Effects of geometry and topology in curvilinear ferro- and antiferromagnets

The behaviour of any physical system is determined by the order parameter whose distribution is governed by the geometry of the physical space of the object, in particular its dimensionality and curvature [1]. Curvilinear magnetism is a framework, which helps understanding the impact of geometrical curvature on complex magnetic responses of curved 1D wires and 2D shells [2-4]. The lack of inversion symmetry and emergence of curvature induced anisotropy and Dzyaloshinskii-Moriya interaction (DMI) stemming from the exchange interaction [5,6] are characteristic of curved surfaces. Recently, a non-local chiral symmetry breaking was discovered [7], which is responsible for the coexistence and coupling of multiple magnetochiral properties within the same magnetic object [8]. 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 [9-11]. This positions curvilinear antiferromagnets as a platform for geometrically tunable antiferromagnetic spinorbitronics.

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