String Phase in an Artificial Spin Ice

Abstract

One-dimensional strings of local excitations are a fascinating feature of the physical behavior of strongly correlated topological quantum matter. Here we study strings of local excitations in a classical system of interacting nanomagnets, the Santa Fe Ice geometry of artificial spin ice. We measured the moment configuration of the nanomagnets, both after annealing near the ferromagnetic Curie point and in a thermally dynamic state. While the Santa Fe Ice lattice structure is complex, we demonstrate that its disordered magnetic state is naturally described within a framework of emergent strings. We show experimentally that the string length follows a simple Boltzmann distribution with an energy scale that is associated with the system’s magnetic interactions and is consistent with theoretical predictions. The results demonstrate that string descriptions and associated topological characteristics are not unique to quantum models but can also provide a simplifying description of complex classical systems with non-trivial frustration.

Topological kinetic crossover in a nanomagnet array

“…1, C and D. SFI lends itself to the study of topological kinetics because, as we previously showed ( 14 ), the lattice geometry forces unhappy vertices to form one-dimensional (1D) strings that can either end within interior plaquettes or form closed loops [( 16 ), section S3]. In Fig.…”

“…Such arrays, known broadly as artificial spin ice systems, have displayed a range of exotic collective phenomena and technological potential ( 11 , 12 ). The particular array geometry that we studied is Santa Fe ice (SFI) ( 13 , 14 ). The structure of SFI is shown in Fig.…”

“…1, A, C, and D, light blue shaded areas) surrounded by six peripheral plaquettes. Much of the physics of this system can be understood through the moment configurations at the vertices where islands converge in the lattice ( 13 , 14 ). The SFI lattice geometry requires that some fraction of the vertices are not in the lowest local energy state, even in the collective ground state.…”

“…In Fig. 1, C and D, we show these strings as olive lines connecting the unhappy vertices in two realizations of the highly degenerate, disordered ground state of the system ( 13 , 14 ). Such strings have naturally complex topological properties ( 17 ), as is readily apparent in a bowl of spaghetti or udon ( 18 , 19 ).…”

Machine learning-based prediction and inverse design of 2D metamaterial structures with tunable deformation-dependent Poisson's ratio

“…ML method 30 is a promising approach for alternatively dealing with a large fraction of data and sweeping over a huge design space, avoiding the rigorous requirements of the aforementioned conditions. For instance, by providing a tailored computational scheme, ML substantially accelerates the satisfactory prediction of mechanical properties and inverse design of metamaterials.…”