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

The fundamental limits currently faced by traditional computing devices necessitate the exploration of ways to store, compute, and transmit information going beyond the current CMOS-based technologies. Here, we propose a three-dimensional (3D) magnetic interconnector that exploits geometry-driven automotion of domain walls (DWs), for the transfer of magnetic information between functional magnetic planes. By combining state-of-the-art 3D nanoprinting and standard physical vapor deposition, we prototype 3D helical DW conduits. We observe the automotion of DWs by imaging their magnetic state under different field sequences using X-ray microscopy, observing a robust unidirectional motion of DWs from the bottom to the top of the spirals. From experiments and micromagnetic simulations, we determine that the large thickness gradients present in the structure are the main mechanism for 3D DW automotion. We obtain direct evidence of how this tailorable magnetic energy gradient is imprinted in the devices, and how it competes with pinning effects that are due to local changes in the energy landscape. Our work also predicts how this effect could lead to high DW velocities, reaching the Walker limit during automotion. This work demonstrates a possible mechanism for efficient transfer of magnetic information in three dimensions., This work was supported by the EPSRC Cambridge NanoDTC EP/L015978/1, the Winton Program for the Physics of Sustainability, the project CALIPSOplus (under Grant Agreement No. 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020), and by the European Community (under the Horizon 2020 Program, Contract No. 101001290, 3DNANOMAG). L.S. acknowledges support from St. Johns College of the University of Cambridge. C.D. was supported by the Leverhulme Trust (No. ECF-2018-016), the Isaac Newton Trust (No. 18-08), and the L’Oréal-UNESCO UK and Ireland Fellowship For Women In Science. A.H.-R. acknowledges support from Spanish AEI, under Project Reference No. PID2019-104604RB/AEI/10.13039/501100011033. The authors acknowledge the University of Vienna research platform MMM Mathematics–Magnetism–Materials, the FWF (Project No. I 4917), and Aragon Government through the Project Q-MAD., Peer reviewed

This paper is part of the Special Topic on Science and Technology of 3D Magnetic Nanostructures., P.F. acknowledges the support by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC0205-CH11231(NEMMprogramMSMAG).A.F.-P.acknowledgesthe funding from the European Community under the Horizon 2020 Program, Contract No. 101001290 (3DNANOMAG), the Spanish MCIN with funding from European Union NextGeneration EU (Grant No.PRTR-C17.I1),and the Aragon Government through the Project Q-MAD. S.L. acknowledges the support from the Engineering and Physics Research Council (Grant No. EP/R009147/1) and the Leverhulme Trust (Grant No. RPG-2021-139)., Peer reviewed

Cylindrical magnetic nanowires are promising systems for the development of three-dimensional spintronic devices. Here, we simulate the evolution of magnetic states during fabrication of strongly-coupled cylindrical nanowires with varying degrees of overlap. By varying the separation between wires, the relative strength of exchange and magnetostatic coupling can be tuned. Hence, we observe the formation of six fundamental states as a function of both inter-wire separation and wire height. In particular, two complex three-dimensional magnetic states, a 3D Landau Pattern and a Helical domain wall, are observed to emerge for intermediate overlap. These two emergent states show complex spin configurations, including a modulated domain wall with both Néel and Bloch character. The competition of magnetic interactions and the parallel growth scheme we follow (growing both wires at the same time) favours the formation of these anti-parallel metastable states. This works shows how the engineering of strongly coupled 3D nanostructures with competing interactions can be used to create complex spin textures., This work was supported by the EPSRC and the Centre for Doctoral Training (CDT) in Photonic Integration and Advanced Data Storage (PIADS), RCUK Grant No. EP/L015323/1, the European Community under the Horizon 2020 Program, Contract No. 101001290 (3DNANOMAG), the MCIN with funding from European Union NextGenerationEU (PRTR-C17.I1), and the Aragon Government through the Project Q-MAD. AH-R acknowledges the support from European Union's Horizon 2020 research and innovation program under Marie Skłodowska-Curie Grant ref. H2020-MSCA-IF-2016-746958, from the Spanish MICIN under Grant PID2019-104604RB/AEI/10.13039/501100011033 and from the Asturias FICYT under Grant AYUD/2021/51185 with the support of FEDER funds. CINN (CSIC—Universidad de Oviedo), El Entrego, Spain LS acknowledges support from the University of Cambridge (EPSRC Cambridge NanoDTC EP/L015978/1) DH acknowledges Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, 91767, Palaiseau, France. CD acknowledges funding from the Max Planck Society Lise Meitner Excellence Program., Peer reviewed

