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In this letter, we have constructed and experimentally investigatedfrustrated arrays of dipoles forming two-dimensional artificial spin ices withdifferent lattice parameters (rectangular arrays with horizontal and verticallattice spacings denoted by $a$ and $b$ respectively). Arrays with threedifferent ratios $\gamma =a/b = \sqrt{2}$, $\sqrt{3}$ and $\sqrt{4}$ arestudied. Theoretical calculations of low-energy demagnetized configurations forthese same parameters are also presented. Experimental data for demagnetizedsamples confirm most of the theoretical results. However, the highest energytopology (doubly-charged monopoles) does not emerge in our theoretical model,while they are seen in experiments for large enough $\gamma$. Our results alsoinsinuate that magnetic monopoles may be almost free in rectangular latticeswith a critical ratio $\gamma = \gamma_{c} = \sqrt{3}$, supporting previoustheoretical predictions.

Realization of Rectangular Artificial Spin Ice and Direct Observation of High Energy Topology