is the most important i.e. the smallest! Jc(3) < Jc(4) < Jc(1) <Jc(2) Achieved List of current-limiting mechanisms • Solsby, Jc ~ Hc/R • Depairing current Jc ~ Hc / l • Depinning current, Jc (U) • Thermal instability current, Jc(C,..)

11. Gaevski et al, APL 1997 Brull et al, Annalen der Physik 1992, v.1, p.243 How to distinguish between Jc’s • J >Jc(3) a small finite resistance appears • J >Jc(4) a catastrophic flux jump occurs (T rises to ~Tc or higher)

12. Global flux jumps M(H) loop • DM ~ M • Critical state is destroyed Muller & Andrikidis, PRB-94

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

14. 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 jumps

15. 7.15 mT = MO image (7.165mT) — MO image (7.150mT) local increase of flux density - linear ramp of Ba 15 MO images flux jump 2300F0 T=3.6K 1100F0 250F0 7.40 mT Analyzing difference images

16. 7,500F0 31,000F0 From the standard measurementsone can not tell what limits Jc: vortex pinning OR thermal instabilities Jc(3) OR Jc(4) ? The problem with microscopic jumps • Too small, DM ~ 10-5 M : invisible in M(H) • Critical state is not destroyedB-distribution looks as usual x edge Flux profiles before and after a flux jump have similar shapes

17. Number of jumps Jump size (F0) What can be done • One should measure dynamics of flux penetration and look for jumps • If any, compare their statistics, B-profiles etc with thermal instability theories • If they fit, then Jc=Jc(4) , determined by instability; actions – improve C, heat removal conditions etc, • if not, then Jc=Jc(3), determined by pinning; actions – create better pinning centers power-law Altshuler et al. PRB 2005 peak(thermalmechanism)

18. Jc(3) Jc(4) Two Jc’s in one sample 300 mm 70 mm Jcleft 2 Jcright

19. Dendritic instability can be suppressed by a contact with normal metal Baziljevich et al 2002

20. 9 mm w 3 mm MgB2 Au Two Jc’s in one sample 300 mm 70 mm Au suppresses jumps, Jc is determined by pinning Jc is determined by jumps Jc(3) Jc(4)

21. J H A graphical way to determine Jc’s: d-lines

22. Jc1 Jc2 MgB2 3 mm Au ?

23. α α

24. α≈π/3 α β α ! jc1≈2jc2 !

25. Conclusions • Thermal avalanches can be truly microscopicas observed by MOI and described by a proposed adiabatic model • These avalanches can not be detected either in M(H) loops or in static MO images => “What determines Jc?” - is an open question • MO images of MgB2 films partly covered with Au show two distinct Jc’s:- Jc determined by stability with respect to thermal avalanches - a higher Jc determined by pinning http://www.fys.uio.no/super/

27. 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

28. 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

29. 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

30. 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:

31. 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

32. 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