Magneto-optical techniques are key tools for the characterization of magnetic effects at the nanoscale. Here, we present the dark-field magneto-optical Kerr effect (DFMOKE), a technique we have recently developed for the characterization of three-dimensional magnetic nanostructures. We introduce the principles of DFMOKE, based on the separation of an incident beam into multiple reflected beams when focusing on a 3D nano-geometry. We show the key modifications needed in a standard focused MOKE magnetometer to perform these measurements. Finally, we showcase the power of this method by detecting the magnetic switching of a single tilted 3D nanowire, independently from the switching of a magnetic thin film that surrounds it. We obtain independent and simultaneous switching detection of the nanowire and the film for all nanowire dimensions investigated, allowing us to estimate a magnetic sensitivity of 7 × 10-15 A m2 for DFMOKE in the setup used. We conclude the article by providing perspectives of future avenues where DFMOKE can be a very powerful characterization tool in future investigations of 3D magnetic nanostructures., DSH and AFP are grateful to the University of Cambridge, where part of this research was performed. DSH acknowledges funding from ANR/CNRS under the French Plan Relance de l’Etat for the preservation of R&D. This work was supported by the European Community under the Horizon 2020 Program, Contract No. 101001290 (3DNANOMAG), the MCIN with funding from European Union NextGenerationEU (PRTR-C17.I1), and the Aragon Government through the Project Q-MAD. L.S. acknowledges support from the EPSRC Cambridge NanoDTC EP/L015978/1, Peer reviewed

In this study, we demonstrate an enhancement of the measured spin Seebeck coefficient in Fe3O4/Pt bilayer films due to an increase in Fe nanodroplets formed by pulsed laser deposition. Four bilayer films were deposited at the same time from a highly textured target, resulting in a general increase in droplet formation that was confirmed to be Fe rich by scanning electron microscope and transmission electron microscope-dispersive x-ray spectroscopy. Of these four films, there were two distinct groupings with differing density of α-Fe droplets, where the bilayer with higher droplet density exhibited a 64% increase in the measured spin Seebeck coefficient from 38 to 63 nV m/W., This work was supported by the Engineering and Physical Sciences Research Council (No. EP/
P006221/1). N.L. received funding from the European Research Council (ERC) under European Union’s Horizon 2020 Program, Contract No. 101001290 (3DNANOMAG)., Peer reviewed

