Critical state controlled by microscopic flux jumps in superconductors
Daniel ShantsevPhysics 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
What determines the maximal current
a superconductor can carry?
R
II
Magnetic field created by current,
should not exceed the critical magnetic field
H = I / 2 R < Hc
H
1. Solsby Rule
Jc(1) = 2Hc / R
2. Depairing current density
R
II
Ginsburg-Landau equations
have a solution only if
J < Jc(2) Hc /
For J>Jc the kinetic energy of Cooper pairs exceeds
the superconducting energy gap
Vortex lattice
Meissner effect
B dA = h/2e = 0 Flux
quantum:
Å
J
B(r)
normal core
current
Lorentz forceF = j
Vortices are driven by Lorentz force andtheir motion creates electric field E ~ dB/dt
Ba
J
pinningforce
Lorentzforce
Vortices get pinned by tiny defects and start moving only if
Lorentz force > Pinning force
U(r)
3. Depinning current density
J < Jc(3) = U / 0
Superconductor remains in the non-resistive state only if
Lorentz force < Pinning force, i.e. if
Ideal pinning center is
a non-SC column of radius ~ so that U ~ Hc
22 and
similar to the depairing Jc
Jc(3) ~ Hc /
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
Thermal instability criterion
~ Swartz &Bean, JAP 1968
H
0 x
j
QM > QT - instability starts
QT = C(T) T
QM = Jc(T) JcdJc/dT
H > Hfj = (2C Jc [dJc/dT]-1)1/2
Jc(4) = (2C Jc
(3) [d Jc(3) /dT]-1)1/2/2w
Hfj Hfjslab (d/w)1/2
x
Hj
2w
d<<w
D. S. et al. PRB 2005
List of current-limiting mechanisms
1. Solsby, Jc ~ Hc/R2. Depairing current Jc ~ Hc / 3. Depinning current, Jc (U)4. Thermal instability current, Jc(C,..)
Jc(3) < Jc
(4) < Jc(1) < Jc
(2)
We need to know which Jc is the most important i.e. the smallest!
Achieved
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)
Brull et al, Annalen der Physik 1992, v.1, p.243Gaevski et al, APL 1997
Global flux jumps
Muller & Andrikidis, PRB-94
M(H) loop
M ~ M Critical state is destroyed
Dendritic flux jumps
Zhao et al, PRB 2002
M ~ 0.01 M Critical state is destroyed locally
Europhys. Lett. 59, 599-605 (2002)
Magneto-optical imaging
MgB2 film
Microscopic flux jumps
5 mm
MgB2 film
100 m
MgB2 filmfabricated byS.I. Lee (Pohang, Korea)
Magneto-optical movie showsthat flux penetration proceeds
via small jumps
Analyzing difference images
7.15 mT
7.40 mT
linearrampof Ba
15 MO images
T=3.6K
= MO image (7.165mT) — MO image (7.150mT)
local increase of flux density -
flux jump
23000
11000
2500
-100 0 100 2000
10
20
30
40
50 before jump after jump
Ba=5.6mTFlu
x de
nsity
B (
mT
)
distance (m)
Ba=11.6mT
edge
x
edge
31,0000
7,5000
Too small, M ~ 10-5 M : invisible in M(H) Critical state is not destroyed B-distribution looks as usual
The problem with microscopic jumps
Flux profiles before and after a flux jump have similar shapes
From the standard measurementsone can not tell what limits Jc:
vortex pinning OR thermal instabilities
Jc(3) OR Jc
(4) ?
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
-1.5 -1.0 -0.5 0.00.0
0.2
0.4
0.6
0.8
1.0
1.2
Ba = 2Bc
Ba = Bc
before jump after jump
B / 0
j cd
x / w
-100 0 100 2000
10
20
30
40
50 before jump after jump
Ba=5.6mTFlu
x d
en
sity
B (
mT
)
distance (m)
Ba=11.6mT
edge
Jump size (0)
Nu
mb
er
of
jum
ps
power-law
peak(thermalmechanism)
Altshuler et al. PRB 2005
300 m70 m
Two Jc’s in one sample
Jcleft 2 Jc
right
Jc(3) Jc
(4)
Dendritic instability can be suppressed by a contact with normal metal
Baziljevich et al 2002
Au suppresses jumps,Jc is determined by pinning
300 m70 m
Two Jc’s in one sample
Jc(3) Jc
(4)
3 m
m
9 mm
w
Au
MgB2
Jc is determined by jumps
H
J
A graphical way to determine Jc’s: d-lines
3 mm
Au
MgB2
Jc1
Jc2?
αα
ααβ
11
1
cjd
22
1
cjd
1cos22cos2coscos 2
1
2
2
1 c
c
j
j
d
d
1
2
1
2
12
1arccos
12
1arccos
c
c
c
c
j
j
j
j
α ≈ π/3
! jc1 ≈ 2jc2 !
Thermal avalanches can be truly microscopic as 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/
Conclusions
6.8 7.2 7.6 8.0 8.4
0
10
20
30
loc
al
B (
mT
)
Ba (mT)
local flux density calculated from local intensity of MO image;each point on the curve corresponds to one MO image
5x5 m2
linear ramp 6 T/s
Evolution of local flux density
7mT7.4mT
7.9mT
Local B grows bysmall and repeated steps
Jc is determined by
stability with respect to thermal avalanches
But we need to prove that the observed microscopic avalanches are indeed of thermal origin
Jc depends on
thermal coupling to environment, specific heat, sample dimensions
Adiabatic :All energy released by flux motion is absorbed
Flux that has passed through “x” during avalanche
Biot-Savart for thin film
Adiabatic critical state for a thin strip
Critical state
In the spirit of Swartz &Bean in 1968
We fit• Bfj ~ 2 mT• Tth ~ 13 K• (Ba) dependence
using only one parameter:
4 8 12 16 20
102
103
104
105
106
Ba (mT)
Flux
jum
p si
ze (
0) T=0.1Tc
0.3Tc
Thermal originof avalanches
Flux jump size
Ba = 13.6 mT
the flux pattern almost repeats itself
Irreproducibility
B(r)
B(r) is irreproducible!
The final pattern is the same but
the sequences of avalanches are different
MOI(8.7mT) - MOI(8.5mT)
B(r)
T=3.6K
polarizer P
A
mirrorMO indicator
image
largesmall
Faraday rotation
small
SN
light source
Linearlypolarized light
Faraday-active crystal
Magnetic fieldH
(H)F
Magneto-optical Imaging
Square YBaCuO film
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