Magnetic vortices in soft ferromagnetic nano-disks have been extensively studied for at least several decades both for their applied (non-volatile information storage) as well as fundamental value. Here, it is shown that there is another vortex ground state with large radius-dependent core profile in nano-scale ferromagnetic disks of several exchange lengths in size. Its energy is computed numerically and its stability is studied analytically, which allows to plot it on magnetic phase diagram. Large vortices may exist on par with the classical ones, while being separated by an energy barrier, controllable by tuning the geometry and material of ferromagnetic disk.
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