The magneto-optical Kerr effect (MOKE) is widely exploited in laboratory-based setups for the study of thin films and nanostructures, providing magnetic characterization with good spatial and temporal resolutions. Due to the complex coupling of light with a magnetic sample, conventional MOKE magnetometers normally work by selecting a small range of incident wave-vector values, focusing the incident light beam to a small spot, and recording the reflected intensity at that angular range by means of photodetectors. Using this approach, additional methodologies and measurements are required for full vectorial magnetic characterization. Here, we computationally investigate a Fourier-space MOKE setup, where a focused beam ellipsometer using high numerical aperture optics and a camera detector is employed to simultaneously map the intensity distribution for a wide range of incident and reflected wave vectors. We employ circularly incident polarized light and no analyzing optics, in combination with a fitting procedure of the light intensity maps to the analytical expression of the Kerr effect under linear approximation. In this way, we are able to retrieve the three unknown components of the magnetization vector as well as the material' s optical and magneto-optical constants with high accuracy and short acquisition times, with the possibility of single-shot measurements. Fourier MOKE is thus proposed as a powerful method to perform generalized magneto-optical ellipsometry for a wide range of magnetic materials and devices., This work was supported by UKRI through an EPSRC studentship, Grants No. EP/N509668/1 and No. EP/R513222/1, the European Community under the Horizon
2020 Program, Contract No. 101001290 (3DNANOMAG), the MCIN with funding from European Union NextGenerationEU (PRTR-C17.I1), and the Aragon Government
through the Project Q-MAD. A.H.-R. acknowledges the support by Spanish MICIN under Grant No. PID2019-104604RB/AEI/10.13039/501100011033 and by Asturias FICYT under Grant No. AYUD/2021/51185 with the support of FEDER funds. D. S.-H. acknowledges funding from ANR/CNRS under the French “Plan Relance de l’ etat” for
the preservation of R&D. L.S. acknowledges support from the EPSRC Cambridge NanoDTC Grant No. EP/L015978/1. C.N.C. acknowledges the UK EPSRC Centre for Doctoral Training in Sensor Technologies for a Healthy and Sustainable Future. C.D. acknowledges funding from the Max Planck Society Lise Meitner Excellence Program., Peer reviewed

Three-dimensional magnetic metamaterials feature interesting phenomena that arise from a delicate interplay of material properties, local anisotropy, curvature, and connectivity. A particularly interesting magnetic lattice that combines these aspects is that of nanoscale gyroids, with a highly interconnected chiral network with local three-connectivity reminiscent of three-dimensional artificial spin ices. Here, we use finite-element micromagnetic simulations to elucidate the anisotropic behavior of nanoscale nickel gyroid networks at applied fields and at remanence. We simplify the description of the micromagnetic spin states with a macrospin model to explain the anisotropic global response, to quantify the extent of icelike correlations, and to discuss qualitative features of the anisotropic magnetoresistance in the three-dimensional network. Our results demonstrate the large variability of the magnetic order in extended gyroid networks, which might enable future spintronic functionalities, including neuromorphic computing and nonreciprocal transport., N.L. received funding from the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation program under Marie Sklodowska Curie Grant Agreement No. 844304 (LICONAMCO), as well as support from the European
Community under the Horizon 2020 program, Contract No. 101001290 (3DNANOMAG). The work of A.S.K. was financially supported by JSPS KAKENHI Grant No.
18J20396. The work of J.L. and S.F. was supported by JSPS KAKENHI Grants No. 21K04816 and No. 19H05622 and the Graduate Program for Spintronics (GP-Spin) as well as Cooperative Research Projects of RIEC, CSIS, and CSRN, Tohoku University., Peer reviewed

