Extensive degeneracy, Coulomb phase and magnetic monopoles in an artificial realization of the square ice model

TL;DR

This paper demonstrates that a carefully designed artificial square ice lattice can replicate the square ice model's degenerate ground states, Coulomb phase, and magnetic monopoles, enabling real-space visualization of complex frustrated magnetic phenomena.

Contribution

It introduces a novel artificial square ice design that captures the square ice model's key features, including degeneracy and monopole excitations, previously unachieved in nanomagnet arrays.

Findings

Observation of algebraic spin liquid state with pinch points

Detection of free magnetic monopole-like excitations

Realization of a lab-on-chip platform for frustrated magnetism phenomena

Abstract

Artificial spin ice systems have been introduced as a possible mean to investigate frustration effects in a well-controlled manner by fabricating lithographically-patterned two-dimensional arrangements of interacting magnetic nanostructures. This approach offers the opportunity to visualize unconventional states of matter, directly in real space, and triggered a wealth of studies at the frontier between nanomagnetism, statistical thermodynamics and condensed matter physics. Despite the strong efforts made these last ten years to provide an artificial realization of the celebrated square ice model, no simple geometry based on arrays of nanomagnets succeeded to capture the macroscopically degenerate ground state manifold of the corresponding model. Instead, in all works reported so far, square lattices of nanomagnets are characterized by a magnetically ordered ground state consisting of local flux-closure configurations with alternating chirality. Here, we show experimentally and theoretically, that all the characteristics of the square ice model can be observed if the artificial square lattice is properly designed. The spin configurations we image after demagnetizing our arrays reveal unambiguous signatures of an algebraic spin liquid state characterized by the presence of pinch points in the associated magnetic structure factor. Local excitations, i.e. classical analogues of magnetic monopoles, are found to be free to evolve in a massively degenerated, divergence-free vacuum. We thus provide the first lab-on-chip platform allowing the investigation of collective phenomena, including Coulomb phases and ice-like physics.