Curvilinear and 3D micromagnetism: geometrically curved ferro- and antiferromagnets

Curvilinear magnetism is a framework, which helps understanding the impact of geometrical curvature on complex magnetic responses of curved 1D wires and 2D shells [1-3]. The lack of inversion symmetry and emergence of curvature induced anisotropy and Dzyaloshinskii-Moriya interaction (DMI) stemming from the exchange interaction [4,5] are characteristic of curved surfaces. Recently, a non-local chiral symmetry breaking was discovered [6], which is responsible for the coexistence and coupling of multiple magnetochiral properties within the same magnetic object [7].
Regarding antiferromagnets, it is demonstrated that intrinsically achiral one-dimensional curvilinear antiferromagnets behave as a chiral helimagnet with geometrically tunable DMI, orientation of the Neel vector and the helimagnetic phase transition [8-10]. This positions curvilinear antiferromagnets as a platform for geometrically tunable antiferromagnetic spinorbitronics.

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[6] D. Sheka et al., Commun. Phys. 3, 128 (2020).
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[9] O. Pylypovskyi et al., APL 118, 182405 (2021).
[10] Y. Borysenko et al., PRB 106, 174426 (2022).