Tuning magnetic order with geometry: Thermalization and defects in two-dimensional artificial spin ices

Abstract

Artificial spin ices are arrays of correlated nano-scale magnetic islands that prove an excellent playground in which to study the role of topology in critical phenomena. Here, we investigate a continuum of spin ice geometries, parameterised by rotation of the islands. In doing so, we morph from the classic square ice to the recently studied pinwheel geometry, with the rotation angle acting as a proxy for controlling inter-island interactions. We experimentally observe a transition from antiferromagnetic ordering in square ice to a slight preference for ferromagnetic vertices in the weakly-coupled pinwheel ice using Lorentz transmission electron microscopy on thermally annealed cobalt arrays. The rotation angle also affects the relaxation timescales for individual arrays, leading to varying degrees of thermalisation, and an apparent change in the nature of the defects supported: from one-dimensional strings in square ice to two-dimensional vortex-like structures for geometries similar to pinwheel. The numerical scaling of these quantities is consistent with that predicted by the Kibble-Zurek mechanism. Our results show how magnetic order in artificial spin ices can be tuned by changes in geometry and suggest the possibility of realising a truly frustrated icerule phase in two-dimensional systems. Furthermore, we demonstrate this system as a testbed to investigate out-of-equilibrium dynamics across phases.

Quenched dynamics of artificial colloidal spin ice

“…Alternatively, at much faster quench rates than those we consider, there could be a regime of KZ behavior in which the defects simply do not have time to move. There is some recent Monte Carlo-based numerical work on magnetic spin ice systems in which the quench dynamics was shown to be consistent with the KZ mechanism [52]. For 3D magnetic spin ice systems there is evidence for KZ scaling [40]; however, in three dimensions, defects such as monopoles are not bound and are able to wander freely.…”

Tailoring magnetization reversal of a single-domain bar nanomagnet via its end geometry

“…For example, coupled bar nanomagnets were used to design majority logic gates for low dissipation digital computation in magnetic quantum-dot cellular automata systems 1 . In artificial spin ices, the bistable magnetization of these bar nanomagnets behaves like macro-Ising spins [2][3][4][5][6][7][8][9][10][11][12][13][14][15] . Specially arranged interacting single-domain bar magnets in artificial spin ices enable the investigation of geometric frustration 2,3 , emergent magnetic monopoles [6][7][8] and phase transitions [9][10][11][12][13][14] in a materialby-design approach.…”

Field‐Driven Reversal Models in Artificial Spin Ice

“…dimensionality of the reversal mechanism from 1D Dirac strings in square [30] to 2D in pinwheel [31] by varying makes this system particularly interesting for applications and studying models of phase transitions. [32,33] The reconfigurability of this spin system has been used to create modulating fields in hybrid devices, [34,35] while the complex field-driven spatio-temporal patterns it supports has been identified as particularly interesting for reservoir computing due to the presence of non-linearity and memory in the system. [6,36] Importantly, the reversal process in pinwheel ASI [31] is not purely due to changes in the distribution of dipolar coupling strengths, [29] but it has also been attributed to a breaking of the Ising nature of the island magnetization.…”

“…The ability to alter the mesoscale magnetic ordering, the magnetic texture, and the dimensionality of the reversal mechanism from 1D Dirac strings in square [ 30 ] to 2D in pinwheel [ 31 ] by varying α makes this system particularly interesting for applications and studying models of phase transitions. [ 32,33 ] The reconfigurability of this spin system has been used to create modulating fields in hybrid devices, [ 34,35 ] while the complex field‐driven spatio‐temporal patterns it supports has been identified as particularly interesting for reservoir computing due to the presence of non‐linearity and memory in the system. [ 6,36 ]…”