The data utilized to generate the figures shown in the text can be found at the Enlighten repository of the University of Glasgow: https://doi.org/10.5525/gla.researchdata.1511., The interlayer Dzyaloshinskii–Moriya interaction (IL-DMI) chirally couples spins in different ferromagnetic layers of multilayer heterostructures. So far, samples with IL-DMI have been investigated utilizing magnetometry and magnetotransport techniques, where the interaction manifests as a tunable chiral exchange bias field. Here, we investigate the nanoscale configuration of the magnetization vector in a synthetic anti-ferromagnet (SAF) with IL-DMI, after applying demagnetizing field sequences. We add different global magnetic field offsets to the demagnetizing sequence in order to investigate the states that form when the IL-DMI exchange bias field is fully or partially compensated. For magnetic imaging and vector reconstruction of the remanent magnetic states, we utilize x-ray magnetic circular dichroism photoemission electron microscopy, evidencing the formation of 360° domain wall rings of typically 0.5–3.0 μm in diameter. These spin textures are only observed when the exchange bias field due to the IL-DMI is not perfectly compensated by the magnetic field offset. From a combination of micromagnetic simulations, magnetic charge distribution, and topology arguments, we conclude that a non-zero remanent effective field with components both parallel and perpendicular to the anisotropy axis of the SAF is necessary to observe the rings. This work shows how the exchange bias field due to IL-DMI can lead to complex metastable spin states during reversal, important for the development of future spintronic devices., This work was supported by UKRI through an EPSRC studentship, Nos. EP/N509668/1 and EP/R513222/1, the European Community under the Horizon 2020 Program, Contract No. 101001290 (3DNANOMAG), the MCIN with funding from European Union NextGenerationEU (No. PRTR-C17.I1), and the Aragon Government through the Project Q-MAD. A.H.-R. acknowledges the support by Spanish MICIN under Grant No. PID2019-104604RB/AEI/10.13039/501100011033 and by Asturias FICYT under Grant No. AYUD/2021/51185 with the support of FEDER funds. S.R.-G. acknowledges the financial support of the Alexander von Humboldt foundation. L.S. acknowledges support from the EPSRC Cambridge NanoDTC No. EP/L015978/1. C.D. acknowledges funding from the Max Planck Society Lise Meitner Excellence Program. The ALBA Synchrotron is funded by the Ministry of Research and Innovation of Spain, by the Generalitat de Catalunya and by European FEDER funds. We acknowledge Synchrotron SOLEIL for providing the
synchrotron radiation facilities (Proposal No. 20191674). S.M. acknowledges support from EPSRC Project No. EP/T006811/1. M.A.N. and M.F. acknowledge support from MICIN project PID2021-122980OB-C54., Peer reviewed

The magneto-optical Kerr effect (MOKE) is widely exploited in laboratory-based setups for the study of thin films and nanostructures, providing magnetic characterization with good spatial and temporal resolutions. Due to the complex coupling of light with a magnetic sample, conventional MOKE magnetometers normally work by selecting a small range of incident wave-vector values, focusing the incident light beam to a small spot, and recording the reflected intensity at that angular range by means of photodetectors. Using this approach, additional methodologies and measurements are required for full vectorial magnetic characterization. Here, we computationally investigate a Fourier-space MOKE setup, where a focused beam ellipsometer using high numerical aperture optics and a camera detector is employed to simultaneously map the intensity distribution for a wide range of incident and reflected wave vectors. We employ circularly incident polarized light and no analyzing optics, in combination with a fitting procedure of the light intensity maps to the analytical expression of the Kerr effect under linear approximation. In this way, we are able to retrieve the three unknown components of the magnetization vector as well as the material' s optical and magneto-optical constants with high accuracy and short acquisition times, with the possibility of single-shot measurements. Fourier MOKE is thus proposed as a powerful method to perform generalized magneto-optical ellipsometry for a wide range of magnetic materials and devices., This work was supported by UKRI through an EPSRC studentship, Grants No. EP/N509668/1 and No.
EP/R513222/1, the European Community under the Horizon 2020 Program, Contract No. 101001290 (3DNANOMAG), the MCIN with funding from European Union NextGenerationEU (PRTR-C17.I1), and the Aragon Government through the Project Q-MAD. A.H.-R. acknowledges the support by Spanish MICIN under Grant No. PID2019-104604RB/AEI/10.13039/501100011033 and by Asturias FICYT under Grant No. AYUD/2021/51185 with the support of FEDER funds. D. S.-H. acknowledges funding from ANR/CNRS under the French “Plan Relance de l’ etat” for the preservation of R&D. L.S. acknowledges support from the EPSRC Cambridge NanoDTC Grant No. EP/L015978/1.
C.N.C. acknowledges the UK EPSRC Centre for Doctoral
Training in Sensor Technologies for a Healthy and Sustainable
Future. C.D. acknowledges funding from the Max Planck
Society Lise Meitner Excellence Program., Peer reviewed

