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A model for vortex formation in magnetic nanodots

We use Monte Carlo simulation to study the vortex nucleation on magnetic nanodots at low temperature. In our simulations, we have considered a simple microscopic two-dimensional anisotropic Heisenberg model with term to describe the anisotropy due to the presence of the nanodot edge. We have considered the thickness of the edge, which was not considered in previous works, introducing a term that controls the energy associated to the edge. Our results clearly show that the thickness of the edge has a considerable influence in the vortex nucleation on magnetic nanodots. We have obtained the hysteresis curve for several values of the surface anisotropy and skin depth parameter ($ξ$). The results are in excellent agreement with experimental data.