The Dzyaloshinskii-Moriya interaction, i.e., antisymmetric exchange interaction, combined with a Zeeman magnetic field gives rise to various magnetic states such as chiral, helical, and skyrmionic states. This interaction conventionally originates from spin-orbit coupling and thus needs somewhat heavy elements. In contrast, we here show a Dzyaloshinskii-Moriya interaction which is driven by electric current vorticity. We also find that the vorticity acts on localized spins as a Zeeman field, which may explain a recent experiment on current-driven magnetic skyrmion creation and annihilation without an external magnetic field in a device with a notch structure in FeGe. theory explains the control of skyrmion creation and annihilation by current direction and opens different possibilities for studies of magnetic textures by using structural settings.

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• Dzyaloshinskii-Moriya interaction
• Magnetic texture
• Skyrmions
• Finite temperature field theory
• Hydrodynamics