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Freespace 135/9/2023 f, g, In the as-grown state both double helices are composed of two fully black and white helices-corresponding to antiparallel-magnetized single-domain helices. e, The magnetic state is probed using STXM and XMCD using a laminography set-up for three-dimensional imaging, providing nanoscale projections of the magnetization parallel to the X-ray direction (indicated by the purple arrow in f). Additional straight cobalt pillars are included to sustain the nanostructure and facilitate the X-ray microscopy experiments. c, d, Ferromagnetic double-helix nanostructures, with varying p H and r H (2 r H indicated) and a nanowire diameter of ~70–80 nm. Both double helices have a nanowire diameter of approximately 70–80 nm with an interhelix distance of ~50–70 nm and therefore exhibit strong magnetostatic coupling.Ī, b, The pitch p H and radius r H of the helix determine the radius of curvature r c = 1/ κ and the torsion τ of the system. 1d) more elongated with higher pitch and lower radius (geometries defined in Table 1). 1c) with lower pitch and higher radius, the second (double helix B, Fig. Scanning electron microscope (SEM) images of two nanoscale double helices are presented in Fig. ![]() We fabricate the system of two intertwined cobalt nanohelices with focused electron beam induced deposition 23. Specifically, the two helices are designed to have the same chirality, and are offset by half a period, leading to a constant interhelix separation along the length of the system. The nanoscale double helix combines effects of curvature and torsion that may result in curvature-induced magnetic anisotropy and chirality effects 20, 21, 22. ![]() This three-dimensional nanomagnetic system has a complex energy landscape defined by the balance of competing intra- and interhelix effects (terms defined above). We consider a model system that consists of two intertwined, yet spatially separated, ferromagnetic nanohelices. The design and creation of complex three-dimensional magnetic field nanotextures opens new possibilities for smart materials 15, unconventional computing 2, 16, particle trapping 17, 18 and magnetic imaging 19. Micromagnetic simulations reveal that the magnetization configuration leads to the formation of an array of complex textures in the magnetic induction, consisting of vortices in the magnetization and antivortices in free space, which together form an effective B field cross-tie wall 14. By reconstructing the three-dimensional vectorial magnetic state of the double helices with soft-X-ray magnetic laminography 12, 13, we identify the presence of a regular array of highly coupled locked domain wall pairs in neighbouring helices. For this, we harness direct write nanofabrication techniques, creating intertwined nanomagnetic cobalt double helices, where curvature, torsion, chirality and magnetic coupling are jointly exploited. ![]() Here, we advance beyond the control of intrastructure properties in three dimensions and tailor the magnetostatic coupling of neighbouring magnetic structures, an interstructure property that allows us to generate complex textures in the magnetic stray field. In particular, through the design of three-dimensional geometries and curvature, intrastructure properties such as anisotropy and chirality, both geometry-induced and intrinsic, can be directly controlled, leading to a host of new physics and functionalities, such as three-dimensional chiral spin states 7, ultrafast chiral domain wall dynamics 8, 9, 10 and spin textures with new spin topologies 7, 11. The design of complex, competing effects in magnetic systems-be it via the introduction of nonlinear interactions 1, 2, 3, 4, or the patterning of three-dimensional geometries 5, 6-is an emerging route to achieve new functionalities.
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