Non-monotonic Dependence of Magnetic Ordering on Geometry Regulated by Intra-Unit Interactions in Macroscopic Square Ice

Artificial spin ice systems have provided powerful platforms for exploring frustrated magnetism and emergent phenomena. However, nanoscale fabrication constraints limit the direct manipulation and real-time visualization of individual magnetic elements for square ice model. Macroscopic mechanical analogues overcome these limitations by enabling direct observation and flexible control of local interactions. Nevertheless, how geometry-tuned intra-unit interactions regulate global ordering in frustrated systems remains poorly understood. Here, we construct a “macroscopic square ice” experimental platform to investigate this problem, using the unit gap l as a tunable geometric parameter while fixing the vertex gap d at 1.1 mm. By directly monitoring magnetic domain evolution and vertex-type distributions, we reveal a non-monotonic order–disorder–order transition driven by the competition between intra-unit and inter-vertex interactions. This work provides direct experimental insight into the role of geometry-controlled local interactions in governing collective ordering and offers a visible approach for studying emergent behaviors in frustrated systems.