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 choice
s for the ratio $gamma equiv a/b$. Our results show that for $gamma approx sqrt{3}$, i.e., when the center 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 $gamma approx sqrt{3}$. Besides that, our results show that for $gamma > sqrt{3}$ 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.
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 grou
nd-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.
This paper has been withdrawn by the authors due to a possible inconsistency in the program code.
