Controllable morphology of flux avalanches in microstructured superconductors

The morphology of abrupt bursts of magnetic flux into superconducting films with engineered periodic pinning centers (antidots) has been investigated. Guided flux avalanches of thermomagnetic origin develop a treelike structure, with the main trunk perpendicular to the borders of the sample, while secondary branches follow well-defined directions determined by the geometrical details of the underlying periodic pinning landscape. Strikingly, we demonstrate that in a superconductor with relatively weak random pinning the morphology of such flux avalanches can be fully controlled by proper combinations of lattice symmetry and antidot geometry. Moreover, the resulting flux patterns can be reproduced, to the finest details, by simulations based on a phenomenological thermomagnetic model. In turn, this model can be used to predict such complex structures and to estimate physical variables of more difficult experimental access, such as the local values of temperature and electric field.

Figure 1

Scanning electron microscopy image of the central portion of sample Nb-I, showing the abrupt change in antidot geometry, from circle (left) to square (right). Lattice parameter and AD sizes are shown in the zoomed up bottom panel.

Figure 2

MO images for sample MoGe-I, with circular (left side) and square (right side) ADs, taken at (a) $T$ = 4.5 K and $H$ = 1.2 Oe, showing anisotropic flux penetration, and (b) $T$ = 3 K and $H$ = 1.6 Oe, revealing two different morphologies, depending on the AD geometry. (c) MO image for sample MoGe-II (square lattice of square ADs) taken at $T$ = 3 K and $H$ = 1 Oe, showing avalanches with the Christmas Tree morphology. In panel (a) a drawing of the streamline pattern of the critical current flow is superimposed to the actual MO image.

Figure 3

MO images taken for sample Nb-I, with circular (left side) and square (right side) ADs, taken at (a) $T$ = 6 K and $H$ = 48 Oe, showing isotropic flux penetration, and (b) $T$ = 6 K, for $H$ = 14 Oe (after decreasing from $H$ = 48 Oe), revealing different morphologies depending on the AD geometry. (c) MO image for sample Nb-II (square lattice of square ADs) taken at $T$ = 5 K and $H$ = 2.1 Oe, showing avalanches with the Christmas Tree morphology.

Figure 4

Flux avalanche in a square array of square antidots, reproducing avalanches with the Christmas Tree morphology (see text) occurring for $T/T_c=0.4$ and $H=5.3$ Oe with the typical parameters of a Nb thin film. The first set of panels represents the distribution of the magnetic-flux density $B_z$, the second set shows the induced sheet current $J$, the third presents the map of the reduced temperature, and the last depicts the space distribution of the electric field. Time evolves from left to right: 21, 80, 205, and 415 ns.

Figure 5

(a) Magnetic-flux distribution for $H=3.2$ Oe, obtained from simulations for a superconducting film decorated with a centered rectangular 2D Bravais lattice of square ADs, designed to match sample MoGe-III. (b) MO image taken at 3 K and 1.0 Oe for sample MoGe-III. Inset: Optical image showing the nominal angles $\alpha =63.4^{\circ }$ and $\theta =53.2^{\circ }$ of the lattice.