This work presents a detailed analysis of the performance of X-ray magnetic circular dichroism photoemission electron microscopy (XMCD-PEEM) as a tool for vector reconstruction of magnetization. For this, 360° domain wall ring structures which form in a synthetic antiferromagnet are chosen as the model to conduct the quantitative analysis. An assessment is made of how the quality of the results is affected depending on the number of projections that are involved in the reconstruction process, as well as their angular distribution. For this a self-consistent error metric is developed which allows an estimation of the optimum azimuthal rotation angular range and number of projections. This work thus proposes XMCD-PEEM as a powerful tool for vector imaging of complex 3D magnetic structures., Open access funding enabled and organized by Projekt DEAL., This work was supported by UKRI through EPSRC studentships (EP/N509668/1 and EP /R513222/1), the European Community under the Horizon 2020 Programme [contract No. 101001290 (3DNANOMAG)], the Spanish MCIN with funding from the European Union NextGenerationEU (PRTR-C17.I1) and the Aragon Government through Project Q-MAD. A. Hierro-Rodriguez acknowledges support by the Spanish MICIN (grant Nos. PID2019-104604RB/AEI/10.13039/501100011033 and PID2022-136784NB) and by Asturias FICYT (grant AYUD/2021/51185) with the support of FEDER funds. S. Ruiz-Gómez acknowledges the financial support of the Alexander von Humboldt foundation. L. Skoric acknowledges support from the EPSRC Cambridge NanoDTC (studentship No. EP/L015978/1). C. Donnelly acknowledges funding from the Max Planck Society Lise Meitner Excellence Program. The ALBA Synchrotron is funded by the Ministry of Research and Innovation of Spain, by the Generalitat de Catalunya and by European FEDER funds. S. McVitie acknowledges support from the EPSRC (project EP/T006811/1). M. A. Niño and M. Foerster acknowledge support from MICIN (project No. PID2021-122980OB-C54)., Peer reviewed

In operando techniques enable real-time measurement of intricate physical properties at the micro- and nano-scale under external stimuli, allowing the study of a wide range of materials and functionalities. In nanomagnetism, in operando techniques greatly benefit from precise three-dimensional (3D) magnetic field control, enabling access to complex magnetic states forming in systems where multiple energies are set to compete with each other. However, achieving such precision is challenging and uncommon, as specific applications impose constraints on the type and geometry of magnetic field sources, limiting their capabilities. Here, we introduce an approach that leverages machine learning algorithms to achieve precise 3D magnetic field control using a hexapole electromagnet that is composed of three independent, non-collinear dipole electromagnets. In our experimental setup, magnetic field sensors are placed at a distance from the sample position due to inherent constraints, leading to indirect field measurements that differ from the magnetic field experienced by the sample. We find that the existing relationship between the remote and sample frames of reference is non-linear, thus requiring a more complex calibration method. To address this, we employ a multi-layer perceptron neural network that processes multiple inputs from a dynamic magnetic field sequence, effectively capturing the time-dependent non-linear field response. The network achieves high calibration accuracy and demonstrates exceptional generalization to unseen magnetic field sequences. This study highlights the significant potential of machine learning in achieving high-precision control and calibration, crucial for in operando experiments where direct measurement at the point of interest is not possible., This work was supported by the European Community under the Horizon 2020 Program, Contract No. 101001290 (3DNANOMAG). The raw data supporting the findings of this study will be openly available at a repository from TU Wien. A.H.-R. acknowledges support by the Spanish MICIN (Refs. MICIN/AEI/10.13039/501100011033/FEDER, UE under Grant Nos. PID2019-104604RB and PID2022-136784NB) and by Asturias FICYT (Grant No. AYUD/2021/51185) with the support of FEDER funds. L.S. acknowledges support from the EPSRC Cambridge NanoDTC EP/L015978/1. For the purpose of open access, the author(s) has applied a Creative Commons Attribution (CC-BY) licence to any Author Accepted Manuscript version arising from this submission. The financial support by the Austrian Federal Ministry of Labour and Economy, the National Foundation for Research, Technology and Development, and the Christian Doppler Research Association is gratefully acknowledged., Peer reviewed

