Vortex ice pattern evolution in a kagome nanostructured superconductor

The vortex ice system has been proposed as a promising platform to study the geometrical frustration and the emergent exotic phenomena, mainly because of the availability of tunable vortex-vortex interactions and the feasibility to manufacture a variety of nanoscale pinning potential geometries. In this paper, we designed and fabricated a kagome lattice of paired antidots with geometrical frustration. By changing the magnetic field to tune the number of interaction units, the vortex ice pattern formation and its evolution are revealed. We have found that only local topological charge order is formed at low magnetic fields, while the vortex pattern enters a disordered paramagnetic state with no long-range order of chirality or topological charge at relatively high magnetic fields. Instead of the expected half matching field in a vortex ice, the vertices fulfill the ice rule, reaching the maximum proportion at $0.7H_1$ due to the appearance of interstitial vortices. The correlation of vortex interaction also confirms such nontrivial matching field.

Figure 1

(a) Schematic diagram (left panel) showing the side view of the studied nanostructured superconductor. Atomic-force microscope image (right panel) of the sample, where the kagome lattice of the paired antidots is indicated. (b) Various vortex occupation configurations for the paired antidots: empty pair with two free antidots, ice pair with only one antidot being occupied, and saturated pair with both antidots being occupied. (c) Six vertex configurations following the vortex-ice rule: two-occupied/one-free or one-occupied/two-free. (d) Following the way in Ref. [45], for each ice pair, a pseudospin is defined with the direction pointing toward the vortex. Six antidot pairs form a hexagon with the spin chirality defined by arrows (${\chi }_i=1$ clockwise, ${\chi }_i=-1$ counterclockwise). The hexagon is colored according to their net spin chirality: clockwise (blue), counterclockwise (orange).

Figure 2

(a)–(k) The observed vortex ice configurations (upper panels) and their schematic diagrams (lower panels) under various magnetic fields as indicated above each image. $10\mu m$ for all the scale bars. (l) The density of interstitial and pinned vortices as a function of reduced magnetic field.

Figure 3

Statistics of vortex ice states at different fields. (a) The proportion of different pair distributions [ice pairs (red circle), empty pairs (black square), and saturated pairs (cyan triangle)]. (b) The proportion of $q=1$ and $q=-1$ vertices corresponding to the ice rule of ‘two-occupied/one-free’ and ‘one-occupied/two-free,’ respectively.

Figure 4

The defined correlations as a function of magnetic field. The inset shows the definitions of the nearest neighbor pairs (NN) and the next nearest neighbor pairs (NNN).