Field-tunable vortex-ice ordering in a superconducting square lattice of elongated antidots

Artificial spin ice based on ferromagnetic nanoislands enables direct visualization of geometrical frustration, but weak interactions relative to switching barriers often kinetically arrest the arrays before they reach ordered states. Here, we realize a superconducting square vortex ice in a Pb film patterned with elongated antidots, with each antidot providing a binary occupation variable. Low-temperature scanning Hall probe microscopy images field-cooled vortex configurations, enabling vertex-resolved statistics as a function of applied field. The population of two-occupied/two-empty ice-rule vertices peaks at an effective half-matching field, H*=0.55H1. Near H*, collinear vertices assemble into extended string-like domains, whereas perpendicular vertices are enriched at boundaries between orthogonally oriented domains. Ginzburg–Landau calculations capture the field evolution of the vertex populations and the preference for collinear configurations, supporting geometry-induced selection between the two type-3 vertex classes. These results establish elongated-antidot superconducting vortex ice as a directly visualizable, field-tunable complement to magnetic artificial square ice for investigating geometry-induced vertex selection, collective ice ordering, and domain formation.