# The importance of the weak: Interaction modifiers in artificial spin ices

## TL;DR

This paper introduces a novel method using interaction modifiers in artificial spin ices, enabling control over magnetic interactions and revealing new emergent magnetic states and flux lattices.

## Contribution

It presents a new approach with disc-shaped slave-mesospins to modify interactions in artificial spin ice, allowing tailored energy ratios and exploration of spin liquid states.

## Key findings

- Degenerate ice-rule states observed in square artificial spin ice.
- Emergence of flux lattices when energy landscape is reversed.
- Control over interaction strength and ratios via disc diameter.

## Abstract

The modification of geometry and interactions in two-dimensional magnetic nanosystems has enabled a range of studies addressing the magnetic order, collective low-energy dynamics, and emergent magnetic properties, in e.g. artificial spin ice structures. The common denominator of all these investigations is the use of Ising-like mesospins as building blocks, in the form of elongated magnetic islands. Here we introduce a new approach: single interaction modifiers, using slave-mesospins in the form of discs, within which the mesospin is free to rotate in the disc plane. We show that by placing these on the vertices of square artificial spin ice arrays and varying their diameter, it is possible to tailor the strength and the ratio of the interaction energies. We demonstrate the existence of degenerate ice-rule obeying states in square artificial spin ice structures, enabling the exploration of thermal dynamics in a spin liquid manifold. Furthermore, we even observe the emergence of flux lattices on larger length-scales, when the energy landscape of the vertices is reversed. The work highlights the potential of a design strategy for two-dimensional magnetic nano-architectures, through which mixed dimensionality of mesospins can be used to promote thermally emergent mesoscale magnetic states.