The magnetic vortex structure, that is present in several nanoscopic systems, is stable and can be manipulated through the application of a magnetic field or a spin polarized current. The size and shape of the core are strongly affected by the anisotropy, however its role on the core behavior has not yet been clarified. In the present work we investigate the influence of a perpendicular anisotropy on the annihilation and shape of magnetic vortex cores in permalloy disks. We have used both micromagnetic simulations with the OOMMF code, and an analytical model that assumes that the shape of the core does not change during the hysteresis cycle, known as the rigid core model, to calculate the annihilation fields. In both cases we found that the annihilation fields decrease with increasing perpendicular anisotropy for almost all the structures investigated. The simulations show that for increasing anisotropy or dot thickness, or both, the vortex core profile changes its shape, becoming elongated. For every dot thickness, this change does not depend on the dot radius, but on the relative distance of the core from the center of the dot.
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