Vortex Pinning and Sliding
in Superconductors
Charles Simon, laboratoire CRISMAT, CNRS
Laboratoire CRISMAT
A. Pautrat
C. Goupil
Ecole Normale Supérieure Paris
P. Mathieu
LEMA Tours
A. Ruyter
L. Ammor
Laboratoire Léon Brillouin
A. Brûlet
Institut Laue Langevin
C. Dewhurst
I Introduction to vortex pinning and dynamics
II A neutron diffraction study in low Tc materials
III The peak effect in NbSe2
IV The surface pinning in Bi-2212
V Conclusions
Vortex dynamics
E=B. Vff
FL
V
B
I
Vff
V (mV)
3
Nb-Ta
0.3 T
4.2 K
2
0.2 T
I c (B)
1
0.1 T
0
0
V= Rff(B,T) (I-Ic(B,T))
5
10
I (A)
15
20

Typical disordered elastic system with pinning
and sliding with the possibility to vary the
intensity of the pinning by changing the
magnetic field.

But from the beginning: problems (shape of
the IV, …)

Here : Low temperature physics
Neutron scattering, very difficult but quite
simple to interpret (10 years)

Neutron scattering
Niobium
B
Bc2
Normal phase
Bc1
Meissner
T
Nb-Ta
Bi-2212
Cubitt, R. et al.
Nature 365, 407-411 (1993).
B(G)
T. Giamarchi and P. Le Doussal,
Phys. Rev. Lett. 72, 1530 (1994).
and Phys. Rev. B 52, 1242 (1995).
T. Klein et al., Nature 413, (2001) 404
Neutrons with current
Nb-Ta singlecrystal
P. Thorel and al., J. Phys. (Paris) 34, 447 (1973).
A. Pautrat, Phys. Rev. Lett. 90, 087002 (2003).
Neutrons with current
Nb-Ta singlecrystal
How flows the current?
curl B = m0 J
tan (Dw) = by / B = m0Jxe / B
neutrons
Ic/2
Ibulk=0
Ic/2
w
B
Ic/2
Ibulk=(I-Ic)
Ic/2
A. Pautrat, et al. Phys. Rev. Lett. 90, 087002 (2003)
surface pinning (Pb-In)
C
V(I)
1.2
V(mV)
1
0.8
0.6
Ic
0.4
0.2
0
0
2
4
6
8
I (A)
40
Surface treatments
30
IccI(Amp)
(A)
Bc2 (4.2 K)
20
10
0
0
0.1
0.2
0.3
B (T)
0.4
0.5
Why surface pinning?
Normal rough surface
1000 Å
q cr
B
ic (A/m) = e . sin qcr
n
Boundary conditions
MS length
ic
lv l (moe/B)1/2 ao
P. Mathieu et Y. Simon, Europhys Lett 5, 1988
~ 0-100 A/cm
Quantitative prediction
Numerical solution
of Ginzburg equations
by Guilpin and Simon
qcr  0.70  0.10 deg
0.7
0.6
0.5
k = 1Nb film
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
0.8
1
B / BC2
Quantitative analysis of the critical current due to vortex pinning by surface corrugation
A. Pautrat, J. Scola, C. Goupil, Ch. Simon, C. Villard, B. Domengès, Y. Simon,
B. Phys. Rev. B 69, 224504 (2004)
What happens at high current?
B
6
V(mV)
0.12
0A
0.1
0.08
4
3
20 A
0.06
V=Rff (I-Ic)
5
2
0.04
1
0.02
0
0
-0.5
0
0.5
1
0
1.5
5
w (deg)
400
300
200
100
0
1
2
3
4
5
6
0.8
0.6
0.4
0.2
I
0
0
2
250
Dw (deg) V (mV)
Dw (deg) V (mV)
500
0
Rough surface
200
150
100
50
0
0
5
10
15
0.8
0.6
0.4
0.2
I
6
8
10
12
14
I (Amp)
16
20
1
c
4
15
I(A)
Smooth surface
600
10
0
0
5
10
c
15
I (Amp)
20
20
25
30
V (mV)
2000
1500
1000
500
0
0
5
10
15
20
15
20
Inhomogeneous
critical current
Dw (deg)
0.6
0.5
0.4
0.3
I
c min
0.2
0.1
<I >
c
0
0
5
10
Ic2
Ic1 < I < Ic2
Ic1
Ic2
The peak effect in NbSe2
400
60
1.5T
2K 0.4T
V(mV)
V(mV)
40
200
1T
20
ZFC
FC
0.3T
0
0
0
2
4
I(Amps)
6
8
10
0
1
2
3
4
5
6
I(Amps)
Metastable states of a flux-line lattice studied by transport and small-angle neutron
A. Pautrat, J. Scola, Ch. Simon, P. Mathieu, A. Brûlet, C. Goupil, M. J. Higgins,
Phys. Rev. B 71, 064517 (2005)
NbSe2
250
1/2
Jc=sinac e Bc (1-B/Bc2)/2 K
4.2K
NbSe2
200
Jc(A/cm)
150
ac=0.9°
100
ac=9°
50
2
-2
2
Bc2(ac)=Bc2(0)/(cos q+g sin q)
2
tanq=g tana
1/2
g=3
0
0.8
1.0
1.2
1.4
1.6
1.8
B(T)
2.0
2.2
2.4
2.6
Iron doped NbSe2
250
1/2
Jc=sinac e Bc (1-B/Bc2)/2 K
4.2K
NbSe2
200
Jc(A/cm)
150
ac=0.9°
100
ac=9°
50
2
-2
2
Bc2(ac)=Bc2(0)/(cos q+g sin q)
2
tanq=g tana
1/2
g=3
0
0.8
1.0
1.2
1.4
1.6
1.8
B(T)
2.0
2.2
2.4
2.6
T. Klein et al., Nature 413, (2001) 404
Bi-2212 Transport in the peak effect
Bi-2212
Persistence of an ordered flux line lattice above the second peak in Bi2Sr2CaCu2O8+δ
A. Pautrat, Ch. Simon, C. Goupil, P. Mathieu, A. Brûlet, C. D. Dewhurst, and A. I. Rykov
Phys. Rev. B 75, 224512 (2007)
Bi-2212 with columnar defects
Microbridge 50mm
20 mm
BF=1T
5K 0.4T
Surface vortex depinning in an irradiated single crystal microbridge of
Bi2Sr2CaCu2O8+δ : Crossover from individual to collective bulk pinning
A. Ruyter, D. Plessis, Ch. Simon, A. Wahl, and L. Ammor
Phys. Rev. B 77, 212507 (2008)
Do columnar defects product bulk pinning?
No, there is no bulk currents
Do Columnar Defects Produce Bulk Pinning ?
M. V. Indenbom, C. J. van der Beek, M. Konczykowski, and F. Holtzberg
Phys. Rev. Lett. 84, 1792 (2000)
Reversible magnetization
A. Wahl et al.,
Physica C 250 163(1995)
R. J. Drost et al,
PRB 58 R615 (1998)
Conclusions

Very powerful technique
Surface currents
 Peak effect = metastable states

What is the limit of this stability?
 Noise measurements, ac response, Hall
effects…
