Vortex Pinning and Sliding in Superconductors

Charles Simon, laboratoire CRISMAT, CNRS

Laboratoire CRISMATA. PautratC. Goupil

Ecole Normale Supérieure ParisP. Mathieu

LEMA ToursA. RuyterL. Ammor

Laboratoire Léon BrillouinA. Brûlet

Institut Laue LangevinC. 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-2212V Conclusions

Vortex dynamics

V

BFLI Vff

0 5 10 15 200

1

2

3

I (A)

V (

mV

)0.1 T

0.2 T

0.3 T

I c (B)

Nb-Ta

4.2 K

V= Rff(B,T) (I-Ic(B,T))

E=B. Vff

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

B

T

Bc2

Bc1Meissner

Normal phase

Niobium

Nb-Ta

Bi-2212

B(G)

Cubitt, R. et al. Nature 365, 407-411 (1993).

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?

Ic/2Ibulk=0

Ic/2 Ic/2

Ic/2Ibulk=(I-Ic)

Bneutrons

curl B = J

tan by / B = Jxe / B

A. Pautrat, et al. Phys. Rev. Lett. 90, 087002 (2003)

surface pinning (Pb-In)

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8

V(I)

C

V(m

V)

I (A)

Ic

0 0.1 0.2 0.3 0.4 0.50

10

20

30

40

B (T)

I c (A

)

Bc2 (4.2 K)

Ic (

Am

p)

Surface treatments

Why surface pinning?

Normal rough surface

ic (A/m) = . sin cr

B

1000 Å

MS length

P. Mathieu et Y. Simon, Europhys Lett 5, 1988

~ 0-100 A/cm

ic v (o/B)1/2 ao

Boundary conditionsncr

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

/ H

C2

/ BC2

= 1

Numerical solution of Ginzburg equationsby Guilpin and Simon

Nb film

deg10.070.0 cr

Quantitative prediction

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?

0

1

2

3

4

5

6

0 5 10 15 20 25 30

B

V=Rff (I-Ic)V(m

V)

I(A)

0

0.2

0.4

0.6

0.8

0 2 4 6 8 10 12 14 16

Ic

(

deg

)

I (Amp)

0

100

200

300

400

500

600

0 1 2 3 4 5 6

V (V

)

0

50

100

150

200

250

0 5 10 15 20

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

Ic

Smooth surface Rough surface

(d

eg)

I (Amp)

V (V

)

0

0.02

0.04

0.06

0.08

0.1

0.12

-0.5 0 0.5 1 1.5

(deg)

0 A

20 A

Inhomogeneous critical current

0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15 20

Ic min

< Ic >

0

500

1000

1500

2000

0 5 10 15 20

(

deg

)V

(V

)

Ic1 < I < Ic2

Ic1Ic2 Ic2

The peak effect in NbSe2

0 1 2 3 4 5 6

0

20

40

60

FCZFC

2K 0.4TV

(V)

I(Amps)

0 2 4 6 8 100

200

400

0.3T

1T

1.5T

V(V

)

I(Amps)

Metastable states of a flux-line lattice studied by transport and small-angle neutronA. Pautrat, J. Scola, Ch. Simon, P. Mathieu, A. Brûlet, C. Goupil, M. J. Higgins,

Phys. Rev. B 71, 064517 (2005)

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.60

50

100

150

200

250

Bc2

(c)=B

c2(0)/(cos2+-2sin2)1/2

tan=2tan =3

Jc=sinc B

c (1-B/B

c2)/21/2

c=9°

c=0.9°

4.2KNbSe

2

Jc(A

/cm

)

B(T)

NbSe2

Iron doped NbSe2

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.60

50

100

150

200

250

Bc2

(c)=B

c2(0)/(cos2+-2sin2)1/2

tan=2tan =3

Jc=sinc B

c (1-B/B

c2)/21/2

c=9°

c=0.9°

4.2KNbSe

2

Jc(A

/cm

)

B(T)

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

5K 0.4T

B=1T

Microbridge 50m20 m

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)

Very powerful technique

Surface currents Peak effect = metastable states

What is the limit of this stability? Noise measurements, ac response, Hall

effects…

Conclusions