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

Spin glasses, generally defined as disordered systems with randomized competing interactions1,2, are a widely investigated complex system. Theoretical models describing spin glasses broadly used in other systems, such those brain function3,4, error-correcting codes5 or stock-market dynamics6. This wide interest provides strong motivation to generate an artificial glass within the framework of ice systems7–9. Here we present experimental realization consisting dipolar coupled single-domain Ising-type nanomagnets arranged onto interaction network that replicates aspects Hopfield neural network10. Using cryogenic X-ray photoemission electron microscopy (XPEEM), performed temperature-dependent imaging thermally driven moment fluctuations these networks and observed characteristic features two-dimensional Ising glass. Specifically, temperature dependence correlation function follows power-law trend predicted from theoretical on glasses11. Furthermore, observe clear signatures hard-to-observe rugged free energy1 form sub-aging, out-of-equilibrium autocorrelations12 transition stable unstable dynamics1,13. A is system magnetic interactions. Now, metamaterial based reported, rudimentary network.