Logical gates embedding in Artificial Spin Ice

TL;DR

This paper proposes a theoretical framework for implementing and integrating logical gates in artificial spin ice systems, demonstrating their robustness to fabrication imperfections and potential for magnetic computation.

Contribution

It introduces complete sets of logical gates in artificial spin ice and analyzes their integration into circuits, considering disorder effects.

Findings

Logical gates can be realized in artificial spin ice.

Gate structures are robust to small coupling disorder.

Conditions for successful gate integration are identified.

Abstract

The realization and study of arrays of interacting magnetic nanoislands, such as artificial spin ices, have reached mature levels of control that allow design and demonstration of exotic, collective behaviors not seen in natural materials. Advances in the direct manipulation of their local, binary moments also suggest a use as nanopatterned, interacting memory media, for computation {\it within} a magnetic memory. Recent experimental work has demonstrated the possibility of building logic gates from clusters of interacting magnetic domains, and yet the possibility of large scale integration of such gates can prove problematic even at the theoretical level. Here we introduce theoretically complete sets of logical gates, in principle realizable in an experiment, and we study the feasibility of their integration into tree-like circuits. By evaluating the fidelity control parameter between their collective behavior and their expected logic functionality we determine conditions for integration. Also, we test our numerical results against the presence of disorder in the couplings, showing that the design gate structure is robust to small coupling perturbations, and thus possibly to small imperfections in the fabrication of the islands.