High-topological-number magnetic skyrmions

High-topological-number magnetic skyrmions and topologically protected dissipative structure.

Xichao Zhang, Yan Zhou, and Motohiko Ezawa
Phys. Rev. B 93, 024415 (2016)

Time evolution of the high-Q skyrmion (Q=2). (a) Time evolution of the total energy Etotal, the DMI energy EDMI, the topological number Q, the in-plane (mx,my) and out-of-plane mz components of magnetization averaged over the simulation area, and the dissipation functions W. A high-Q skyrmion with Q=2 is created nearly at t=0.38 ns. The DMI constant D=2 mJ m−2. The spin current density j=3×1012 A m−2. The external magnetic field Bz=250 mT. (b) Top views of the magnetization distributions mx,my, and mz of the FM nanodisk, the corresponding topological charge density distribution q, and the Rayleigh dissipation function W at selected times. The green circle indicates the spin current injection region. The nucleation of a high-Q skyrmion with Q=2 occurs nearly at t=0.38 ns, where the dissipation function spreads all over the FM nanodisk, implying that the spin wave propagates. The DMI is turned off at t=10 ns. It is remarkable that the high-Q skyrmion remains stable even if the DMI is switched off, which demonstrates the topological protection against the change of a variable, that is, the DMI.