We show that triangle-based antiferromagnets with “antichiral” order display a nontrivial dependence of the spin orientation with an in-plane field. The spins evolve from rotating in the opposite sense to the field at very low fields to rotating in the same sense as the field above some critical field scale. In the latter regime the system displays first-order transitions at which the spin angles jump, and these first-order lines terminate in critical points in the Ising universality class. Application to ${\mathrm{Mn}}_3\mathrm{Sn}$ is discussed.

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• Antiferromagnetism
• Frustrated magnetism
• Magnetic anisotropy
• Magnetic phase transitions
• Landau-Ginzburg-Wilson theory
• Symmetries in condensed matter