Geometry-driven effects in curvilinear spin chains with antiferromagnetic exchange

Curvilinear magnetism is a research field studying curved nanowires and thin films with anisotropic and chiral magnetic responses are tailored by the geometry. The contemporary theories reach the level of maturity for ferromagnets [1,2]. At the same time, very little is done for antiferromagnets (AFMs), which are promising for low-power consuming and high-speed spintronic devices [2].

The simplest systems uncovering the specific features of AFM exchange in curvilinear geometries are spin chains, which can be arranged along plane and space curves. If the dipolar interaction is the dominating source of anisotropy, it renders the chain as the hard-axis AFM with the anisotropy axis along the tangential direction. There are two families of effects of geometry stemming from exchange. The first ones come from the spatial gradients of the Néel vector. A direction of local twists and bends of the chain manifests itself as the geometry-driven DMI and contributes to the tensor of total anisotropy [3]. As a consequence, the curvilinear AFM spin chain along space curve with exchange and dipolar interaction behaves as the chiral helimagnet, with the helimagnetic transition determined by the curvature and torsion of the curve. Such a chain arranged along the plane curve has the one ground state with the equilibrium Néel ordering perpendicular to the curve plane. In both cases, the easy axis of anisotropy arises from the exchange [3]. Localized bends of the curve also lead to the pinning of domain walls [4]. In addition to the chiral and anisotropic effects, the locally broken spatial symmetry of the AFM chain leads to the geometry-driven weak ferromagnetism. The strength of the emergent magnetization scales linearly with the curvature and torsion [5].

A unit cell of AFM contains a few spins. For the case of the single-ion anisotropy, its direction is varyring within the unit cell. This leads to the specific contributions to the magnetic responses stemming from anisotropy, such as an anisotropic term which mixes the tangential and normal components of the Néel and ferromagnetic order parameters as the DMI of longitudinal symmetry [5]. This can be of importance for non-collinear textures in one-dimensional AFMs, where the finite magnetization appears at inhomogeneity of the Néel vector.

[1] P. Fischer et al, APL Mater., 8, 010701 (2020); R. Streubel et al. Journal of Applied
Physics, 129, 210902 (2021)
[2] D. Makarov et al, Adv. Mater., 34, 2101758 (2022)
[3] O. Pylypovskyi, D. Kononenko et al, Nano Lett., 20, 8157–8162 (2020)
[4] K. Yershov, Phys. Rev. B, 105, 064407 (2022)
[5] O. Pylypovskyi et al, App. Phys. Lett., 118, 182405 (2021)