Curvilinear magnetism: geometrically curved ferro- and antiferromagnets

The main origin of the chiral symmetry breaking in magnetic materials is associated with the intrinsic Dzaloshinskii-Moriya interaction (DMI). At present, tailoring of DMI is done rather conventionally by optimizing materials, either doping a bulk single crystal or adjusting interface properties of thin films and multilayers. A viable alternative to the conventional material screening approach can be the exploration of the interplay between geometry and topology. The research field in magnetism, which is dealing with the study of the impact of geometrical curvature on magnetic responses of curved 1D wires and 2D shells is known as curvilinear magnetism [1]. The perspective of the development of curvilinear magnetism is outlined in the 2017 and 2020 Magnetism Roadmaps [2,3]. In this presentation, we will discuss on the recent achievements in the field and address the following topics:

A fully 3D approach to treat curvilinear effects in ferromagnetic nanowires and thin shells of arbitrary shape is established by Gaididei et al. back in 2014 [4] and was recently extended by Sheka et al. [5] to properly account for effects of non-locality due to the presence of long-range magnetostatic interaction. Volkov et al. has proven that the exchange-driven chiral effects in curvilinear ferromagnets are experimental observables [6] and can be used to realize nanostructures with tunable magnetochiral properties from standard magnetic materials.
In contrast to the intrinsic DMI, a concept of mesoscale Dzyaloshinskii-Moriya interaction was put forth, which is a result of the interplay between the intrinsic (spin-orbit-driven) and extrinsic (curvature-driven) DMI terms [7]. The mesoscale DMI governs the magnetochiral properties of any curvilinear ferromagnetic nanosystem and depends both on the material and geometrical parameters. Its strength and orientation can be tailored by properly choosing the geometry, which allows stabilizing distinct magnetic chiral textures including skyrmion and skyrmionium states as well as skyrmion lattices [8-10]. Interestingly, skyrmion states can be formed in a material even without an intrinsic DMI [8,10].
Sheka et al. [5] discovered a novel non-local chiral symmetry breaking effect, which does not exist in planar magnets: it is essentially non-local and manifests itself even in static spin textures living in curvilinear magnetic nanoshells. To identify this new interaction, a generalized micromagnetic theory of curvilinear ferromagnets was constructed accounting for local and nonlocal effects. The curvature leads to the emergence of the new magnetostatic charge, the geometrical charge, determined by the local characteristics of the surface. This newcomer is responsible for the appearance of novel fundamental chiral symmetry breaking effect.
The field of curvilinear magnetism was recently extended towards curvilinear antiferromagnets. Pylypovskyi et al. [11] demonstrated that intrinsically achiral one-dimensional curvilinear antiferromagnet behaves as a chiral helimagnet with geometrically tunable DMI, orientation of the Neel vector and the helimagnetic phase transition. This positions curvilinear antiferromagnets as a novel platform for the realization of geometrically tunable chiral antiferromagnets for antiferromagnetic spinorbitronics.

[1] Streubel et al., J. Phys. D: Appl. Phys. 49, 363001 (2016).
[2] Sander et al., J. Phys. D: Appl. Phys. 50, 363001 (2017).
[3] Vedmedenko et al., J. Phys. D: Appl. Phys. 53, 453001 (2020).
[4] Gaididei et al., PRL 112, 257203 (2014).
[5] Sheka et al., Communications Physics 3, 128 (2020).
[6] Volkov et al., PRL 123, 077201 (2019).
[7] Volkov et al., Scientific Reports 8, 866 (2018).
[8] Kravchuk et al., PRB 94, 144402 (2016).
[9] Kravchuk et al., PRL 120, 067201 (2018).
[10] Pylypovskyi et al., Phys. Rev. Appl. 10, 064057 (2018).
[11] Pylypovskyi et al., Nano Letters (2020). doi:10.1021/acs.nanolett.0c03246.