Effects of geometry on antiferromagnetic textures: boundaries and geometric curvature

Geometric curvature in nanowires and shells is established as a powerful method to tailor chiral and anisotropic responses in ferromagnets. Here, we apply the framework of curvilinear magnetism to antiferromagnetic (AFM) systems. First, we consider curvilinear AFM spin chains with the nearest-neighbor exchange and hard axis of anisotropy along the chain. Their shape is characterized by curvature κ and torsion τ. These functions determine the direction of the geometry-driven Dzyaloshinskii vector D and easy axis of anisotropy stemming from exchange. Furthermore, the broken translation symmetry in AFM chains arranged along space curves leads to the weakly ferromagnetic response proportional to κ and τ even if the magnetic texture is locally homogeneous. While the plane AFM chains possess the uniform ground state, the geometry-induced anisotropy axes and chiral response become pronounceable approaching spin-flop phase. Namely, in AFM rings the non-zero D leads to the appearance of canted state for the large enough κ, while spin-flop phase splits in two phases by the value of K with different topology of the order parameter. For 3D chiral AFMs, the sample boundaries alter the width and produce an additional twist of domain walls and skyrmions near the surface.