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Magnetic vortex-antivortex crystals generated by spin-polarized current

We study vortex pattern formation in thin ferromagnetic films under the action of strong spin-polarized currents. Considering the currents which are polarized along the normal of the film plane, we determine the critical current above which the film goes to a saturated state with all magnetic moments being perpendicular to the film plane. We show that stable square vortex-antivortex superlattices (\emph{vortex crystals}) appears slightly below the critical current. The melting of the vortex crystal occurs with current further decreasing. A mechanism of current-induced periodic vortex-antivortex lattice formation is proposed. Micromagnetic simulations confirm our analytical results with a high accuracy.