Geometry-induced effects in antiferromagnetic spin chains

Antiferromagnetic nanostructures as objects with ultrahigh eigenfrequencies and low sensitivity to demagnetizing fields are promising candidates for applications in data storage and information processing. Three-dimensional architectures enable new ways for tuning magnetic responses and extend ideas of spintronic devices. Here, we analyze anitferromagnetically ordered curvilinear spin chains and derive a Lagrangian taking into account the exchange interaction and effective anisotropy arising from the dipolar interaction. The static and dynamic properties of the spin system are influenced by emergent geometry-induced anisotropies and Dzyaloshinskii--Moriya interaction, which are illustrated by ring and helix geometries as case studies. Ground states and coupling of spin wave modes due to curvilinear geometry are described.