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 codes 5 or stock-market dynamics 6 . 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 network 10 . 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 glasses 11 . Furthermore, we observe clear signatures of the hard-to-observe rugged spin glass free energy 1 in the form of sub-aging, out-of-equilibrium autocorrelations 12 and a transition from stable to unstable dynamics 1 , 13 . A spin glass is a disordered system with randomized competing magnetic interactions. Now, a metamaterial artificial spin glass based on nanomagnets is reported, with rudimentary features of a neural network.