dendritic thermo-magnetic instability in superconductors daniel v. shantsev amcs group, department...
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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, UiOA. L. Rakhmanov, Inst. Th&Appl. Electrodyn., Moscow, RussiaA. V. Bobyl, A. F. Ioffe Institute, St. Petersburg, RussiaS.-I.Lee, Pohang University, Korea
Supported by FUNMAT@UiO since July 2003
Linearlypolarized light
Faraday-active crystal
Magnetic fieldH
(H)F
P
A
image
mirrorMO indicator
SN
largesmall small
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 pinningVortex pinning
B dA = h/2e = 0 Flux quantum:
Å
J
B(r)
normal core
Ba
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=Ba
• get pinned and cannot penetrate much further
=> Flux density gradient (critical state)
Sand pile and Vortex pile areMetastable states
Metastable statesare subject to avalanches
current
velocity
E ~ dB/dt Vortex motiondissipates energy,
J*E
Local TemperatureIncreases
+kT
It is easier for vortices to overcome pinning barriers
Vortices movefaster
positivefeedback
Dendritic flux avalanches
Zhao et al, PRB 2002
MgB2 new superconductor (Jan 2001), Tc=39K
Magneto-optical movie(Mar 2001)
MgB2 film
How to explain noisy M(H) curve ???
Samples: S.-I. Lee, Pohang Univ, Korea
dendrite velocity10-100 km/s
T = 10 K
remanent state
T-dependent topologyT-dependent topology
T = 4 K
Europhys. Lett. 59, 599-605 (2002)
D=1.05
D=1.35
D=1.65
D=1.75
temperature
Tthresh ~ 10K
Fractal dimensionFractal dimensionof the dendritesof the dendrites
Appl.Phys.Lett. 87, 042502 (2005)
Dendrites avoid crossingDendrites avoid crossing
BEFORE AFTER
Supercond. Sci. Technol. 14, 726 (2001)
MO indicator
MgB2 film
Al-foil (10 micron)
Suppression of Suppression of the dendritic the dendritic
instability by a metal instability by a metal filmfilm
Physica C 369, 93 (2002)
Appl.Phys.Lett. 87, 152501 (2005)
0 100 200 300 400 500 600
0
5
10
15
20
25
30
35
40
45
50
55
60
H
G
F
E
D
C
B
Flu
x d
en
sit
y (
mT
)
Distance (m)
Flux density at the dendrite core is Bmax 12 mT
• Bmax remains the same for all branches of the same dendrite, and along every particular branch.
• Bmax does not depend on Ba , at least for Ba = 2 - 8 mT
• Bmax also gives the peak field at the film edge
Flux density profiles across the dendritic Flux density profiles across the dendritic branchesbranches
Phys.Rev.B 67, 064513 (2003)
3 identical experiments: field ramp from 0 to 13.6 mT for 10 sec
the nucleation place: well reproducedthe exact flux pattern: never reproduced
Irreproducibility
Dendritic patterns in various MgB2 films and other materials
Screen printing, Al2O3 substrate3000 nm, Tc=35KG. Gritzner, Univ. of Linz, Austria
Pulse Laser Deposition on 1102 Al2O3 substrate400nm, Tc=39KS.I. Lee, Pohang Univ., Korea
PLD, SrTiO3 substrate,250nm, Tc=28KS.X. Dou, Wollongong, Australia
NbN
Nb3Sn
Supercond. Sci. Technol. 18, 1391 (2005)
Supercond. Sci. Technol. 17, 764 (2004)
Cryogenics 43, 663 (2003)
Appl.Phys.Lett. 87, 042502 (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
YNi2B2C
Wimbush et al. JAP 2004
Theory
Why does instability develop into dendritic pattern ?
Under what conditions does the dendritic instability occur ?
x
y
z
Ba
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
Dendriticjumps
0
ky
Re
Phys. Rev. B 70, 224502 (2004) Phys. Rev. B 73, 014512 (2006) Phys. Rev. B 72, 024541 (2005)
Comparison with experiments
Curves – theory, Symbols – experiment
MD Simulations