Vortex avalanches with robust statistics observed in superconducting niobium

By combining micro-Hall probe and magneto-optical imaging techniques we have been able to examine vortex avalanches at different locations of the ridgelike magnetic topography of superconducting niobium samples as the external field is slowly increased. The avalanche size distributions are shown to be power laws for two decades with very similar critical exponents at all locations, thus demonstrating a remarkable robustness in the details of the flux penetration dynamics.

Figure 1

Magnetic landscape of the Nb superconductor. The magneto-optical image (top) shows how the flux penetrates into one-half of a $1.5\times 1.5\times 0.25{\mathrm{mm}}^3$ Nb foil at a field of $400\mathrm{Oe}$ applied perpendicular to the sample at $T=4.8\mathrm{K}$. The image brightness represents the local density of the magnetic vortices. The 3D plot (bottom) of the penetration pattern shows that the magnetic landscape consists of several ridges with smooth slopes, which rise up from the flat Meissner state (flux free) area. Included in the figure is the location of a Hall probe array where each of the 11 probes detects the flux under an area of $10\times 10\mu {\mathrm{m}}^2$. As the applied magnetic field increases all the ridges grow gradually on a macroscopic scale, quite similarly to the way sandpiles increase in size when grains are added.

Figure 2

Magneto-optical image of the sample with an overlay showing five different locations of the Hall probe array used for supplementary measurements. The image was taken at $450\mathrm{Oe}$ and $4.8\mathrm{K}$, and the scale bar is $0.2\mathrm{mm}$ long. Location (I) is identical to the one in Fig. 1, and provided the data plotted in Fig. 3. The first four probes, counting from the left in location (IV), provided the data plotted in the inset of Fig. 4.

Figure 3

Vortex avalanches seen by a Hall probe during field increase. The main curve was obtained from probe number 4 from the sample edge in Fig. 1, and contains more than 40 000 data points. The insets show zooms in two different field windows revealing distinct steps as a manifestation of avalanche dynamics. The experiment was performed at $T=4.8\mathrm{K}$. Similar measurements performed slightly above $T_c$ show no measurable steps, demonstrating that those reported in the figure are not mere instrumental noise.

Figure 4

Size distribution of avalanches. The statistics is based on nearly 200 000 avalanche events measured in the Hall probes located as shown in Fig. 1. Steps less than $0.7{\Phi }_o$ were excluded from the counting of events. $P\left(s\right)$ was averaged within exponentially increasing intervals along the $s$ axis, giving equidistant points in the log-log plot. The data are fitted by the straight line $P\left(s\right)\sim s^{-\tau }$, with $\tau =3.1\pm 0.2$. The inset shows analogous results using data from a very different Hall probe location (see Fig. 2), giving $\tau =3.1\pm 0.2$.