This document summarizes research on flux pinning in defect-engineered superconductors. It discusses how flux pinning is determined by a material's microstructure and how it relates to critical current density. The vortex path model is introduced, which considers the statistical population of pinned vortex paths through a sample. Pulsed laser deposited YBCO thin films are examined, showing a broad in-plane peak that results from large-scale through-thickness defects, rather than mass anisotropy. Films with Ba2YNbO6 additions are also summarized, demonstrating enhanced c-axis pinning from nanorods in the material.

1. A new understanding of flux pinning
in defect-engineered superconductors
Stuart Wimbush, Nick Long
Superconductivity & Energy Group
Image: ORNL
NZIP Conference, Wellington, New Zealand 17–19 October 2011

2. 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 Φ0
H = nΦ0
5×1014 Φ0/m2 = 1T
{ 500 in every µm2 }
J F FLorentz = J × B
Jc× B = Fpinning
{B = Φ0/A}
Sources of pinning:
• Flux line (vortex-vortex) interactions.
• Non-superconducting regions of the sample (defects).
• Exotic sources (magnetic interactions).
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3. Introduction — Critical current anisotropy
•
1.0
H||ab H||c H||ab H
Critical current density Jc (MA/cm ) 0.9 θ=0°
2
0.8
J
0.7
0.6
0.5
0.4 0.1 T
0.3
0.2
0.1
Nb isotropic γ=1
0.0
-120 -90 -60 -30 0 30 60 90 120
Applied field angle  (°)
L. Civale et al. Appl. Phys. Lett. 84 (2004) 2121.
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4. The vortex path model
• We consider mathematically the statistical population of pinned
vortex paths through the sample.
Surface pinning
(open and substrate interface) J
θ H
Intrinsic pinning
due to planar structure
F
SUBSTRATE Jc
θ
N. Long Supercond. Sci. Technol. 21 (2008) 025007.
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5. The vortex path model
• We consider mathematically the statistical population of pinned
vortex paths through the sample.
Surface pinning
(open and substrate interface) J
θ H F
Intrinsic pinning
due to planar structure
F
Random pinning
(nanoparticles, point defects)
SUBSTRATE Jc
• A population of defects providing pinning in the direction
orthogonal to the primary pinning defects broadens the Jc peak. θ
N. Long Supercond. Sci. Technol. 21 (2008) 025007.
www.irl.cri.nz

6. The vortex path model
• We consider mathematically the statistical population of pinned
vortex paths through the sample.
Surface pinning
(open and substrate interface) J
Intrinsic pinning
due to planar structure
F
Random pinning
(nanoparticles, point defects)
ab-plane pinning c-axis pinning
(platelets) (grain boundaries, twin plane intersections, threading dislocations)
SUBSTRATE Jc
θ
H
• We sum the multiplicity of possible vortex paths through the
sample for a given field direction. θ
N. Long Supercond. Sci. Technol. 21 (2008) 025007.
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7. The vortex path model — Summary
•
N. Long Supercond. Sci. Technol. 21 (2008) 025007.
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8. The vortex path model — Features
• Shape of the angular peak functions:
Γ = 0.2
Γ = 0.3
Γ = 0.5
Angular Lorentzian Γ = 1.0 Angular Gaussian
Γ = 1 uniform distribution
0 30 60 90 120 150 180 0 30 60 90 120 150 180
 (°)  (°)
• The vortex path model is a maximum entropy formulation:
Entropy (natural units)
7 Uniform Uniform No preferred direction
Increasing
Lorentzian Preferred direction
entropy
6 Gaussian Preferred direction and
defined angular spread
5
Lorentzian
Gaussian
4
0 1 2 3
Scale factor 
E. T. Jaynes, Phys. Rev. 106 (1957) 620; 108 (1957) 171.
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9. Pulsed laser deposited YBCO thin films
The broad ab-peak is The absence of a c-axis
commonly mistaken as peak is often mistakenly
a signature of mass taken as evidence of a
anisotropy. lack of c-axis pinning.
• 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.
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10. YBCO thin films with Ba2YNbO6 additions
c-axis
• 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.
G. Ercolano et al. Supercond. Sci. Technol. 23 (2010) 022003.
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11. 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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12. 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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13. 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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14. 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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15. 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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16. 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.
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