We study the magnetic excitations of a square lattice spin-ice recently produced in an artificial form, as an array of nanoscale magnets. Our analysis, based upon the dipolar interaction between the nanomagnetic islands, correctly reproduces the ground-state observed experimentally. In addition, we find magnetic monopole-like excitations effectively interacting by means of the usual Coulombic plus a linear confining potential, the latter being related to a string-like excitation binding the monopoles pairs, what indicates that the fractionalization of magnetic dipoles may not be so easy in two dimensions. These findings contrast this material with the three-dimensional analogue, where such monopoles experience only the Coulombic interaction. We discuss, however, two entropic effects that affect the monopole interactions: firstly, the string configurational entropy may loose the string tension and then, free magnetic monopoles should also be found in lower dimensional spin ices; secondly, in contrast to the string configurational entropy, an entropically driven Coulomb force, which increases with temperature, has the opposite effect of confining the magnetic defects.

We study a modified frustrated dipolar array recently proposed by Möller and Moessner [Phys. Rev. Lett. 96, 237202 (2006)], which is based on an array manufactured lithographically by Wang et al. [Nature (London) 439, 303 (2006)] and consists of introducing a height offset h between islands (dipoles) pointing along the two different lattice directions. The ground-states and excitations are studied as a function of h. We have found, in qualitative agreement with the results of Möller and Moessner, that the ground-state changes for h > h1, where h1 = 0.444a (a is the lattice parameter or distance between islands). In addition, the excitations above the ground-state behave like magnetic poles but confined by a string, whose tension decreases as h increases, in such a way that for h ≈ h1 its value is around 20 times smaller than that for h = 0. The system exhibits an anisotropy in the sense that the string tension and magnetic charge depends significantly on the directions in which the monopoles are separated. In turn, the intensity of the magnetic charge abruptly changes when the monopoles are separated along the direction of the longest axis of the islands. Such a gap is attributed to the transition from the anti to the ferromagnetic ground-state when h = h1.

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.

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.

The interactions between an excitation (similar to a pair of Nambu monopoles connected by their associated string) and a lattice defect are studied in an artificial two-dimensional square spin ice. This is done by considering a square array of islands containing only one island different from all others. This difference is incorporated in the magnetic moment (spin) of the "imperfect" island and several cases are studied, including the special situation in which this distinct spin is zero (vacancy). We show that the two extreme points of a defective island behave like two opposite magnetic charges. Then, the effective interaction between a pair of Nambu monopoles with the defective island is a problem involving four magnetic charges (two pairs of opposite poles) and a string. We also sketch the configuration of the field lines of these four charges to confirm this picture. The influence of the string on this interaction decays rapidly with the string distance from the defect.