The design of complex, competing effects in magnetic systems – be it via the introduction of nonlinear interactions, or the patterning of three-dimensional geometries – is an emerging route to achieve new functionalities. Here, we combine 3D geometric effects with non-linear and non-local interactions to produce magnetic field textures in free space. For this, we harness direct write nanofabrication techniques, creating intertwined nanomagnetic cobalt double helices, where curvature, torsion, chirality, and magnetic coupling are jointly exploited. By reconstructing the 3D vectorial magnetic state of the double helices with soft X-ray magnetic laminography, we identify the presence of a regular array of highly coupled locked domain wall pairs in neighbouring helices. Micromagnetic simulations reveal that the magnetisation configuration leads to the formation of an array of complex textures in the magnetic induction, consisting of vortices in the magnetisation and antivortices in free space, which together, form an effective B-field cross-tie wall. The design and creation of complex three-dimensional magnetic field nanotextures opens new possibilities for smart materials, unconventional computing, particle trapping and magnetic imaging.

This work was funded by an EPSRC Early Career Fellowship EP/M008517/1 and the Winton Program for the Physics of Sustainability. C.D. acknowledges funding from the Leverhulme Trust (ECF-2018-016), the Isaac Newton Trust (18-08), the L’Oréal-UNESCO UK and Ireland Fellowship For Women In Science 2019, and the Max Planck Society Lise Meitner Excellence Program. A.F.P. acknowledges funding by the European Community under the Horizon 2020 Program, Contract no. 101001290, 3DNANOMAG. A.H.-R. and S.MV. acknowledge the support from European Union’s Horizon 2020 research and innovation program under Marie Skłodowska-Curie grant ref. H2020-MSCA-IF-2016-746958. A.H.-R. acknowledges funding from Spanish AEI under project reference PID2019–104604RB/AEI/10.13039/501100011033. The PolLux end station was financed by the German Ministerium für Bildung und Forschung (BMBF) through contracts 05K16WED and 05K19WE2. K.W. acknowledges the funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement no. 701647. A.F.P. is grateful to the University of Cambridge and the University of Glasgow, where part of this research was performed.

Peer reviewed