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

## TL;DR

This study constructs and examines rectangular artificial spin ice arrays with varying lattice ratios, revealing experimental evidence of high-energy monopole topologies and suggesting conditions for magnetic monopole freedom.

## Contribution

The paper provides the first experimental observation of high-energy monopole topologies in rectangular artificial spin ice and explores the critical lattice ratio for magnetic monopole deconfinement.

## Key findings

- High-energy monopoles observed experimentally at large lattice ratios.
- Experimental results largely agree with theoretical calculations.
- Magnetic monopoles may be nearly free at a critical lattice ratio of √3.

## Abstract

In this letter, 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 ratios $\gamma =a/b = \sqrt{2}$, $\sqrt{3}$ and $\sqrt{4}$ 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 $\gamma$. Our results also insinuate that magnetic monopoles may be almost free in rectangular lattices with a critical ratio $\gamma = \gamma_{c} = \sqrt{3}$, supporting previous theoretical predictions.