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Curvilinear Antiferromagnetism: Current State and Perspectives
Antiferromagnets (AFMs) emerged as a versatile material science platform, which enabled numerous fundamental discoveries including the observation of monopole quasiparticles in frustrated systems and collective quantum effects, such as spin superfluidity and Bose–Einstein condensation of magnetic excitations . Primary advantages of antiferromagnets are their terahertz operating frequencies, the absence of stray fields, magnetic field robustness, all of which result in numerous advantages including those in spintronics and spinorbitronics . The key enabler of those applications is the presence of the Dzyaloshinskii-Moriya interaction (DMI). This, in turn, put stringent requirements on the magnetic symmetry of AFM, which should support weak ferromagnetism and chiral helimagnetism. This makes the portfolio of material systems available for these studies very limited that renders the progress in AFM-related fundamental and technological research to depend on time-consuming material screening and optimization of intrinsic chiral properties of AFMs. The field of curvilinear magnetism is well explored for ferromagnets, where magnetic responses are tailored by local curvatures . By contrast, the topic of curvilinear AFMs is at its infancy [4-9]. The energy landscape of ring AFM and geometrically frustrated chains at non-zero temperature is characterized by a large number of metastable states including long-living noncollinear textures if anisotropy is strong enough . In experiment, curvilinear AFMs are mainly represented by the molecular magnets  and metalized DNA molecules . The shape anisotropy stemming from magnetostriction plays the major role in the ordering of the Neel vector in perovskite zig-zag stripes and nanodots determining the easy direction as the parallel or perpendicular to the boundary . In this presentation, we will demonstrate that chiral responses of AFMs can be tailored by a geometrical curvature without the need to adjust material parameters. In a general case, an intrinsically achiral one-dimensional curvilinear AFM spin chain behaves as a chiral helimagnet with geometrically tunable DMI, orientation of the Neel vector and the helimagnetic phase transition, see Fig. 1 . The helix-shaped spin chain possesses two ground states: the so-called homogeneous and periodic ones with respect to the motion along the chain. The energetically favorable state is determined by the direction of the geometry-driven DMI vector. In contrast to ferromagnets, there is no easy axis anisotropy competing with the geometry-driven one. Furthermore, the curvature-induced DMI results in the hybridization of spin wave modes. The low-frequency branch is gapless for straight chains and possesses the gap for any finite curvature. In addition, the DMI enables a geometrically-driven local minimum of the low frequency branch which increases for larger curvature and torsion, see Fig. 2. This opens exciting perspectives to study long-lived collective magnon states in AFMs. These findings position curvilinear 1D antiferromagnets as a novel platform for the realization of geometrically tunable chiral antiferromagnets for antiferromagnetic spinorbitronics and fundamental discoveries in the formation of coherent magnon condensates in the momentum space. The proposed description of vector fields living at curvilinear geometries can be applied for other systems with complex order parameters, such as ferroelectrics  or liquid crystals .
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Keywords: antiferromagnetism; curvilinear magnetism
Invited lecture (Conferences)
IEEE International Magnetic Virtual Conference INTERMAG21, 26.-30.04.2021, Online, Online