Vortex pinning: A probe for nanoscale disorder in iron-based superconductors
Introduction
Quantifying the effects of material disorder is important for the understanding of the superconducting ground state of iron-based superconductors (IBS). On the one hand, the proximity of the superconducting state to anti-ferromagnetism may lead to phase segregation that will be heavily influenced, for example, by macroscopic heterogeneity of the chemical composition. On the other hand, the superconducting ground state in these materials was proposed to have a so-called symmetry [1], [2], in which the superconducting gap not only has a different value on different Fermi surface sheets, but may also change sign from one sheet to another. Then, superconductivity is thought to be exquisitely sensitive to interband scattering [3], [4].
The effect of impurities is usually characterized by the scattering rate such as this can be extracted from resistivity measurements in the normal state, or from the surface resistance in the superconducting state. Another well-known but little exploited probe of microscopic disorder is the pinning of vortex lines in the superconducting mixed state. The radius of their core, of the order of the coherence length , makes vortices ideal probes for impurities. The fact that the vortex density can be easily varied by orders of magnitude simply by adjusting the value of the applied magnetic field Ha makes “vortex matter” sensitive to local variations of material properties on different length scales. The bulk pinning force Fp exerted by the material disorder on the vortex ensemble inhibits the latter's motion for currents smaller than the critical current density . In the following, we analyze vortex distributions and jc-data in IBS, show how these can be used to characterize the type of disorder, and to bracket impurity scattering rates.
Section snippets
Critical currents
Fig. 1 shows hysteresis loops of the irreversible magnetization versus the applied magnetic field Ha, measured on a single crystal of Ba(Fe0.925Co0.075)2As2, with critical temperature , using a commercial Superconducting Quantum Interference Device magnetometer. As in all IBS, the hysteretic magnetic moment features a pronounced low-field maximum, superposed on a nearly field-independent contribution. A double-logarithmic plot of the critical current density as this follows from
Heterogeneity and strong pinning
Fig. 4 shows the vortex ensemble in single crystalline Ba(Fe0.9Co0.1)2As2 (with ), at (1 mT). Vortex positions are revealed using Bitter decoration at 4.2 K, after field-cooling through the superconducting transition [8]. The featureless Fourier transform of the set of vortex positions indicates the absence of long-range positional- or orientational order, and the presence of large fluctuations in the nearest-neighbor distance. The very disordered vortex structure is the combined
Quasiparticle scattering and weak pinning
The intermediate field () plateau of constant is attributed to weak collective pinning [13] by fluctuations of the dopant atom density at length scales much less than the coherence length [15]. This contribution to pinning is found in all charge-doped IBS, as well as in Ru-doped BaFe2As2 and FeSe1−xTex [14], but not in the P-doped materials [15]. The magnitude and temperature dependence of jccoll indicate [15] that dopant atom density fluctuations are effective through
Summary and conclusions
The bulk vortex pinning force Fp and the critical current density jc in single crystalline Ba(Fe1−xCox)2As2 are representative of that found in other iron-based superconductors and can be consistently described in terms of two additive contributions. At low magnetic fields, strong pinning by nm-scale variations of the vortex line energy (of the order of 5%) is the most relevant. Such variations may arise from the inhomogeneity of the gap [17] or from that of the superfluid density [12]. At
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