Direct observation of a dynamical glass transition in a nanomagnetic artificial Hopfield network

Spin glasses, generally defined as disordered systems with randomized competing interactions^1,2, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those describing brain function^3,4, error-correcting codes⁵ or stock-market dynamics⁶. This wide interest in spin glasses provides strong motivation to generate an artificial spin glass within the framework of artificial spin ice systems^7–9. Here we present the experimental realization of an artificial spin glass consisting of dipolar coupled single-domain Ising-type nanomagnets arranged onto an interaction network that replicates the aspects of a Hopfield neural network¹⁰. Using cryogenic X-ray photoemission electron microscopy (XPEEM), we performed temperature-dependent imaging of thermally driven moment fluctuations within these networks and observed characteristic features of a two-dimensional Ising spin glass. Specifically, the temperature dependence of the spin glass correlation function follows a power-law trend predicted from theoretical models on two-dimensional spin glasses¹¹. Furthermore, we observe clear signatures of the hard-to-observe rugged spin glass free energy¹ in the form of sub-aging, out-of-equilibrium autocorrelations¹² and a transition from stable to unstable dynamics^1,13.