Sandra Ruiz-Gómez, Claire Donnelly, et al., Topological defects, or singularities, play a key role in the statics and dynamics of complex systems. In magnetism, Bloch point singularities represent point defects that mediate the nucleation of textures such as skyrmions and hopfions. While these textures are typically stabilised in chiral magnets, the influence of chirality and symmetry breaking on Bloch point singularities remains relatively unexplored. Here, we harness advanced three-dimensional nanofabrication to explore the influence of symmetry breaking on Bloch point textures by introducing controlled nano-curvature in a ferromagnetic nanowire. Combining X-ray magnetic microscopy with the application of in situ magnetic fields, we demonstrate that Bloch point singularity-containing domain walls are stabilised in straight regions of the sample, and determine that curvature can be used to tune the energy landscape of the Bloch points. Not only are we able to pattern pinning points but, by controlling the gradient of curvature, we define asymmetric potential wells to realise a robust Bloch point texture shift-register with non-reciprocal behaviour. These insights into the influence of symmetry on singularities offer a route to the controlled nucleation and propagation of topological textures, providing opportunities for logic and computing devices., Open Access funding enabled and organized by Projekt DEAL., These experiments were performed at CIRCE beamline at ALBA Synchrotron Light Facility and at DEMETER beamline at National Synchrotron Radiation Center SOLARIS with the collaboration of ALBA and SOLARIS staff. S. R-G., P. M-F, C. F-G and C.D. acknowledge funding from the Max Planck Society Lise Meitner Excellence Program and funding from the European Research Council (ERC) under the ERC Starting Grant No. 3DNANOQUANT 101116043. P.F-G acknowledges support from the International Max Planck Research School for Chemistry and Physics of Quantum Materials. S. R-G acknowledges support from the Humboldt foundation grant 1223621 and Marie Curie fellowship grant GAP-101061612. C.A. acknowledges funding from FWF through the projects. MF and MAN acknowledge funding through MICIN, project PID2021-122980OB-C54. N.B and S. R.-G. acknowledge funding through Advanced Materials program supported by MCIN with funding from the European Union NextGenerationEU (PRTR-C17.I1) and by the Generalitat de Catalunya. A. F.-P. Acknowledges funding from the European Community under the Horizon 2020 program. Contract NO 101001290 (3DNANOMAG). G.S.-S. acknowledges financial support from Grant RYC2022-038027-I funded by MICIU/AEI/10.13039/501100011033 and by ESF + . Electron microscopy observations at ICTS ELECMI (Centro Nacional de Microscopia Electrónica) sponsored by grants Spanish MICINN PID2021-122980OB-C51 and Comunidad de Madrid “Materiales avanzados” MAD2D-UCM3., Peer reviewed

