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

Michael Saccone*, Francesco Caravelli, Kevin Hofhuis, Sergii Parchenko, Yorick A. Birkhölzer, Scott Dhuey, Armin Kleibert, Sebastiaan van Dijken, Cristiano Nisoli, Alan Farhan

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

15 Citations (Scopus)


Spin glasses, generally defined as disordered systems with randomized competing interactions1,2, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those describing brain function3,4, 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 systems7–9. 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 dynamics1,13.

Original languageEnglish
Pages (from-to)517-521
Number of pages5
JournalNature Physics
Issue number5
Early online date17 Mar 2022
Publication statusPublished - May 2022
MoE publication typeA1 Journal article-refereed


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