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 5nm and a diameter of 1200nm using micromagnetic simulations. Upon starting from the initial random configuration of in-plane magnetizations, a great number of vortex (V)–antivortex (V¯) pairs are generated at a lot of nucleation sites where both types of V and V¯ are energetically favorable to form. The V and V¯ 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 VV¯ pairs, followed by their propagation and annihilation. The dynamic process driven by VV¯ 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 α=0.01 and confirmed that the resultant microstructures on V and V¯ remain similar to those calculated using α=0.5, except for the occurrence and propagation of magnetization waves starting at a position where V and V¯ collapse, as also found in Ref. 12. Further studies on the spin waves will be carried out.

19.

Also, the values of Eex, Ems, and EexEms abruptly decrease when V or V¯ is taken out through the boundary.

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