Magnetic disks or dots of soft magnetic material of sub-micron dimensions may have as the lowest energy magnetic configuration a single-domain structure, with magnetization either perpendicular of parallel to the plane, or else may form magnetic vortices. The properties of these vortices may be used to encode data bits, in magnetic memory applications. In the present work the OOMMF code was used to compute by micromagnetic simulation the energy and the magnetization of circular and elliptical nanodots of permalloy. For the elliptical magnetic dots the analysis was made for variable thickness and length of major axis, keeping a 2:1 axis ratio. From the simulations, a phase diagram was constructed, where the ground state configurations of the nanodots are represented in a diagram of nanodot height versus length of the major axis $2a$ of the ellipse. The phase diagram obtained includes regions with one and two vortices; it is similar, but more complex than that derived using a numerical scaling approach, since it includes configurations with lateral vortices. These diagrams are useful as guides for the choice of dimensions of elliptical nanodots for practical applications.
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