The behavior of superconducting vortices in the presence of a periodic array of holes reveals rich and unexpected static and dynamic phenomena. Transport and magnetization studies show distinctive features at matching fields where the vortex structure is commensurate with the hole array. Commensurability can arise from vortex configurations in which each hole contains an integer number of flux quanta, or from interstitial structures where vortices occupy the regions between flux-saturated holes. Interesting configurations also arise at fractional matching fields, where the occupation number of each hole or the number of interstitial vortices forms a superstructure locked to the basic hole array. Although magnetization and transport studies have elucidated much of the basic phenomenology of the array/vortex system, they can measure only its global properties and cannot deduce details of the local configurational vortex state. Here we present large-area scanning Hall probe microscope (SHM) images of vortex configurations in arrays containing approximately a million holes. Our images span some 5000 holes, and so yield important information on the large-scale structure of the vortex configurations. These studies reveal striking multi-quantum and interstitial vortex patterns in a square-periodic hole array. At fractional matching fields we resolve distinctive domains of phase-slip related vortex superstructures that are separated by domain walls with characteristic internal structure.
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| (Top) Schematic of the hole array samples. The actual samples used were 100-nm-thick Nb films with a square array of holes on a square 2-µm-pitch array. (Bottom) As the magnetic field is increased, the holes begin to fill with vortices. At the matching field of 6.0 G, each hole contains exactly one vortex. Above this field, additional vortices may enter as either interstitials (shown) or multiquanta holes. | (Top row) Images as the field is swept from H = -0.15 to +0.15; here H is measured in units of the matching field. For negative fields vortices appear as white spots, and for positive fields as black ones. (Middle row) Near H = 1 the progression looks nearly identical. Here, however, at H = 1 the smooth gray represents areas where every hole contains one vortex. The microscope's limited resolution smears this out into a uniform gray. A similar progression is seen near H = 2. However, at H = 3 (lower right) we see only a disordered muddle. |
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| When H = 1/2, we see smooth, ordered domains separated by striking striped features (a). Zooming in (b) we see that the ordered regions consist vortices in a checkerboard-like configuration, with all vortices sitting, for instance, on the black squares. The striped features are grain boundaries, separating regions with "black square" vortices from regions with all vortices sitting on the red squares. The schematic (c) shows clearly how the striped features arise from this change in polarity. | At other fractions, different domain structures are visible, although none as ordered as at H = 1/2. |
