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

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 = , and 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 = γ c = , supporting previous theoretical predictions.

Effects of magnetic monopoles charge on the cracking reversal processes in artificial square ices

“…Indeed, vertices T 2 have a resulting dipole moment not present in vertices type T 1 . The other two categories (T 3 and T 4 ) are excited states usually associated with monopole like excitation 6,7,[12][13][14][15][16][17][18] . Of course, the ground-state of this system requires all vertices to be category T 1 .…”

Advances in artificial spin ice

“…One possible solution is to raise one sublattice with respect to the other [40][41][42][43][44] , so that, at a critical vertical separation, the so-called Coulomb phase is achieved 45 , with emergent magnetic monopoles freely moving in a highly degenerate, divergence-free background. Another possibility to reduce the string tension is to use two different sublattice parameters 46,47 . In lattices of connected nanomagnets, modifying the shape and size of the vertex, for example, by fabricating a hole at the vertex centre or making the nanomagnets narrower, can also make the type I and type II vertices similar in energy 48,49 .…”

“…3a), are easier in terms of the fabrication. For example, stretching the lattice to a rectangular shape increases the degeneracy of vertex states 46,47 . In another example, introducing magnetic nanodiscs into the gaps at the vertices 21 , as so-called 'slave' macrospins, equalizes the energy between type I and type II vertices.…”

Colloquium : Ice rule and emergent frustration in particle ice and beyond

“…Because the two components are uncoupled at the lowest order in the effective free energy, dipolar correlations and pinch points survive at non-zero temperature. Artificial realization of topological phases was achieved in the Shakti geometry (Lao et al, 2018) as well as in magnetic square ice (Möller and Moessner, 2006;Perrin et al, 2016) and rectangular (Loreto et al, 2019;Ribeiro et al, 2017) ice. No equivalent phase has yet been realized with colloids, though those magnetic realization provide directions.…”