Abstract
In this work, we have constructed and experimentally investigated frustrated arrays of dipoles forming two-dimensional artificial spin ices with different lattice parameters (rectangular arrays with horizontal and vertical lattice spacings denoted by a and b respectively). Arrays with three different aspect ratios γ = a/b = sqrt{{bf{2}}}, sqrt{{bf{3}}} and sqrt{{bf{4}}} are studied. Theoretical calculations of low-energy demagnetized configurations for these same parameters are also presented. Experimental data for demagnetized samples confirm most of the theoretical results. However, the highest energy topology (doubly-charged monopoles) does not emerge in our theoretical model, while they are seen in experiments for large enough γ. Our results also insinuate that the string tension connecting two magnetic monopoles in a pair vanishes in rectangular lattices with a critical ratio γ = γc = sqrt{{bf{3}}}, supporting previous theoretical predictions.
Highlights
A recent theoretical proposal for vanishing the string tension was made to transform the square array into a rectangular one[17]
Inspired by this modified system, here we propose to realize an experimental study based on magnetic atomic force (MFM) measurements of the ground state and excited states of rectangular artificial spin ices (RASI)
We have to mention that the charge shown in Fig. 2 was constructed by the magnetic moment divided by the vertex-vertex lattice spacing, as used in natural spin ices[2], where the atomic magnets can be treated as point dipoles
Summary
A recent theoretical proposal for vanishing the string tension was made to transform the square array into a rectangular one[17] Inspired by this modified system, here we propose to realize an experimental study based on magnetic atomic force (MFM) measurements of the ground state and excited states of rectangular artificial spin ices (RASI). At the critical value γ = γc = 3 , these two different configurations GSQ and GSM have the same energy and, the ground state at this particular γc becomes degenerate, suggesting a residual entropy at absolute zero temperature similar to what happens in natural[1,2] and (3d) artificial[9,16,24] spin ice materials.
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