Dendritic Thermo-magnetic Instability in Superconductors Daniel V. Shantsev AMCS group, Department of Physics, UiO Collaboration: D. V. Denisov, A.A.F.Olsen, Y. M. Galperin, T. H. Johansen, UiO A. L. Rakhmanov, Inst. Th&Appl. Electrodyn., Moscow, Russia A. V. Bobyl, A. F. Ioffe Institute, St. Petersburg, Russia S.-I.Lee, Pohang University, Korea Supported by since July 2003

Linearly polarized light Faraday-active crystal Magnetic field H  (H)(H) F P A image mirror MO indicator S N large small FF Magneto-Optical Imaging MO-crystal MO image of UiO magnetic card MO image of UiO magnetic card

Vortex lattice (uniform B) Type-II, intermediate H Meissner effect (B=0) Type-I Type-II, small H

Vortex pinning  B dA = h/2e =  0 Flux quantum:  Å J B(r) normal core BaBa J f Vortices get pinned by tiny defects (inhomogeneities) that create a sort of friction => vortices cannot be moved easily

Critical state Vortices : enter superconductor from the edge where B=B a get pinned and cannot penetrate much further => Flux density gradient (critical state)

Sand pile and Vortex pile are Metastable states

are subject to avalanches

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

Dendritic flux avalanches Zhao et al, PRB 2002 MgB 2 new superconductor (Jan 2001), T c =39K Magneto-optical movie (Mar 2001) MgB 2 film How to explain noisy M(H) curve ??? Samples: S.-I. Lee, Pohang Univ, Korea dendrite velocity km/s

T = 10 K remanent state T-dependent topology T = 4 K Europhys. Lett. 59, (2002)

D=1.05 D=1.35 D=1.65 D=1.75 temperature T thresh ~ 10K Fractal dimension of the dendrites Appl.Phys.Lett. 87, (2005)

Dendrites avoid crossing BEFOREAFTER Supercond. Sci. Technol. 14, 726 (2001)

MO indicator MgB 2 film Al-foil (10 micron) Suppression of the dendritic instability by a metal film Physica C 369, 93 (2002) Appl.Phys.Lett. 87, (2005)

Flux density at the dendrite core is B max  12 mT B max remains the same for all branches of the same dendrite, and along every particular branch. B max does not depend on B a, at least for B a = mT B max also gives the peak field at the film edge Flux density profiles across the dendritic branches Phys.Rev.B 67, (2003)

3 identical experiments: field ramp from 0 to 13.6 mT for 10 sec the nucleation place: well reproduced the exact flux pattern: never reproduced Irreproducibility

Dendritic patterns in various MgB 2 films and other materials Screen printing, Al 2 O 3 substrate 3000 nm, T c =35K G. Gritzner, Univ. of Linz, Austria Pulse Laser Deposition on 1102 Al 2 O 3 substrate 400nm, T c =39K S.I. Lee, Pohang Univ., Korea PLD, SrTiO 3 substrate, 250nm, T c =28K S.X. Dou, Wollongong, Australia NbN Nb 3 Sn Supercond. Sci. Technol. 18, 1391 (2005) Supercond. Sci. Technol. 17, 764 (2004) Cryogenics 43, 663 (2003) Appl.Phys.Lett. 87, (2005)

Nb : C.A. Duran et al. PRB 52, 75 (1995) YBaCuO, induced by laser P. Leiderer et al. PRL (1993) Dendritic patterns in other materials Pb : Menghini et al, PRB 2005 YNi 2 B 2 C Wimbush et al. JAP 2004

Theory Why does instability develop into dendritic pattern ? Under what conditions does the dendritic instability occur ?

x y z BaBa B j 2w>>d d Stability analysis for a thin film Non-local electrodynamics: Heat removal into the substrate: Thermal diffusion + Maxwell Linear Analysis

H(E) stability diagram Dendritic jumps 0 k y Re Phys. Rev. B 70, (2004) Phys. Rev. B 73, (2006) Phys. Rev. B 72, (2005)

Comparison with experiments Curves – theory, Symbols – experiment MD Simulations