Magnetic artificial spin ice provides examples of how competing interactions between magnetic nanoelements can lead to a range of fascinating and unusual phenomena. We examine theoretically a class of spin ice tilings, called pinwheel, for which near degeneracy of spin configuration energies can be achieved. The pinwheel tiling is a simple but crucial variant on the square ice geometry, in which each nanoelement of square ice is rotated some angle about its midpoint. Surprisingly, this rotation leads to an intriguing phase transition; and even though the spins are not parallel to one another, a ferromagnetic phase is found for rotation angles near 45• . Here, magnetic domains and domain walls are found when viewed in terms of net magnetisation. Moreover, the ferromagnetic behaviour of the system depends on its anisotropy which we can control by array shape and size.

For over ten years, arrays of interacting single-domain nanomagnets, referred to as artificial spin ices, have been engineered with the aim to study frustration in model spin systems.Here, we use Fresnel imaging to study the reversal process in 'pinwheel' artificial spin ice, a modified square ASI structure obtained by rotating each island by some angle about its midpoint. Our results demonstrate that a simple 45 • rotation changes the magnetic ordering from antiferromagnetic to ferromagnetic, creating a superferromagnet which exhibits mesoscopic domain growth mediated by domain wall nucleation and coherent domain propagation. We observe several domain-wall configurations, most of which are direct analogues to those seen in continuous ferromagnetic films. However, novel charged walls also appear due to the geometric constraints of the system. Changing the orientation of the external magnetic field allows control of the nature of the spin reversal with the emergence of either 1-D or 2-D avalanches. This unique property of pinwheel ASI could be employed to tune devices based on magnetotransport phenomena such as Hall circuits.Artificial spin ice (ASI) systems have been used not only as a route to new physical phenomena, but also to gain insight into fundamental physics. Such capabilities are only possible because these structures are able to emulate the behaviour of assemblies of the individual spins in atomic 1 arXiv:1808.10490v1 [cond-mat.dis-nn]

Rotating all islands in square artificial spin ice (ASI) uniformly about their centres gives rise to the recently reported pinwheel ASI. At angles around 45 o , the antiferromagnetic ordering changes to ferromagnetic and the magnetic configurations of the system exhibit near-degeneracy, making it particularly sensitive to small perturbations. We investigate through micromagnetic modelling the influence of dipolar fields produced by physically extended islands in field-driven magnetisation processes in pinwheel arrays, and compare the results to hysteresis experiments performed in-situ using Lorentz transmission electron microscopy. We find that magnetisation end-states induce a Heisenberg pseudo-exchange interaction that governs both the inter-island coupling and the resultant array reversal process. Symmetry reduction gives rise to anisotropies and array-corner mediated avalanche reversals through a cascade of nearest-neighbour (NN) islands. The symmetries of the anisotropy axes are related to those of the geometrical array but are misaligned to the array axes as a result of the correlated interactions between neighbouring islands. The NN dipolar coupling is reduced by decreasing the island size and, using this property, we track the transition from the strongly coupled regime towards the pure point dipole one and observe modification of the ferromagnetic array reversal process. Our results shed light on important aspects of the interactions in pinwheel ASI, and demonstrate a mechanism by which their properties may be tuned for use in a range of fundamental research and spintronic applications.

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.

We present a design for an omnidirectional transformation-optics (TO) cloak comprising thin lenses and glenses (generalized thin lenses) [J. Opt. Soc. Am. A33, 962 (2016)1084-7529JOAOD610.1364/JOSAA.33.000962]. It should be possible to realize such devices in pixelated form. Our design is a piecewise nonaffine generalization of piecewise affine pixelated-TO devices [Proc. SPIE9193, 91931E (2014)PSISDG0277-786X10.1117/12.2061404; J. Opt18, 044009 (2016)]. It is intended to be a step in the direction of TO devices made entirely from lenses, which should be readily realizable on large length scales and for a broad range of wavelengths.