Conditions for free magnetic monopoles in nanoscale square arrays of dipolar spin ice

We study a modified frustrated dipolar array recently proposed by M\"{o}ller and Moessner [Phys. Rev. Lett. \textbf{96}, 237202 (2006)], which is based on an array manufactured lithographically by Wang \emph{et al.} [Nature (London) \textbf{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 M\"{o}ller and Moessner, that the ground-state changes for $h>h_{1}$, where $h_{1}= 0.444a$ ($a$ 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 $h\approx h_1$ 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 $h=h_1$.Comment: 6 pages, 7 figures. Published versio

Phase transition in the two-dimensional dipolar Planar Rotator model

In this work we have used extensive Monte Carlo simulations and finite size scaling theory to study the phase transition in the dipolar Planar Rotator model (dPRM), also known as dipolar XY model. The true long-range character of the dipolar interactions were taken into account by using the Ewald summation technique. Our results for the critical exponents does not fit those from known universality classes. We observed that the specific heat is apparently non-divergent and the critical exponents are $\nu=1.277(2)$, $\beta=0.2065(4)$ and $\gamma=2.218(5)$. The critical temperature was found to be $T_c=1.201(1)$. Our results are clearly distinct from those of a recent Renormalization Group study from Maier and Schwabl [PRB 70, 134430 (2004)] and agrees with the results from a previous study of the anisotropic Heisenberg model with dipolar interactions in a bilayer system using a cut-off in the dipolar interactions [PRB 79, 054404 (2009)].Comment: 6 pages, 8 figures, Submitted to Journal of Physics: Condensed Matte