Vortex pinning: A probe for nanoscale disorder in iron-based superconductors

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Abstract

The pinning of quantized flux lines, or vortices, in the mixed state is used to quantify the effect of impurities in iron-based superconductors (IBS). Disorder at two length scales is relevant in these materials. Strong flux pinning resulting from nm-scale heterogeneity of the superconducting properties leads to the very disordered vortex ensembles observed in the IBS, and to the pronounced maximum in the critical current density jc at low magnetic fields. Disorder at the atomic scale, most likely induced by the dopant atoms, leads to “weak collective pinning” and a magnetic field-independent contribution jccoll. The latter allows one to estimate quasiparticle scattering rates.

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 s± 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 ξ1.5nm, 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 jc=Fp/B. 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 M(Ha) versus the applied magnetic field Ha, measured on a single crystal of Ba(Fe0.925Co0.075)2As2, with critical temperature Tc=23.5K, 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 Tc=19.5K), at Ha=10G (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 (μ0Ha1T) plateau of constant jc=jccoll is attributed to weak collective pinning [13] by fluctuations of the dopant atom density ndξ3 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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