Effect of Dzyaloshinsky–Moriya interaction on magnetic vortex: A real-space phase-field study

• A real-space phase field model is developed to for the magnetic vortex with DM interaction.
• The phase field model includes coupling between the magnetization and magnetization gradient.
• Governing equations are solved simultaneously by a nonlinear finite elements method.
• Simulation results show that DM interaction has significant influence on magnetization vortex.

A real-space phase field model is developed to investigate the effect of Dzyaloshinsky–Moriya (DM) interaction on magnetic vortex in ultrathin ferromagnetic film. Based on the time-dependent Ginzburg–Landau (TDGL) equation, the phase field model takes into account the DM interaction of magnetizations, which includes the coupling between the magnetization and magnetization gradient. The governing equations in the phase field model are solved simultaneously by means of a nonlinear finite elements method, which can be employed to simulate magnetization vortex without periodic boundary condition. The simulation results demonstrate that the DM interaction has significant influence on the structure of the magnetization vortex. It is found that the DM interaction induces an out-of-plane magnetization on the edge of the vortex and enlarges the size of the vortex core. The magnitude of the out-of-plane magnetization at the vortex core and the edge increases with the increase of DM constant. Besides, the handedness of magnetization vortex also changes when the sign of DM constant changes.

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