Vortex polarity in 2-D magnetic dots by Langevin dynamics simulations

Two-dimensional magnetic plots of finite size were simulated by integrating the Landau-Lifshitz equation for the isotropic Heisenberg model with a systematic exploration of the effect of dipole-dipole interactions of various strengths d, at a low temperature. Structures with or without vortices are observed, and in the cases in which vortices are present, out-of-plane contributions show only for relatively weak dipolar strengths: the integrated intensity of the out-of-plane component decreases roughly as 1/d with increasing dipolar strength while the vortex core width decreases as d−12. The coexistence of several vortices with an out-of-plane component seems limited to a narrow d-range, at least for the sample sizes studied. The size limit below which the vortices disappear decreases roughly as 1/d.