Tunable artificial vortex ice in nanostructured superconductors with frustrated kagome lattice of paired antidots

Theoretical proposals for spin ice analogs based on nanostructured superconductors have suggested larger flexibility for probing the effects of fluctuations and disorder than in the magnetic systems. In this work, we unveil the particularities of a vortex ice system by direct observation of the vortex distribution in a kagome lattice of paired antidots using scanning Hall probe microscopy. The theoretically suggested vortex ice distribution, lacking long range order, is observed at half matching field (H_{1}/2). Moreover, the vortex ice state formed by the pinned vortices is still preserved at 2H_{1}/3. This unexpected result is attributed to the introduction of interstitial vortices at these magnetic field values. Although the interstitial vortices increase the number of possible vortex configurations, it is clearly shown that the vortex ice state observed at 2H_{1}/3 is less prone to defects than at $H_{1}/2$. In addition, the non-monotonic variations of the vortex ice quality on the lattice spacing indicates that a highly ordered vortex ice state cannot be attained by simply reducing the lattice spacing. The optimal design to observe defect free vortex ice is discussed based on the experimental statistics. The direct observations of a tunable vortex ice state provides new opportunities to explore the order-disorder transition in artificial ice systems.