Introduction Critical state models Pinning regimes Kinds of pinning sites HTS Results on YBCO Conclusions. Flux pinning.

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1 Department of Physics and Astronomy

2 Contents Introduction Critical state models Pinning regimes Kinds of pinning sites HTS Results on YBCO

3 Type II superconductors and vortices Type I ξ < λ S/N surface energy is negative SC maximizes the S/N surface area Vortices with single flux quantum Type II Φ 0 = h 2e = Wb Bleaney& Bleaney, Electr. and Magn.

4 Abrikosov lattice Mixed state B c1 < B < B c2 The vortices repel each other A triangular lattice forms The vortex lattice has the usual defects and interacts with the crystal lattice DOE Courtesy of T.H. Johansen DOE = Basic research needs for superconductivity, DOE

5 Lorentz force Current causes a Lorentz force f L = J φ 0 Vortices move sideways, which produces a voltage E = v L B = v L nφ 0 The movement is balanced by a viscous force ηv L = f L We get dissipative flux flow resistivity DOE ρ f = E J = Bφ 0 η

6 Reversible superconductors Magnetization follows the same curve in increasing and decreasing fields Vortices start entering at B c1 At B c2 the normal vortex cores fill up the whole sample superconductivity is destroyed With little pinning the magnetization curve lags behind the theoretical curve

7 Irreversible superconductors Vortices enter the sample from edges and jump to the potential wells created by the pinning sites Magnetization is the difference between the external field and the vortex filled area of the sample (marked with green)

8 Critical state models The current flowing in the sample is either the critical current J c or zero J c is proportional to the magnetic flux gradient in the sample as J c = B First version presented by Bean in Rev. Mod. Phys The main difference between the models is magnetic field dependence of J c. Courtesy of T.H. Johansen

9 Bean model J c is assumed to be independent of the magnetic field This leads to constant flux gradient inside the sample Rev. Mod. Phys. 36,31 (1964) Widely used although J c clearly depends on B for most samples at high fields J c M PRB 61, 9699 (2000)

10 Other critical state models Anderson-Kim model J c (B) = J c(0) 1 + B/B 0 Power-law model J c (B) = J c (0) 1 + (B/B 0 ) k Exponential model J c (B) = J c (0) exp( B/B 0 ) PRB 61, 9699 (2000)

11 Flux creep At finite temperature vortices can jump out the pinning sites with velocity v = v c exp( U(j)/kT ) At T T c rigid vortex glass phase, ρ = 0 At higher T, flux creep, ρ exp( U/kT ) At even higher T, thermally actived flux flow (TAFF), ρ ρ n Blatter, I2CAM Cargèse Summer School The vortex state, Kluwer

12 Pinning force Lorenz force caused by the current is counteracted by the pinning force F p = J B The total pinning force depends on the amount of pinning sites, n p and the pinning force of individual site f p F p = n p f p Blatter, I2CAM Cargèse Summer School

13 Pinning regimes Weak vs strong pinning Collective pinning: many weak pins a 0 = Φ 0 /B = distance between the vortices f Lab cross over from weak to strong pinning PRL 92, (2004)

14 Strong pinning J c = J c (0) when B < B φ and r p > 2ξ B φ is the matching field, 1 vortex/pinning site or field where vortex-vortex interaction is negligable J c (r p /ξ) 2 when r p < 2ξ At high temperature J c is decreased by thermal fluctuations exp( T /T dl ) At B > B φ, J c B α Rev.Mod.Phys (1994) SUST (2005)

15 Weak pinning Many pinning sites for a single vortex Pinning comes from the fluctuations of the potential J c J c (0)(ξ/L c ) 2 J c (0) Flux creep is very important U = kt ln(dm/dt) + C Maley plot Phys. Rev. B 66, (2002).

