We report the formation of a ${\mathbb{Z}}_2$ vortex crystal in the tetrahedral antiferromagnetic order on a triangular lattice. The noncoplanar tetrahedral state consists of four sublattices with spins oriented along the faces of a tetrahedron in spin space. The long-range order characterized by a ${\mathbb{Z}}_2$ topology arises due to the Dzyaloshinskii-Moriya interaction and appears at zero temperature and without external fields. Each vortex carries a half-integer electric charge relative to the uniform background in itinerant magnets, enabling the emergence of anyonic excitations. Its magnetic excitations include magnetically active gyrotropic and breathing modes, which—under an external magnetic field—carry nontrivial Chern numbers that stabilize chiral magnon edge states.

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• Magnetic vortices
• Magnons
• Skyrmions
• Topological defects
• Antiferromagnets
• Noncollinear magnets
• Topological materials