Magnetic skyrmions are chiral spin textures with rich physics and great potential for unconventional computing. Typically, skyrmions form in bulk crystals with reduced symmetry or ultrathin film multilayers involving heavy metals. Here, the formation of fractional Bloch skyrmion tubes at room temperature is demonstrated by 3D printing ferromagnetic double-helix nanowires with two regions of opposite chirality. Using X-ray microscopy and micromagnetic simulations, it is shown that the coexistence of vortex and anti-parallel spin states induces the formation of fractional skyrmion tubes at zero magnetic fields, minimizing the energy cost of breaking the coupling between geometric and magnetic chirality. Control over zero-field states is also demonstrated, including pure vortex, or mixed skyrmion-vortex states, highlighting the magnetic reconfigurability of these 3D nanowires. This work shows how interfacing chiral geometries at the nanoscale can enable advanced forms of topological spintronics., This work was supported by the EPSRC and the Centre for Doctoral Training (CDT) in Photonic Integration and Advanced Data Storage (PIADS), RCUK Grant No. EP/L015323/1, the European Community under the Horizon 2020 Program, Contract No. 101001290 (3DNANOMAG). J.F. would also like to acknowledge the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division. The work of N.L. was also supported by a UKRI Future Leader Fellowship [grant number MR/X033910/1 (LIONESS)]. L.S. acknowledges support from the EPSRC Cambridge NanoDTC EP/L015978/1. A.H.-R. acknowledges the support from the Spanish Ministry of Science, Innovation and Universities MCIN/AEI/10.13039/501100011033/FEDER, UE under grant PID2022-136784NB, and by Agencia SEKUENS (Asturias) under grant UONANO IDE/2024/000678 with the support of FEDER funds. The authors acknowledge Synchrotron SOLEIL for providing the synchrotron radiation facilities (Proposal No. 20191674). The authors would also like to thank Sam McFadzean and William Smith at the Kelvin Nanocharacterisation Centre at the University of Glasgow for technical support. The authors acknowledge TU Wien Bibliothek for financial support through its Open Access Funding Program., Open access funding provided by Technische Universitat Wien/KEMÖ., Peer reviewed

The raw data supporting the findings of this study will be openly available at a repository from TU Wien., Chiral magnetic textures are key for the development of modern spintronic devices. In multilayered thin films, these are typically stabilized via the interfacial intralayer Dzyaloshinskii-Moriya interaction (DMI). Additionally, it has been recently observed that DMI may also promote vector spin chirality along the third dimension, coupling spins in different magnetic layers via nonmagnetic spacer layers, an effect referred to as interlayer DMI (IL-DMI). This interaction holds promise for 3D nanomagnetism, from the creation of 3D spin structures such as hopfions to new forms of magnetic functionality in the vertical direction via remote control of chiral spin states. In this work, we provide direct experimental evidence that the in-plane vector spin chirality of magnetic textures within a ferromagnetic layer can be controlled via the net out-of-plane spin configuration of an adjacent one. Both ferromagnetic layers form part of a synthetic antiferromagnet, previously shown to have IL-DMI. This in-plane vector chirality dependence on the out-of-plane configuration of another layer implies that the overall scalar spin chirality is preserved when computed across layers. We draw these conclusions from a combination of magnetic x-ray scattering and imaging experiments, complemented by various simulations. These findings thus uncover a type of chiral interlayer interactions, which can lead to the formation of intricate spin states across a metallic interface, demonstrating other ways to control magnetic chirality in three dimensions., This work was supported by the European Community under the Horizon 2020 Program, Contract No. 101001290 (3DNANOMAG), and UKRI through an EPSRC studentship, EP/N509668/1 and EP/R513222/1. A.H.-R. acknowledges support by the Spanish MICIN (Refs. MICIN/AEI/ 10.13039/501100011033/FEDER, UE under Grants No. PID2019-104604RB and No. PID2022-136784NB) and by Asturias FICYT (Grant No. AYUD/2021/51185) with the support of FEDER funds. S.R-G. acknowledges the financial support of the Alexander von Humboldt Foundation. L.S. acknowledges support from the EPSRC Cambridge NanoDTC EP/L015978/1. The ALBA Synchrotron is funded by the Ministry of Research and Innovation of Spain, by the Generalitat de Catalunya and by European FEDER funds. S.M. acknowledges support from EPSRC Project No. EP/T006811/1. M.A.N. and M.F. acknowledge support from MICIN Project No. PID2021-122980OB-C54. E.Y.V. acknowledges financial support provided by the Deutsche Forschungsgemeinschaft (DFG) via Project No. 514141286., The authors acknowledge TU Wien Bibliothek for financial support through its Open Access Funding Program., Technischen Universität Wien, Peer reviewed

