# Proposal to recover an extensive ground state degeneracy in a two-dimensional square array of nanomagnets

## TL;DR

This paper explores how connecting nanomagnets in a square array affects their magnetic degeneracy, revealing tunable ground states and potential realization of square ice models for studying disordered magnetic states.

## Contribution

It demonstrates that connected nanomagnet arrays can exhibit extensive ground state degeneracy, unlike disconnected systems, and shows how geometry influences magnetic properties and degeneracy.

## Key findings

- Extensive ground state manifold observed in connected nanomagnet arrays.
- Degeneracy depends on nanomagnet geometry, such as width and thickness.
- Potential to realize square ice models with connected nanomagnets.

## Abstract

We investigate numerically the micromagnetic properties and the low-energy physics of an artificial square spin system in which the nanomagnets are physically connected at the lattice vertices. Micromagnetic simulations reveal that the energy stored at the vertex sites strongly depends on the type of magnetic domain wall formed by the four connected nanomagnets. As a consequence, the energy gap between the vertex types can be partially modified by varying the geometrical parameters of the nanomagnets, such as their width and thickness. Based on the energy levels given by the micromagnetic simulations, we compute the thermodynamic properties of the corresponding spin models using Monte Carlo simulations. We found two regimes, both being characterized by an extensive ground state manifold, in sharp contrast with similar lattices with disconnected nanomagnets. For narrow and thin nanomagnets, low-energy spin configurations consist of independent ferromagnetic straight lines crossing the whole lattice. The ground state manifold is thus highly degenerate, although this degeneracy is subdominant. In the limit of thick and wide nanomagnets, our findings suggest that the celebrated square ice model may be fabricated experimentally from a simple square lattice of connected elements. These results show that the micromagnetic nature of artificial spin systems involves another degree of freedom that can be finely tuned to explore strongly correlated disordered magnetic states of matter.