Publikationsrepositorium - Helmholtz-Zentrum Dresden-Rossendorf

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]. 3D shaped magnetic objects enable realization of non-linear systems accommodating multiple solitons with complex interactions. Those are relevant for numerous research and technology fields ranging from non-conventional computing, spin-wave splitters for low-energy magnonics, superconducting electronics and small scale robotics. In our recent work, we combined theory, simulations and experimental explorations to demonstrate that magnetic vortices and antivortices can be stabilised in magnetic wireframe structures prepared using nanoscale direct writing methods like focused electron beam induced deposition [9]. This method allows designing magnetic wireframes with arbitrary complexity including helices, tripods, tetrapods, cube-shaped or buckyball-shaped architectures. The unique feature is that magnetic wireframes can support large number of vortices and antivortices. The fundamental beauty is that the topological properties of the surface of the wireframe object determine uniquely the number and type of magnetic solitons. For instance, magnetic N-pod is topologically equivalent to a sphere and hence can support N vortices and N-2 antivortices (i.e., 2N-2 magnetic solitons per object). Even more interesting is that it is possible to realise objects with topology of N-torus, which can support only one type of magnetic solitons. Yet these are antivortices but not vortices. In 3D geometries, the prevailing type of magnetic solitons is antivortices rather than vortices. For instance, 4-torus supports 6 antivortices only. The key aspect is that these are solitons of the same type which do not annihilate upon interaction. Hence, they are attractive for implementation of reservoir and neuromorphic computing. In particular, the stability of antivortex lattices combined with spin-wave propagation into wireframe structures may be useful for potential application in magnonic-based computing. Moreover, the direct integration of nanofabricated 3D wireframes into standard 2D lithographically created systems with coplanar or Ω-shaped antennas or detectors should allow extending unconventional computing into 3D offering additional functionalities such as a higher degree of interconnectivity.

[1] P. Gentile et al.; Electronic materials with nanoscale curved geometries; Nature Electronics (review) 2022 5, 551.
[2] D. Makarov et al.; Curvilinear micromagnetism: from fundamentals to applications (Springer, Zurich, 2022).
[3] D. Makarov et al.; New dimension in magnetism and superconductivity: 3D and curvilinear nanoarchitectures; Adv. Mat. (review) 2022 34, 2101758.
[4] D. Sheka et al.; Fundamentals of curvilinear ferromagnetism: statics and dynamics of geometrically curved wires and narrow ribbons; Small (review) 2022 18, 2105219.
[5] Y. Gaididei et al.; Curvature effects in thin magnetic shells; Phys. Rev. Lett. 2014 112, 257203.
[6] O. Volkov et al.; Experimental observation of exchange-driven chiral effects in curvilinear magnetism; Phys. Rev. Lett. 2019 123, 077201.
[7] D. Sheka et al.; Nonlocal chiral symmetry breaking in curvilinear magnetic shells; Commun. Phys. 2020 3, 128.
[8] O. Volkov et al.; Chirality coupling in topological magnetic textures with multiple magnetochiral parameters; Nature Com. 2023 14, 1491.
[9] O. Volkov et al.; Three-dimensional magnetic nanotextures with high-order vorticity in soft magnetic wireframes; Nature Com. 2024 15, 2193.