Five-stage ordering to a topological-defect-mediated ground state in a buckyball artificial spin ice

Artificial spin ices are arrays of interacting nanomagnets where collective behaviour can be created from tailored design. [1] While artificial spin ices are well-explored in two dimensions, less is known about their behaviour in three dimensions, due to challenges in fabrication and characterisation. Extending artificial spin ice into the third dimension offers opportunities to exploit topology and curvature for exotic forms of magnetic order. [2]

Here, we introduce the buckyball artificial spin ice, where the spins are located on the edges of a regular buckyball. [3] Using Monte Carlo simulations, we uncover an intricate spectrum of thermal behaviour with five crossovers, each marking a transition between different cooperative spin structures. At high temperatures, the buckyball transitions from paramagnetism to a Spin-Ice sector, with short-range correlations constrained by ice rules. As it cools, magnetic charges at the vertices order, but topology prevents full charge crystallisation, leading to an imperfect charge crystal. Partial spin order then emerges in three distinct steps, with a ground state defined by two robust topological defects.

This work shows how curved finite lattices can host novel magnetic states and provides a lodestar for experimentally capturing the rich phase diagrams in three-dimensional artificial spin ices.

[1] S. H. Skjærvø et al., Nat. Rev. Phys. (2020)

[2] L. Berchialla et al., accepted Appl. Phys. Lett. (2024)

[3] G. M. Macauley et al., arXiv:2407.05907 (2024)