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Artificial spin ices are arrays of correlated nano-scale magnetic islandsthat prove an excellent playground in which to study the role of topology incritical phenomena. Here, we investigate a continuum of spin ice geometries,parameterised by rotation of the islands. In doing so, we morph from theclassic square ice to the recently studied pinwheel geometry, with the rotationangle acting as a proxy for controlling inter-island interactions. Weexperimentally observe a change in ground state magnetic order fromantiferromagnetic to ferromagnetic across this class of geometries usingLorentz transmission electron microscopy on thermally annealed cobalt arrays.The change in ordering leads to an apparent change in the nature of the defectssupported: from one-dimensional strings in the antiferromagnetic phase totwo-dimensional vortex-like structures in the ferromagnetic one, consistentwith the scaling predicted by the Kibble-Zurek mechanism. Our results show howmagnetic order in artificial spin ices can be tuned by changes in geometry sothat a truly frustrated ice-rule phase is possible in two-dimensional systems.Furthermore, we demonstrate this system as a testbed to investigateout-of-equilibrium dynamics across phases.

Ice-rule made manifold: phase transitions, topological defects and manifold restoration in two-dimensional artificial spin systems