Elastic Constants of the Fluxoid Lattice Near the Upper Critical Field

Labusch, R.

doi:10.1002/pssb.19690320145

Cited by 194 publications

(87 citation statements)

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confidence: 99%

“…Here, our goal is to derive an expression for δF pin starting from a microscopic perspective. This can be done within the framework of strong pinning theory which goes back to work of Labusch [10] and Larkin and Ovchinnikov arXiv:1508.00757v1 [cond-mat.supr-con] 4 Aug 2015 [11], with recent further studies on the critical currents in strong and weak pinning scenaria [12], numerical simulations of vortex motion [13], and the current-voltage characteristic [14]; note that the qualitative framework of weak collective pinning theory [11] is not sufficient to develop a quantitative understanding of λ C .…”

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“…The maximal slope in f p (realized at x m ) defines the regime of strong pinning [10]: for κ ≡ [f p (x m )]/C > 1, the condition (7) generates two stable solutions for the displacement field u(x), a pinned and an unpinned branch, see Fig. 1.…”

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“…1. The condition κ = 1 is the famous Labusch criterion [10] separating strong pins with κ > 1 from weak pins when κ < 1. Assuming a homogeneous random distribution of defects with small density n p , the macroscopic pinning force density F pin derives from averaging the pinning forces f p [x + u o (x)] over all positions |x| < a 0 /2 within a lattice period, with u o denoting the branch that is occupied with vortices.…”

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“…where ∆e pin is the sum of jumps at −x − and x + in e pin (x) where the occupation changes between unoccupied and occupied branches [10,11], see Fig. 1.…”

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Campbell Response in Type-II Superconductors under Strong Pinning Conditions

et al. 2015

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Measuring the ac magnetic response of a type II superconductor provides valuable information on the pinning landscape (pinscape) of the material. We use strong pinning theory to derive a microscopic expression for the Campbell length λC, the penetration depth of the ac signal. We show that λC is determined by the jump in the pinning force, in contrast to the critical current jc which involves the jump in pinning energy. We demonstrate that the Campbell lengths generically differ for zero-field-cooled and field-cooled samples and predict that hysteretic behavior can appear in the latter situation. We compare our findings with new experimental data and show the potential of this technique in providing information on the material's pinscape. 74.25.Op, 74.25.Wx, 74.25.Ha Technologically useful superconductors are of second type and acquire their desired transport and magnetic properties through vortex pinning, i.e., vortices [1] get immobilized by material defects. The characterization of the pinning landscape (or pinscape) is of great importance but presents quite a formidable task. Measurements of dc transport properties, either dynamically through the current-voltage characteristic [2] or statically through magnetization [3], are standard techniques used to gain information on the pinscape. Similarly, the ac magnetic response of superconducting samples [4] provides insight into the shape of pinning potentials. Unfortunately, the relation between the measured penetration depth of the ac signal, the so-called Campbell length λ C , and the parameters of the pinscape is only known on a phenomenological level. In this letter, we present a microscopic derivation of the Campbell length within the framework of strong pinning theory, thereby providing access to microscopic parameters of pinning defects and substantially enlarging the scope of applications of this measurement technique.Probing superconductors via their ac magnetic response goes back to the 60-ies and culminated in Campbell's work [4] which provided the first consistent explanation of the penetration phenomenon (see Refs.[5] for further developments): for small ac magnetic-field amplitudes h ac and frequencies ω, vortices oscillate reversibly within their pinning potentials (described as harmonic wells α x 2 /2), with the external signal h ac penetrating the sample on a distance λ C ∝ B/ √ α of order micrometers. Later work by Lowell [6] and Campbell [7] provided a more quantitative but still phenomenological understanding within a model pinscape. Here, we make use of the strong pinning scenario allowing us to perform a quantitative and microscopic analysis of the ac magnetic response. In particular, we find the dependence of the Campbell penetration depth λ C on the vortex state, e.g., the critical (Bean [3]) state with a linear vortex density gradient supporting the critical current density j c or a field-cooled state with a constant induction B, and predict the occurrence of new hysteretic effects. The comparison with recent experiments [8] confirms...

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confidence: 99%

“…where ∆e pin is the sum of jumps at −x − and x + in e pin (x) where the occupation changes between unoccupied and occupied branches [10,11], see Fig. 1.…”

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Campbell Response in Type-II Superconductors under Strong Pinning Conditions

et al. 2015

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Mechanical Spectroscopy

Batist

2006

Materials Science and Technology

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Magnetic irreversibility and microstructure of a Nb–40 at% Ti alloy

Witcomb

Narlikar

1972

Phys. Stat. Sol. (a)

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The effect of various heat-treatments on magnetization of a Nb-40 atyo Ti alloy has been investigated. Microstructural detail was observed by transmission electron microscopy.The results indicate that the main flux pinning mechanism in this material is due to a rearrangement of dislocations after heat-treatment rather than to a interstitial ordering found in alloys having higher Ti content. This conclusion has been supported by X-ray diffraction and detailed size effect measurements. Magnetic hysteresis was a maximum when a nonuniform dislocation distribution was present; dislocations being in the form of tangles. L'effet de diffkrents traitments par la chaleur sur le magnktisation d'un alliage Nb--40 atyo Ti a 6t6 etudik. La microstructure a 6tb examine6 par la microscopie 6lectroniqne. Les r6sultats donnbs montrent que le mecanisme bloquant le flux magdtique principal dans ce materiel est dii A une rkorganisation des composants dpar6s par le traitement it la chaleur, plut8t que a une ordonnance interstitielle se trouve dans les alliages A plus haute teneur en Ti. Cette conclusion a 6th confirmbe par une diffraction faite aux rayons-X et par des mesures d6taille6s des modifications de dimension. L'hysteresis magn6tiqne 6tait & son maximum au moment oh une distribution non uniform6 de dislocation etait prbsente, ces dislocations formant des noeuds. l) Present address : Electron Microscope Unit, University of the Witwatersrand, Johan-2, Present address :

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Elastic Constants of the Fluxoid Lattice Near the Upper Critical Field

Cited by 194 publications

References 4 publications

Campbell Response in Type-II Superconductors under Strong Pinning Conditions

Campbell Response in Type-II Superconductors under Strong Pinning Conditions

Mechanical Spectroscopy

Magnetic irreversibility and microstructure of a Nb–40 at% Ti alloy

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