Artificial spin-ice systems (ASI) have been studied for 15 years, allowing detailed studies to examine the frustration, ordering and monopole transport in a variety of two-dimensional geometries [1]. The nanostructuring of magnetic materials in three-dimensions presents a new paradigm in condensed matter physics and allows access to a wide range of new physical phenomena [2]. With respect to ASI systems, there are several reasons why 3D geometries are interesting. This includes the realisation of a degenerate ice-rule, mimicking of bulk spin-ice geometries and studying the influence of surfaces upon ordering. In this talk, I will outline the realisation of a 3D artificial spin-ice system [3] which takes the geometry of a diamond-bond lattice (Fig. 1), capturing the arrangement of spins in bulk pyrochlore systems. By using magnetic force microscopy (Fig. 2), I will show that the vertex states upon the surface can be determined, and the global switching of the lattice can be measured. We find very different magnetic charge dynamics along two principal directions upon the lattice. For a field applied along the surface termination, local energetics force magnetic charges to nucleate over a larger characteristic distance, reducing their magnetic Coulomb interaction and producing lone, uncorrelated monopoles. In contrast, applying a field transverse to the surface termination yields large numbers of highly correlated monopole-antimonopole pairs. A combination of micromagnetic and Monte-Carlo simulations are used to understand the results. These suggest it is the difference in effective chemical potential that yields the striking differences in monopole transport. We anticipate that our study will inspire a new generation in artificial spin-ice research whereby the ground states in complex 3D frustrated lattices are explored.

![](https://assets.underline.io/uploads/markdown_image/1/image/68e61fe5f53c1aa5f59122b57dafa546.jpg)

Fig 1. Atomic force microscopy image of the 3DASI system. Distinct layers within the system are labelled L1 - L3.

![](https://assets.underline.io/uploads/markdown_image/1/image/6da2b1e596bc9e183b4530846549ee08.jpg)

Fig 2. Magnetic force microscopy of the 3DASI surface, showing a number of ice-rule and monopole states.

Magnetic charge propagation upon a 3D artificial spin-ice

Spin glasses, generally defined as disordered systems with randomized competing interactions that result in an extensively degenerate ground state1, 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, error-correcting codes4, or stock-market dynamics5. This wide interest in spin glasses provides strong motivation to generate an artificial spin glass within the framework of artificial spin ice systems6. Here, we present the first 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 network7. 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. Furthermore, we observe clear signatures of the hard to observe rugged spin glass free energy1 in the form of sub-aging, out of equilibrium autocorrelations1 and a transition from convergent to divergent dynamics1, 8.

![](https://assets.underline.io/uploads/markdown_image/1/image/b3ae2199ab934834ddc1bb2571df82f4.jpg)

Direct observation of a Dynamical Glass Transition in a Nanomagnetic Artificial Hopfield Network

**Session chair:** Pavel Ripka, Czech Technical University



EOA - 3D Nanomagnetism and Nanowire Arrays

technical paper

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

2022 Joint MMM-INTERMAG

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

**Session chairs:** Tom Thomson, University of Manchester and Hikaru Nomura, Yoshishige Suzuki Lab, Osaka University



Michael Saccone

2

6

SHORT BIO

Presentations

Magnetic charge propagation upon a 3D artificial spin-ice

Direct observation of a Dynamical Glass Transition in a Nanomagnetic Artificial Hopfield Network

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