Intermediate States in Artificial Spin Ice Inspired Computation

Computing with dipolar coupled nanomagnets provides us with a unique future towards energy efficiency and exploration of opportunities in innovative computing architectures for beyond-Moore applications such as brain-inspired computation. An often-neglected problem with nanomagnet computation is the presence of intermediate states, which are metastable states that arise during computation. These errors, leading to a low operational reliability of a device, are often attributed to lithographic defects, inefficient field/thermal protocols, and local disorder. In this work, we theoretically and experimentally demonstrate that operational inefficiency in nanomagnet based computing is primarily due to the presence of metastable intermediate states. We make use of a simple toy model of four nanomagnets arranged onto a square plaquette to systematically engineer intermediate states with tunable energies, thus leading to tunable outcomes. These intermediate states naturally arise as they connect an initial input with the final output through multipolar moment reorientations dubbed an energy relaxation pathway. We show that the outcome is the aftermath of the energy landscape profile which is deeply connected to the geometrical arrangement of the nanomagnets, and in turn is controlled by emerging multipolar moments. Finally, we argue that designer lattices can and must be considered to side-step or leverage intermediate states for novel computing opportunities. We hope our proposed design framework will assist future research in artificial spin ice, nanomagnetic logic, and spintronics communities, encouraging them to consider geometry-induced energetics in designer lattices.