Flux dendrites of opposite polarity in superconducting $\mathrm{Mg}{\mathrm{B}}_2$ rings observed with magneto-optical imaging

Magneto-optical imaging was used to observe flux dendrites with opposite polarities simultaneously penetrate superconducting, ring-shaped $\mathrm{Mg}{\mathrm{B}}_2$ films. By applying a perpendicular magnetic field, branching dendritic structures nucleate at the outer edge and abruptly propagate deep into the rings. When these structures reach close to the inner edge, where flux with opposite polarity has penetrated the superconductor, they occasionally trigger anti-flux-dendrites. These antidendrites do not branch, but instead trace the triggering dendrite in the backward direction. Two trigger mechanisms, a nonlocal magnetic and a local thermal mechanism, are considered as possible explanations for this unexpected behavior. Increasing the applied field further, the rings are perforated by dendrites which carry flux to the center hole. Repeated perforations lead to a reversed field profile and new features of dendrite activity when the applied field is subsequently reduced.

Figure 1

(Color online) The flux distribution in the large ring at $B_a=3.6\mathrm{mT}$. The numbers next to dendrites indicate the order in which they appeared. The profile plot is obtained by averaging vertically within the rectangle. The kink in the profile inside the central hole is an artifact caused by the presence of zigzag domains in the MO indicator film.

Figure 2

(Color online) MO images on ZFC samples in increasing applied field. The large ring is shown in (a), the small ring in (c). In both images the antidendrites nucleate near a bright tip, in most cases tracing a bright finger deep into the superconductor. The areas within the rectangles are shown in more detail in (b) and (d).

Figure 3

(Color online) MO image on FC samples in increasing applied field. The FC field was $15\mathrm{mT}$. A new detail not seen in the ZFC experiment in Fig. 2 is shown in the zoomed-in view of the image. Dark and bright dendrites are woven together in what appears to have been multiple avalanche events. The image has been background corrected by subtracting an image acquired on the virgin sample at $15\mathrm{mT}$.

Figure 4

(Color online) An MO image of a ZFC sample during field descent is shown in (a). The image in (b) is obtained by subtracting the previous image in the sequence, thus highlighting the growth of specific dendrites, as well as showing small-scale flux rearrangements in a large region in response to the dendritic avalanches.

Figure 5

(Color online) (a) The MO image shows the field distribution near a bright dendrite which has grown nearly all the way to the center hole. Note the relatively strong negative field at the inner edge close to the finger. (b) A current density map obtained by inverting the $B$-field image using the Biot-Savart law. The arrows show the direction of current. There is an increased current density between the inner edge and the tip of the bright finger. The images suggest that if bright dendrites come close enough to the inner edge, they may trigger growth of a dark dendrite.

Figure 6

(Color online) (a) MO image recorded at maximum applied field of $20\mathrm{mT}$. Notice that the field is positive near the inner edge. (b) Image recorded at $12.6\mathrm{mT}$ after subtracting the peak field image. Dark pixels indicate decrease in flux, and bright pixels indicate increase. The difference image resembles what we see in a virgin sample at small applied fields, with a regular flux decrease at the outer edge and flux increase at the inner edge. The nucleation spot of the first dendrite is a region where we find a large positive edge field at peak $B_a$, while the flux density in the superconductor is quite low.