Magnetization dynamics approaching an equilibrium vortex state from an initial nonequilibrium state under zero magnetic field has been studied in a circular-shaped Fe disk with a thickness of and a diameter of using micromagnetic simulations. Upon starting from the initial random configuration of in-plane magnetizations, a great number of vortex –antivortex pairs are generated at a lot of nucleation sites where both types of and are energetically favorable to form. The and are propagated and then annihilated by their attractive interactions during the relaxation dynamic process. These results reveal that temporal magnetization evolutions can be dominated by the nucleation of pairs, followed by their propagation and annihilation. The dynamic process driven by pairs can play a significant role in various magnetization reversals.
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This large value is used to save computation time for micromagnetic simulations, although a much lower value is suitable for investigating such picotime-scale dynamic process. We also performed it with and confirmed that the resultant microstructures on and remain similar to those calculated using , except for the occurrence and propagation of magnetization waves starting at a position where and collapse, as also found in Ref. 12. Further studies on the spin waves will be carried out.
Also, the values of , , and abruptly decrease when or is taken out through the boundary.