Publications Repository - Helmholtz-Zentrum Dresden-Rossendorf

Non-linear systems accommodating multiple solitons with complex interactions 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. The challenge here is to realize small scale confined magnetic systems hosting multiple interacting solitons, which cannot be non-reversibly erased upon manipulation using external fields. We combine 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. This method allows to design 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 determines 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 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.

O. Volkov et al., Nature Communications 15, 2193 (2024).