Research 6: S Wimbush

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).
www.irl.cri.nz

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.
www.irl.cri.nz

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.
www.irl.cri.nz

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.
www.irl.cri.nz

7. The vortex path model — Summary
•
N. Long Supercond. Sci. Technol. 21 (2008) 025007.
www.irl.cri.nz

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.
www.irl.cri.nz

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.
www.irl.cri.nz

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.
www.irl.cri.nz

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.
www.irl.cri.nz

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.
www.irl.cri.nz

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.
www.irl.cri.nz

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.
www.irl.cri.nz

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.
www.irl.cri.nz

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.
www.irl.cri.nz