Abstract
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 $0.7{H}_{1}$ due to the appearance of interstitial vortices. The correlation of vortex interaction also confirms such nontrivial matching field.
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