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Register a new userProbing the pinning landscape in type-II superconductors via Campbell penetration depth
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Type-II superconductors owe their magnetic and transport properties to vortex pinning, the immobilization of flux quanta through material inhomogeneities or defects. Characterizing the potential energy landscape for vortices, the pinning landscape (or short, pinscape), is of great technological importance. Besides measurement of the critical current density $j_c$ and of creep rates $S$, the $ac$ magnetic response provides valuable information on the pinscape which is different from that obtained through $j_c$ or $S$, with the Campbell penetration depth $lambda_{rm scriptscriptstyle C}$ defining a characteristic quantity well accessible in an experiment. Here, we derive a microscopic expression for the Campbell penetration depth $lambda_{rm scriptscriptstyle C}$ using strong pinning theory. Our results explain the dependence of $lambda_{rm scriptscriptstyle C}$ on the state preparation of the vortex system and the appearance of hysteretic response. Analyzing different pinning models, metallic or insulating inclusions as well as $delta T_c$- and $delta ell$-pinning, we discuss the behavior of the Campbell length for different vortex state preparations within the phenomenological $H$-$T$ phase diagram and compare our results with recent experiments.
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Magnetic penetration depth, $lambda_{m}$, was measured as a function of temperature and magnetic field in single crystals of low carrier density superconductor YPtBi by using a tunnel-diode oscillator technique. Measurements in zero DC magnetic field yield London penetration depth, $lambda_{L}left(Tright)$, but in the applied field the signal includes the Campbell penetration depth, $lambda_{C}left(Tright)$, which is the characteristic length of the attenuation of small excitation field, $H_{ac}$, into the Abrikosov vortex lattice due to its elasticity. Whereas the magnetic field dependent $lambda_C$ exhibit $lambda_{C}sim B^{p}$ with $p=1/2$ in most of the conventional and unconventional superconductors, we found that $papprox 0.23ll1/2$ in YPtBi due to rapid suppression of the pinning strength. From the measured $lambda_{C}(T,H)$, the critical current density is $j_{c}approx40,mathrm{A}/mathrm{cm^{2}}$ at 75 mK. This is orders of magnitude lower than that of conventional superconductors of comparable $T_{c}$. Since the pinning centers (lattice defects) and vortex structure are not expected to be much different in YPtBi, this observation is direct evidence of the low density of the Cooper pairs because $j_{c}propto n_s$.
The $AC$ magnetic penetration depth $lambda (T,H,j)$ was measured in presence of a macroscopic $DC$ (Bean) supercurrent, $j$. In single crystal BSCCO below approximately 28 K, $lambda (T,H,j)$ exhibits thermal hysteresis. The irreversibility arises from a shift of the vortex position within its pinning well as $j$ changes. It is demonstrated that below a new irreversibility temperature, the nonequilibrium Campbell length depends upon the ratio $j/j_c$. $lambda (T,H,j)$ {it increases} with $j/j_c$ as expected for a non-parabolic potential well whose curvature {it decreases} with the displacement. Qualitatively similar results are observed in other high-$T_{c}$ and conventional superconductors.
A true critical current density, $j_{c}$, as opposite to commonly measured relaxed persistent (Bean) current, $j_{B}$, was extracted from the Campbell penetration depth, $lambda_{C}(T,H)$ measured in single crystals of LiFeAs. The effective pinning potential is non-parabolic, which follows from the magnetic field - dependent Labusch parameter $alpha$. At the equilibrium (upon field - cooling), $alpha(H)$ is non-monotonic, but it is monotonic at a finite gradient of the vortex density. This behavior leads to a faster magnetic relaxation at the lower fields and provides a natural emph{dynamic} explanation for the fishtail (second peak) effect. We also find the evidence for strong pinning at the lower fields. The inferred field dependence of the pinning potential is consistent with the evolution from strong pinning, through collective pinning and, eventually, to a disordered vortex lattice. The values of $j_{c}(2text{K}) simeq 2times10^{6}$ A/cm$^{2}$ provide an upper estimate of the current carrying capability of LiFeAs. Overall, vortex behavior of almost isotropic, fully-gapped LiFeAs is very similar to highly anisotropic d-wave cuprate superconductors, the similarity that requires further studies in order to understand unconventional superconductivity in cuprates and pnictides.
We predict a novel buckling instability in the critical state of thin type-II superconductors with strong pinning. This elastic instability appears in high perpendicular magnetic fields and may cause an almost periodic series of flux jumps visible in the magnetization curve. As an illustration we apply the obtained criteria to a long rectangular strip.
We study the effect of disorder on the London penetration depth in iron-based superconductors. The theory is based on a two-band model with quasi-two-dimensional Fermi surfaces, which allows for the coexistence region in the phase diagram between magnetic and superconducting states in the presence of intraband and interband scattering. Within the quasiclassical approximation we derive and solve Eilenbergers equations, which include a weak external magnetic field, and provide analytical expressions for the penetration depth in the various limiting cases. A complete numerical analysis of the doping and temperature dependence of the London penetration depth reveals the crucial effect of disorder scattering, which is especially pronounced in the coexistence phase. The experimental implications of our results are discussed.
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