Topological geometric frustration in a cube-surface artificial spin ice

Artificial spin ices provide a controlled platform for investigating diverse\nphysical phenomena, such as geometric frustration, magnetic monopoles, and\nphase transitions, via deliberate design. Here, we introduce a novel approach\nby developing artificial spin ice on the surfaces of a three-dimensional cube,\nwhich leads to emergent geometric frustration mediated by topologically\nprotected domain walls, distinct from its flat counterparts. These domain walls\nconnect vertices at the corners of cube that acting as intrinsic topological\ndefects. Utilizing Monte Carlo simulations, we observe robust, topologically\nprotected correlations among the intrinsic topological defects, regardless of\ntheir spatial separation. Our findings demonstrate that three-dimensional\nsurfaces can unveil emergent properties absent in flat architectures.\n