Boundary sensitivity in finite-sized artificial spin ice explored via AI-assisted genetic algorithms

Abstract Frustrated magnetic systems such as spin ice are key platforms for novel metamaterials. However, identifying their ground states in finite arrays is a formidable challenge, as boundary sensitivity and metastable states trap conventional optimization methods. We introduce a virtuous-cycle AI pipeline where a genetic algorithm explores the latent space of a variational autoencoder (VAE), with the best candidates progressively refining the VAE’s representation. Applied to Kagome spin ice, this method reveals how the boundary magnetism is determined: boundaries break the symmetry of the $$\sqrt{3\,}\times \sqrt{3\,}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:mrow> <mml:mn>3</mml:mn> <mml:mspace/> </mml:mrow> </mml:msqrt> <mml:mo>×</mml:mo> <mml:msqrt> <mml:mrow> <mml:mn>3</mml:mn> <mml:mspace/> </mml:mrow> </mml:msqrt> </mml:mrow> </mml:math> magnetic superstructure while the bulk superstructure order in the interior maintains. Furthermore, it demonstrates that high geometric confinement induces a novel quasi-ferromagnetic phase, which breaks the interior superstructure order. Our work provides a predictive framework for designing frustrated materials and demonstrates a powerful AI approach for boundary-sensitive physical systems.