We investigate the thermodynamics of artificial square spin ice systems assuming only dipolar interactions among the islands that compose the array. Emphasis is given to the effects of temperature on elementary excitations (magnetic monopoles and their strings). By using Monte Carlo techniques we calculate the specific heat, the density of poles and their average separation as functions of temperature. The specific heat and average separation between monopoles with opposite charges exhibit a sharp peak and a local maximum, respectively, at the same temperature, T p ≈ 7.2D/k B (here, D is the strength of the dipolar interaction and k B the Boltzmann constant). When the lattice size is increased, the amplitude of these features also increases but very slowly. Really, the specific heat and the maximum of the average separation d max between oppositely charged monopoles increase logarithmically with system size, indicating that completely isolated charges could be found only at the thermodynamic limit. In general, the results obtained here suggest that, for temperatures T T p , these systems may exhibit a phase with separated monopoles, although the quantity d max should not be larger than a few lattice spacings for viable artificial materials.

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.

Abstract. We study a frustrated two-dimensional array of dipoles forming an artificial rectangular spin ice with horizontal and vertical lattice parameters given by a and b respectively. We show that the ice regime could be stabilized by appropriate choices for the ratio γ ≡ a/b. Our results show that for γ ≈ √ 3, i.e. when the centers of the islands form a triangular lattice, the ground state becomes degenerate. Therefore, while the magnetic charges (monopoles) are excitations connected by an energetic string for general rectangular lattices (including the particular case of a square lattice), they are practically free to move for a special rectangular lattice with γ ≈ √ 3. Besides that, our results show that for γ > √ 3 the system is highly anisotropic in such a way that, even for this range out of the ice regime, the string tension almost vanishes along a particular direction of the array. We also discuss the ground state transition and some thermodynamic properties of the system.

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]

In this work, we have constructed and experimentally investigated frustrated arrays of dipoles forming two-dimensional artificial spin ices with different lattice parameters (rectangular arrays with horizontal and vertical lattice spacings denoted by a and b respectively). Arrays with three different aspect ratios γ = a/b = , and are studied. Theoretical calculations of low-energy demagnetized configurations for these same parameters are also presented. Experimental data for demagnetized samples confirm most of the theoretical results. However, the highest energy topology (doubly-charged monopoles) does not emerge in our theoretical model, while they are seen in experiments for large enough γ. Our results also insinuate that the string tension connecting two magnetic monopoles in a pair vanishes in rectangular lattices with a critical ratio γ = γ c = , supporting previous theoretical predictions.