16 Natural pinning sites All superconductors contain some pinning sites Crystallographic defects Vacancies, interstitials Point Dislocations Columnar Twin boundaries Plane Growth defects Stacking faults Plane Antiphase boundaries Columnar Misoriented grains 3D Point Secondary phases Precipitates 3D Point Atomic substitutions Point Nanorods Columnar

17 Natural pinning sites Nat.Mat. 6,632 (2007)

18 Isotropic pinning sites Vacancies, interstitials etc are generally weak pinning sites Atomic substitutions can be either weak or strong Precipitates of non-superconducting phase are strong Misaligned grains often produce weak links Point pinning sites do not change the angular dependency of J c Nat.Mat. 6, 367 (2007)

19 Columnar pinning sites Columnar sites are very strong in the direction of the column Nanorods of secondary phase are stronger than dislocations Angular dependency of J c has a maximum in the direction of columns DOE

20 Planar pinning sites Twin planes act as a natural pinning site Cu-O planes also act as pinning sites in HTS peak at a/b-plane Planar defects channel vortices along planes and prevent movement across planes Angular dependency of J c has a maximum in the plane direction PRB 48, 6612 (1993) Nat.Mat. 6,632 (2007)

21 Artificial pinning sites Pinning sites, which are added artificially Heavy ion irradiation Columnar Substrate decoration Columnar Antidots (holes) Columnar Magnetic dots Columnar Used mainly for studying vortex physics, not in applications

22 Heavy ion irradiation PRL 76, 2563 (1996)

23 Substrate decoration PRB 74, (2006)

24 Antidots J.Elec.Micr. 51, S3 (2002) PRB 54, 7385 (1996)

25 Magnetic dots ZFC FC APL 91, (2007)

26 Irreversibility line J c (B > B irr, T > T irr ) = 0 For HTS B irr B c2 Large unusable area in the phase diagram For YBCO B irr (77K) = 8 T, and B c2 (77K) 30 T Irreversibility line is determined by pinning room for improvement Nature 414, 368 (2001)

27 Anisotropy All HTS are highly anisotropic Electronic mass anisotropy varies from 5-7 of YBCO to of BSCCO It arises from the crystal structure And leads to anisotropy of all parameters, including flux pinning Cu-O-planes act as natural pinning sites JAP 103, (2008)

28 Pancake vortices In the most anisotropic HTS the vortices break between the Cu-O-layers forming pancake vortices The pancake vortices move much more easily than normal vortices This is one of the main reasons why BSCCO performs poorly in magnetic field Nat.Mat. 4, 658 (2005) Nature 414, 728 (2001)

29 Twin planes and dislocations All YBCO films contain twin planes and dislocations, amount depends on preparation conditions Single crystals have much less of both J c of thin films is 10 3 times higher than J c of single crystals Irregularity of twin lattice and increasing the number of dislocations enhances pinning IEEE T Appl Super 17, 3608 (2007) Z.Phys B 72, 305 (1988)

30 BZO-doping BaZrO 3 addition in physical deposition methods to YBCO forms nanorods, which act as columnar pinning sites The rods are 5-10 nm in diameter and penetrate the whole film With chemical deposition methods BZO particles with diameter of nm SUST 21, (2008) IEEE T Appl Super 17, 3608 (2007). Nat.Mat. 6, 367 (2007)

31 Angular dependency of J c Nanorods lead to a very pronounced c-axis peak Splay in nanorods widens the c-axis peak Nanoparticles lead to more isotropic J c (θ), but no c-axis peak Isotropic J c (θ) is desired for applications JAP, in press (2008) Nat.Mat. 6, 367 (2007)

32 Modelling the angular dependency of J c Ginzburg-Landau equations YBCO thin films with dislocations, straight nanorods and splayed nanorods Dislocations enhance J c in c-direction, but no extended peak Nanorods produce a peak in c-direction Splayed nanorods produce a wide high plateau in c-direction These should be produced

33 Conclusions determines the applicability of superconductors Most effective pinning sites are columnar defects along the magnetic field Disorder usually lowers T c optimization One of the DOE grand challenges is pinscape engineering, modifying the pinning landscape to best suit the application in question