Colloidal Spin Ice Cellular Automata for Logic Design

An engineered system that exhibits a variety of interesting properties, such as collective dynamics that are not inherited in their building blocks, is the artificial spin ice (ASI) meta-materials. The building block of such a system is a dipolar nanomagnet with sub-micrometer dimensions. These nanomagnets are arranged in specific designs usually in square or kagome shape and are coupled together by their magnetic interactions. With external magnetic fields, it is possible to create magnetic moments or monopoles that cause a frustration to the system. Because of the local interactions, those moments travel through the topology. The observation of such structures is a very challenging procedure, because of the extremely fast flipping process of the spins. This is why the researchers use mesoscopic systems with materials such as colloids or spheres of nanomagnets which are placed inside of islands in periodic lattices that generate frustration by design. The interactions between those nanomagnets are based on Coulomb forces and are usually modeled by Brownian equations. In this paper, we propose a simple yet effective Cellular Automata (CA) model that can describe effectively the dynamics between nanomagnets in a square lattice structure. The manipulation of the initial positions of nanomagnets via an external magnetic field and the movement of magnetic moments from one site to another are capable to create Boolean logic. Using the CA model we propose the design of logic gates, computing structures such as half adders and rewritable memory elements.