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Chiral antiferromagnets are currently considered for broad range ofapplications in spintronics, spin-orbitronics and magnonics. In contrast to theestablished approach relying on materials screening, the anisotropic and chiralresponses of low-dimensional antifferromagnets can be tailored relying on thegeometrical curvature. Here, we consider an achiral, anisotropicantiferromagnetic spin chain and demonstrate that these systems possessgeometry-driven effects stemming not only from the exchange interaction butalso from the anisotropy. Peculiarly, the anisotropy-driven effects arecomplementary to the curvature effects stemming from the exchange interactionand rather strong as they are linear in curvature. These effects areresponsible for the tilt of the equilibrium direction of vector orderparameters and the appearance of the homogeneous Dzyaloshinskii-Moriyainteraction. The latter is a source of the geometry-driven weak ferromagnetismemerging in curvilinear antiferromagnetic spin chains. Our findings provide adeeper fundamental insight into the physics of curvilinear antiferromagnetsbeyond the $\sigma$-model and offer an additional degree of freedom in thedesign of spintronic and magnonic devices.

Curvature-driven homogeneous Dzyaloshinskii-Moriya interaction and emergent weak ferromagnetism in anisotropic antiferromagnetic spin chains