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We have used soft x-ray photoemission electron microscopy to image themagnetization of single domain La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ nano-islandsarranged in geometrically frustrated configurations such as square ice andkagome ice geometries. Upon thermal randomization, ensembles of nano-islandswith strong inter-island magnetic coupling relax towards low-energyconfigurations. Statistical analysis shows that the likelihood of ensemblesfalling into low-energy configurations depends strongly on the annealingtemperature. Annealing to just below the Curie temperature of the ferromagneticfilm (T$_{C}$ = 338 K) allows for a much greater probability of achieving lowenergy configurations as compared to annealing above the Curie temperature. Atthis thermally active temperature of 325 K, the ensemble of ferromagneticnano-islands explore their energy landscape over time and eventually transitionto lower energy states as compared to the frozen-in configurations obtainedupon cooling from above the Curie temperature. Thus, this materials systemallows for a facile method to systematically study thermal evolution ofartificial spin ice arrays of nano-islands at temperatures modestly above roomtemperature.

Nanostructured complex oxides as a route towards thermal behavior in artificial spin ice systems