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We show that the interaction of the magnetic subsystem of a curved magnet with the magnet curvature results in the coupling of a topologically nontrivial magnetization pattern and topology of the object. The mechanism of this coupling is explored and illustrated by an example of a ferromagnetic Möbius ring, where a topologically induced domain wall appears as a ground state in the case of strong easy-normal anisotropy. For the Möbius geometry, the curvilinear form of the exchange interaction produces an additional effective Dzyaloshinskii-like term which leads to the coupling of the magnetochirality of the domain wall and chirality of the Möbius ring. Two types of domain walls are found, transversal and longitudinal, which are oriented across and along the Möbius ring, respectively. In both cases, the effect of magnetochirality symmetry breaking is established. The dependence of the ground state of the Möbius ring on its geometrical parameters and on the value of the easy-normal anisotropy is explored numerically.

Antiferromagnets offer remarkable promise for future spintronics devices, where antiferromagnetic order is exploited to encode information [1][2][3]. The control and understanding of antiferromagnetic domain walls (DWs) -the interfaces between domains with differing order parameter orientations -is a key ingredient for advancing such antiferromagnetic spintronics technologies. However, studies of the intrinsic mechanics of individual antiferromagnetic DWs remain elusive since they require sufficiently pure materials and suitable experimental approaches to address DWs on the nanoscale. Here we nucleate isolated, 180 • DWs in a single-crystal of Cr2O3, a prototypical collinear magnetoelectric antiferromagnet, and study their interaction with topographic features fabricated on the sample. We demonstrate DW manipulation through the resulting, engineered energy landscape and show that the observed interaction is governed by the DW's elastic properties. Our results advance the understanding of DW mechanics in antiferromagnets and suggest a novel, topographically defined memory architecture based on antiferromagnetic DWs.

Abstract.A ribbon is a surface swept out by a line segment turning as it moves along a central curve. For narrow magnetic ribbons, for which the length of the line segment is much less than the length of the curve, the anisotropy induced by the magnetostatic interaction is biaxial, with hard axis normal to the ribbon and easy axis along the central curve. The micromagnetic energy of a narrow ribbon reduces to that of a one-dimensional ferromagnetic wire, but with curvature, torsion and local anisotropy modified by the rate of turning. These general results are applied to two examples, namely a helicoid ribbon, for which the central curve is a straight line, and a Möbius ribbon, for which the central curve is a circle about which the line segment executes a 180 • twist. In both examples, for large positive tangential anisotropy, the ground state magnetization lies tangent to the central curve. As the tangential anisotropy is decreased, the ground state magnetization undergoes a transition, acquiring an in-surface component perpendicular to the central curve. For the helicoid ribbon, the transition occurs at vanishing anisotropy, below which the ground state is uniformly perpendicular to the central curve. The transition for the Möbius ribbon is more subtle; it occurs at a positive critical value of the anisotropy, below which the ground state is nonuniform. For the helicoid ribbon, the dispersion law for spin wave excitations about the tangential state is found to exhibit an asymmetry determined by the geometric and magnetic chiralities.

The concept of curvature and chirality in space and time are foundational for the understanding of the organic life and formation of matter in the Universe. Chiral interactions but also curvature effects are tacitly accepted to be local. A prototypical condensed matter example is a local spin-orbit-or curvature-induced Rashba or Dzyaloshinskii-Moriya interactions. Here, we introduce a chiral effect, which is essentially nonlocal and resembles itself even in static spin textures living in curvilinear magnetic nanoshells. Its physical origin is the nonlocal magnetostatic interaction. To identify this interaction, we put forth a self-consistent micromagnetic framework of curvilinear magnetism. Understanding of the nonlocal physics of curved magnetic shells requires a curvature-induced geometrical charge, which couples the magnetic subsystem with the curvilinear geometry. The chiral interaction brings about a nonlocal chiral symmetry breaking effect: it introduces handedness in an intrinsically achiral material and enables the design of magnetolectric and ferrotoroidic responses.

A Bloch Point singularity can form a metastable state in a magnetic nanosphere. We classify possible types of Bloch points and derive analytically the shape of magnetization distribution of different Bloch points. We show that external gradient field can stabilize the Bloch point: the shape of the Bloch point becomes radial-dependent one. We compute the magnetization structure of the nanosphere, which is in a good agrement with performed spin-lattice simulations.

Dynamics of topological magnetic textures are typically induced externally by, e.g. magnetic fields or spin/charge currents. Here, we demonstrate the effect of the internal-to-the-system geometryinduced motion of a domain wall in a curved nanostripe. Being driven by the gradient of the curvature of a biaxial stripe, transversal domain walls acquire remarkably high velocities of up to 100 m/s and do not exhibit any Walker-type speed limit. We pinpoint that the inhomogeneous distribution of the curvature-induced Dzyaloshinskii-Moriya interaction is a driving force for the motion of a domain wall. Although we showcase our approach on the specific Euler spiral geometry, the approach is general and can be applied to a wide class of geometries.

Manipulation of the domain wall propagation in magnetic wires is a key practical task for a number of devices including racetrack memory and magnetic logic. Recently, curvilinear effects emerged as an efficient mean to impact substantially the statics and dynamics of magnetic textures. Here, we demonstrate that the curvilinear form of the exchange interaction of a magnetic helix results in an effective anisotropy term and Dzyaloshinskii–Moriya interaction with a complete set of Lifshitz invariants for a one-dimensional system. In contrast to their planar counterparts, the geometrically induced modifications of the static magnetic texture of the domain walls in magnetic helices offer unconventional means to control the wall dynamics relying on spin-orbit Rashba torque. The chiral symmetry breaking due to the Dzyaloshinskii–Moriya interaction leads to the opposite directions of the domain wall motion in left- or right-handed helices. Furthermore, for the magnetic helices, the emergent effective anisotropy term and Dzyaloshinskii–Moriya interaction can be attributed to the clear geometrical parameters like curvature and torsion offering intuitive understanding of the complex curvilinear effects in magnetism.

Antiferromagnets host exotic quasiparticles, support high frequency excitations and are key enablers of the prospective spintronic and spin–orbitronic technologies. Here, we propose a concept of a curvilinear antiferromagnetism where material responses can be tailored by a geometrical curvature without the need to adjust material parameters. We show that an intrinsically achiral one-dimensional (1D) curvilinear antiferromagnet behaves as a chiral helimagnet with geometrically tunable Dzyaloshinskii–Moriya interaction (DMI) and orientation of the Néel vector. The curvature-induced DMI results in the hybridization of spin wave modes and enables a geometrically driven local minimum of the low-frequency branch. This positions curvilinear 1D antiferromagnets as a novel platform for the realization of geometrically tunable chiral antiferromagnets for antiferromagnetic spin–orbitronics and fundamental discoveries in the formation of coherent magnon condensates in the momentum space.

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