14.40 o8 s wimbush

A new understanding of flux pinning in defect-engineered superconductors

Stuart Wimbush, Nick Long

Superconductivity & Energy Group

NZIP Conference, Wellington, New Zealand 17–19 October 2011

Image: ORNL

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Introduction — Flux pinning in superconductors

• Flux pinning is determined by the microstructure of the sample.

• It manifests itself in the measured critical current density, Jc.

H

FLorentz = J × B

Jc× B = Fpinning

{B = Φ0/A}

F

H = nΦ0

5×1014 Φ0/m2 = 1T

500 in every µm2 { }

J

Sources of pinning:

• Flux line (vortex-vortex) interactions.

• Non-superconducting regions of the sample (defects).

• Exotic sources (magnetic interactions).

Φ0

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-120 -90 -60 -30 0 30 60 90 1200.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

H||c H||abH||ab

Cri

tica

l cu

rre

nt d

en

sity J

c (

MA

/cm

2)

Applied field angle (°)

0.1 T

Introduction — Critical current anisotropy

•

L. Civale et al. Appl. Phys. Lett. 84 (2004) 2121.

-120 -90 -60 -30 0 30 60 90 1200.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

H||c H||abH||ab

Cri

tica

l cu

rre

nt d

en

sity J

c (

MA

/cm

2)

Applied field angle (°)

0.1 T

Nb isotropic γ = 1

H

J

θ=0°

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• We consider mathematically the statistical population of pinned

vortex paths through the sample.

SUBSTRATE

The vortex path model

Intrinsic pinning due to planar structure

Surface pinning (open and substrate interface) J

F

H θ

θ

Jc

N. Long Supercond. Sci. Technol. 21 (2008) 025007.

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• We consider mathematically the statistical population of pinned

vortex paths through the sample.

• A population of defects providing pinning in the direction

orthogonal to the primary pinning defects broadens the Jc peak.

SUBSTRATE

The vortex path model

J

F

θ

Jc

Random pinning (nanoparticles, point defects)

F

N. Long Supercond. Sci. Technol. 21 (2008) 025007.

Intrinsic pinning due to planar structure

Surface pinning (open and substrate interface)

H θ

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• We consider mathematically the statistical population of pinned

vortex paths through the sample.

• We sum the multiplicity of possible vortex paths through the

sample for a given field direction.

SUBSTRATE

The vortex path model

J

F

H θ

c-axis pinning (grain boundaries, twin plane intersections, threading dislocations)

ab-plane pinning (platelets)

N. Long Supercond. Sci. Technol. 21 (2008) 025007.

Random pinning (nanoparticles, point defects)

Intrinsic pinning due to planar structure

Surface pinning (open and substrate interface)

θ

Jc

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•

The vortex path model — Summary

N. Long Supercond. Sci. Technol. 21 (2008) 025007.

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• Shape of the angular peak functions:

• The vortex path model is a maximum entropy formulation:

The vortex path model — Features

E. T. Jaynes, Phys. Rev. 106 (1957) 620; 108 (1957) 171.

0 1 2 34

5

6

7

En

tro

py (

na

tura

l u

nits)

Lorentzian

Gaussian

Scale factor

Uniform Uniform No preferred direction

Lorentzian Preferred direction

Gaussian Preferred direction and

defined angular spread

Increasing

entropy

0 30 60 90 120 150 180

(°)0 30 60 90 120 150 180

(°)

Angular Lorentzian Angular Gaussian

Γ = 0.2

Γ = 0.3

Γ = 0.5

Γ = 1.0

Γ = 1 uniform distribution

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Pulsed laser deposited YBCO thin films

• Three components:

– Narrow ab-peak: Intrinsic pinning broadened by short-scale

interactions with surface roughness.

– Broad ab-peak: Intrinsic pinning broadened by large-scale

interactions with through-thickness defects (grain boundaries,

twin plane intersections, threading dislocations).

– Uniform component: Indication of the existence of strong

c-axis and ab-plane pinning able to combine to effectively

pin at all angles.

The broad ab-peak is

commonly mistaken as

a signature of mass

anisotropy.

The absence of a c-axis

peak is often mistakenly

taken as evidence of a

lack of c-axis pinning.

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YBCO thin films with Ba2YNbO6 additions

• Ba2YNbO6 forms nanorods (15 nm diameter, 100 nm long, 40 nm

spacing) oriented along the c-direction in YBCO.

• Additionally, many randomly-positioned nanoparticle inclusions are

seen.

c-axis

G. Ercolano et al. Supercond. Sci. Technol. 23 (2010) 022003.

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YBCO thin films with Ba2YNbO6 additions

• Here, the strong c-axis pinning initially dominates until the field is

increased beyond the matching field of the nanorods (~1.5 T). Then

the broad ab-plane pinning peak reappears.

• We predict that increasing the field still further will cause the broad

ab-peak to dominate further while the c-axis peak drops out

completely, as for the pure YBCO films.

G. Ercolano et al. Supercond. Sci. Technol. 24 (2011) 095012.

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YBCO films with Gd3TaO7 + Ba2YNbO6 additions

• (Unexpectedly) forms c-axis Ba2R(Nb,Ta)O6 segmented nanorods (7

nm diameter, 30 nm long, 30 nm spacing), together with ab-plane

R2O3 platelets (25-30 nm long), and R248 nanoparticles.

• Unsurprisingly, this dense defect structure results in a complex

behaviour. G. Ercolano et al. Supercond. Sci. Technol. 24 (2011) 095012.

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YBCO films with Gd3TaO7 + Ba2YNbO6 additions

• Intensely dominating c-axis peak drops out by 3 T matching field.

• Other components at low field are all related to this strongly dominant

pinning interacting with the other sources.

• Beyond 3 T, the interactions with ab-pinning sources become

comparable and then dominate to higher fields.

G. Ercolano et al. Supercond. Sci. Technol. 24 (2011) 095012.

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Conclusion

• We have identified multiple deficiencies in the mass anisotropy

approach currently taken to analyse angular Jc data of superconductors:

– At best, it describes the data in terms of generally meaningless

parameters, unrelated to any physical property.

– It cannot explain the data because it offers no link between the

observed Jc and the underlying microstructure responsible for it.

– All features of the data resulting from this approach are also

present in isotropic superconductors, where it does not apply.

• We have proposed an alternative statistical model of vortex paths in the

superconductor that directly links the angular Jc data to the underlying

microstructure responsible for pinning.

• We have shown that the model robustly describes the behaviour of many

different classes of sample, succinctly explaining features of the data for

which an explanation is otherwise lacking.

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YBCO thin films with Gd3TaO7 additions

• Gd2TaO7 forms highly linear, through-thickness nanorods (5 nm

diameter, 10-20 nm spacing).

• If deposited too quickly, the rods do not have time to form and

nanoparticles are formed instead.

S. A. Harrington et al. Supercond. Sci. Technol. 22 (2009) 022001.

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YBCO thin films with Gd3TaO7 additions

• High rate deposition doesn’t allow nanorods to form, but they can

propagate through thin (single) layers.

S. A. Harrington et al. Nanotechnology 21 (2010) 095604.