C. Xue, J.-Y. Ge, A. He, V. S. Zharinov, V. V. Moshchalkov, Y. H. Zhou, A. V. Silhanek, and J. Van de Vondel
Physical Review B 97, 134506 (2018)
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 paper, we unveiltheparticularitiesofavortexicesystembydirectobservationofthevortexdistributioninakagomelattice of paired antidots using scanning Hall probe microscopy. The theoretically suggested vortex ice distribution, lacking long-range order, is observed at half matching ﬁeld (H1/2). Moreover, the vortex ice state formed by the pinned vortices is still preserved at 2H1/3. 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,itisclearlyshownthatthevortexicestateobservedat2H1/3islesspronetodefectsthanat H1/2. In addition, the nonmonotonic 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-freevortexiceisdiscussedbasedontheexperimentalstatistics.Thedirectobservationsofatunablevortex ice state provides new opportunities to explore the order-disorder transition in artiﬁcial ice systems.