For the last decade, active research on magnetic nanosystems of curved geometry was motivated by their outstanding properties and great application potential . For instance, recent theoretical studies of low-dimensional magnets with complex geometry propose a description of fascinating geometry-induced effects including pattern formation and magnetochiral effects in quasi-one-dimensional wires , for review see . Despite these advances in the study of curvilinear low-dimensional ferromagnets, significant knowledge gaps exist in the study of curvilinear antiferromanetic systems.
The purpose of the current study is the theoretical investigation of equilibrium states in antiferromagnetic ring-shaped and helix-shaped spin chains with hard-tangential anisotropy. For this purpose we use both analytical methods and computer spin-lattice simulations in SLaSi software package . In our study, we consider two sublattice antiferromagnet in the frame of the sigma-model approach where its statics and dynamics are described in terms of Neel vector only.
We analytically show that the global energy minimum of the antiferromagnetic ring-shaped spin chain is reached when Neel vector is perpendicular to the ring plane. An equilibrium phase diagram is constructed for the antiferromagnetic helix-shaped spin chain: (i) a quasi-binormal state is realized in the case of relatively large curvatures and (ii) spatial-periodic state is typical in the opposite case. Both states are described analytically and well confirmed by SLaSi.
Stability regions of both ground states are determined using spin-lattice simulator SLaSi.
 R. Streubel, P. Fischer, F. Kronast, V. P. Kravchuk, D. D. Sheka, Y. Gaididei, O. G. Schmidt and D. Makarov, J. Phys. D, 49, 363001, (2016).
 D. D. Sheka, V. P. Kravchuk, Y. Gaididei, J. Phys. A, 48, 125202, (2015).