Clocking emergent magnetic monopoles in square artificial spin ice

Dipolar-coupled single-domain nanomagnet lattices, known as artificial spin ice (ASI), exhibit geometric frustration, emergence, reconfigurability, and collective magnetization dynamics, making them a promising platform for magnetic logic devices, reconfigurable magnonics, and unconventional computing. One local feature that could serve as an information carrier in such systems is the emergent magnetic monopole. However, applied global magnetic fields often trigger uncontrolled avalanchelike switching of nanomagnets, leading to detrimental loss of encoded information. Microstate control and stepwise monopole motion remain a key challenge. In this work, we explore the nature of monopole motion in square ASI via so-called astroid clocking protocols and demonstrate controlled stepwise propagation. Using x-ray magnetic circular dichroism and magneto-optical Kerr microscopy imaging, we experimentally verify controlled single-step monopole motion in square ASI. We reveal a rich spectrum of emergent monopole pathways referred to as string, zigzag, and ferromagnetic domain regimes. Our finding shows that these pathways of monopole propagation are determined by the angle and strength of the clocking field. This approach offers a higher level of control of emergent magnetic monopole propagation in ASI, with potential applications in data storage and unconventional computing.