Manipulation by magnetic frustration in ferrotoroidal spin chains via curvature and torsion

Geometric effects in curvilinear nanomagnets can enable chiral, anisotropic, and even magnetoelectric responses. Here, we study the effects of magnetic frustration in curvilinear (quasi-)one-dimensional magnets represented by spin chains arranged along closed space curves of constant torsion. Considering the cases of easy- and hard-axis anisotropy in ferro- and antiferromagnetic samples, we determine their ground states and analyze the related magnetoelectric multipoles. A constant torsion along the chain results in alternating regions of high and low curvature, facilitating the spin spiral state perturbed by the (anti)periodic boundary conditions on the magnetic order parameter. While easy-axis ferromagnetic chains develop a purely toroidal configuration with the magnetic toroidal moment oriented along the geometry symmetry axis, hard-axis antiferromagnetic chains support multiple magnetic toroidal domains. Our findings suggest that tailoring curvature and torsion of a spin chain enables a different physical mechanism for magnetic frustration, which can be observed in the inhomogeneity of the magnetic order parameter and in the local ferrotoroidal responses.