At the outset of this program, it was important to understand how atomic-scale spins can be interlinked to form a so-called attractor network. In neuroscience, the concept of an attractor is often equated to an associative memory. In physics, an attractor network is linked to creating an energy landscape, where the attractor is represented by a local minimum in that landscape. The machine learning problem in materials becomes two-fold in this paradigm: how does one create an energy landscape with multiple minima/attractors, and how can these minima/attractors be tuned or learn based on information? We first showed in a theoretical study that arrays of interacting atomic spins can realize two interesting energy landscapes. The first we call a spin-Q glass, based on a recent proposition of a self-induced spin glass. The idea is strongly linked to the concept of a glass, where there are many minima in the energy landscape, but without the complex disorder characteristic of such systems. The second landscape we discovered was a multi-well landscape, that mimicked the attractor networks often found in machine learning models like the Hopfield model. Shortly after this theoretical study, we discovered that the magnetic behavior of elemental neodymium could be described by this notion of a spin-Q glass. This study resolved a 50-year-long debate about the magnetic behavior of this element on the periodic table. While the discovery of the first spin-Q glass has already lead to many new physical questions, we found that the behavior of neodymium was too glassy to be used for attractor networks as a result of aging.
In a second endeavor, we developed an atomic-scale platform to realize the first atom-by-atom neural network. This was based on a discovery in 2018, where we discovered the so-called single atom orbital memory derived from a cobalt atom on black phosphorus. In this program, we found that arrays of closely placed cobalt atoms “talk” to each other, and these interactions lead to an energy landscape the identically mimics an attractor network. Using a concept of separation of time scales, we were able to show the fabrication of an atomic synapse coupled to a chain of neurons, the smallest such neural network to date and contained in one material system. Using this discovery, we showed that this new materials platform could be used to mimic a seminal model in machine learning: the Boltzmann machine. Its novelty is not only in its size scale, but also that we have found evidence of self-adaption in this material. Using this simple model system, we can strive to answer many open fundamental questions linking materials to future paradigms in brain-inspired computing.
