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

We have used soft x-ray photoemission electron microscopy to image the magnetization of single domain La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ nano-islands arranged in geometrically frustrated configurations such as square ice and kagome ice geometries. Upon thermal randomization, ensembles of nano-islands with strong inter-island magnetic coupling relax towards low-energy configurations. Statistical analysis shows that the likelihood of ensembles falling into low-energy configurations depends strongly on the annealing temperature. Annealing to just below the Curie temperature of the ferromagnetic film (T$_{C}$ = 338 K) allows for a much greater probability of achieving low energy configurations as compared to annealing above the Curie temperature. At this thermally active temperature of 325 K, the ensemble of ferromagnetic nano-islands explore their energy landscape over time and eventually transition to lower energy states as compared to the frozen-in configurations obtained upon cooling from above the Curie temperature. Thus, this materials system allows for a facile method to systematically study thermal evolution of artificial spin ice arrays of nano-islands at temperatures modestly above room temperature.