Effects of static magnetic fields in antiferromagnetic ring-shaped spin chains

While antiferromagnets with the easy axis of anisotropy are considered to be robust against external magnetic fields of a moderate strength, strong-field-driven spin reorientations provide an insight into subtle properties of the material usually hidden by the high symmetry of the ground state. Here, we address theoretically the effects of curvature in the curvilinear antiferromagnetic achiral anisotropic ring-shaped spin chains in strong magnetic fields. We identify the geometry-driven helimagnetic phase transition above the spin-flop field between the vortex and onion states. The spin-flop transition is of the first- or second-order depending on the ring curvature, which is influenced by the geometry-induced Dzyaloshinskii–Moriya interaction. Inhomogeneity of the Néel vector distribution in spin-flop phase generates weakly ferromagnetic response, which lies in the plane perpendicular to the applied magnetic field. Our findings provide an understanding of complex responses of curvilinear antiferromagnets on magnetic fields and allow further experimental study of geometrical effects relying on spin-chain-based nanomagnets.