Micro-SQUID microscopy of vortices in a perforated superconducting Al film

A scanning micro-superconducting quantum interference-device microscope is used to directly image vortices in a superconducting Al thin film. We observe the temperature dependence of the vortex distribution in a regular defect (hole) array patterned into the Al film. The direct observation of the localized superconducting state around the holes is shown as well as the effect of the hole size on nucleation of the superconducting state.

Figure 1

Schematic view of the hole array unit cell and SEM images of the holes made in an Al thin film. The holes are $10\mu \mathrm{m}$ apart and they have three different diameters: $0.5\mu \mathrm{m}$, $1\mu \mathrm{m}$, and $1.5\mu \mathrm{m}$. The entire hole array size is $3\times 3{\mathrm{mm}}^2$.

Figure 2

Temperature dependence of the critical magnetic field $H_{c2}$ (dots) determined by transport measurement. The full line represents $H_{c2}\left(T\right)$ predicted by Ginzburg–Landau theory using a coherence length $\xi \left(0\right)=240\mathrm{nm}$. The theoretical critical field $H_{c3}(H_{c3}=1.69H_{c2})$ is shown with the dashed line.

Figure 3

Images (a), (b), (c) $(28\times 28\mu {\mathrm{m}}^2)$ realized by $\mu \mathrm{SQUID}\text{‐}\mathrm{FM}$ after cooling under a magnetic field of $1.14\mathrm{G}$ down to three different temperatures: (a) $T=0.4\mathrm{K}$, (b) $T=1.18\mathrm{K}$, and (c) $T=1.2\mathrm{K}$. The arrows point out the location of the hole array in the Al film. (d), (e), (f) present, schematically, the flux and vortex configuration (white) in registry with the underlying hole array. The open circles represent the holes and the dots the flux, superconducting regions are gray. (g), (h), (i) show line profiles along the dark lines of (a), (b), (c) in units of ${\varphi }_0$ of the $\mu \mathrm{SQUID}$.

Figure 4

$H\text{‐}T$ diagram showing $H_{c2}$ and $H_{c3}=1.69H_{c2}$ temperature dependence and the temperature and magnetic field where images of Figs. 3b, 3c were acquired.

Figure 5

Comparison in between the magnetic image of the Al film cooled at $1.2\mathrm{K}$ under a magnetic field of $1.14\mathrm{G}$ and a schematic view of the underlying hole array. The cross shows the place of a large defect in the Al film that disturbs the magnetic order. Aligned along a diagonal, the smallest diameter holes do not expel magnetic flux anymore.

Figure 6

Flux pattern observed by magnetic imaging at a temperature of $1.15\mathrm{K}$ after cooling in a field of $0.15\mathrm{G}$, $2∕3$ of the matching field of $0.22\mathrm{G}$. The flux is preferentially localized at the off-diagonal sites of the square hole array, leaving the holes of smallest diameter unoccupied.