Double-helix (DH) nanowires provide a platform to study the influence of geometric chirality on spin chirality. Their three-dimensional (3D) helical architecture and tunable inter-strand coupling enable control of spin chirality, including the stabilization of topological 3D magnetic states such as helical domains and domain walls, topological stray fields, and extended helical vortex/skyrmion tubes. So far, the study of these and other 3D nanostructures is usually confined to a limited number of magnetic microscopy experiments in large facilities. Here, we investigate the reversal mechanism of a single DH nanowire using dark-field magneto-optical Kerr effect (DF-MOKE) magnetometry under external 3D magnetic fields. By analyzing the angular dependence of the DF-MOKE signal, we fit the reversal process using established models for domain-wall nucleation and propagation, finding a characteristic behavior similar to that reported for cylindrical nanowires. Micromagnetic simulations indicate that the reversal process goes through nucleation of the helical vortex tube in a curling manner, while ptychographic x-ray magnetic circular dichroism data reveal that this helical vortex tube state forms through a mixed nucleation-propagation process. These observations provide a consistent microscopic picture of reversal mediated by a helical vortex tube extending along the nanowire. Our work provides a comprehensive characterization of magnetization reversal in DH nanowires and demonstrates that DF-MOKE magnetometry is effective for probing reversal mechanisms in single 3D nanostructures. This lab-based approach expands the range of accessible experiments beyond large-scale facilities, enabling extensive exploration of the rich spin states supported by 3D nano-geometries., This work was supported by the European Community under the Horizon 2020 program, Contract No. 101001290 (3DNANOMAG). C.D. acknowledges support from the Max Planck Society Lise Meitner Excellence Program and funding from the European Research Council (ERC) through the ERC Starting Grant No. 101116043 (3DNANOQUANT). The authors acknowledge Synchrotron SOLEIL for providing the synchrotron radiation facilities (Proposal No. 20231960). The authors acknowledge the use of instrumentation and the technical assistance provided by the National Facility ELECMI ICTS, Laboratorio de Microscopias Avanzadas (LMA) at Universidad de Zaragoza. A.A. acknowledges support through project 3D-Sky (Grant No. GAP-101108063), part of the Marie Skłodowska-Curie Actions under the Horizon Europe Program of the EU. The authors acknowledge financial support from the Blue-Sky Research Fund – Phoenix, TU Wien. N.L. acknowledges funding from UKRI via the Future Leader Fellowship MR/X033910/1 (LIONESS). The authors acknowledge TU Wien Bibliothek for financial support through its Open Access Funding Programme., Peer reviewed

The fundamental limits currently faced by traditional computing devices necessitate the exploration of ways to store, compute, and transmit information going beyond the current CMOS-based technologies. Here, we propose a three-dimensional (3D) magnetic interconnector that exploits geometry-driven automotion of domain walls (DWs), for the transfer of magnetic information between functional magnetic planes. By combining state-of-the-art 3D nanoprinting and standard physical vapor deposition, we prototype 3D helical DW conduits. We observe the automotion of DWs by imaging their magnetic state under different field sequences using X-ray microscopy, observing a robust unidirectional motion of DWs from the bottom to the top of the spirals. From experiments and micromagnetic simulations, we determine that the large thickness gradients present in the structure are the main mechanism for 3D DW automotion. We obtain direct evidence of how this tailorable magnetic energy gradient is imprinted in the devices, and how it competes with pinning effects that are due to local changes in the energy landscape. Our work also predicts how this effect could lead to high DW velocities, reaching the Walker limit during automotion. This work demonstrates a possible mechanism for efficient transfer of magnetic information in three dimensions.

For nearly half a century, the era of nanoscience was driven by the paradigm that the reduction in dimensions in nanomaterials would provide a deeper understanding of the fundamental building blocks at the atomic and molecular level, resulting in novel material properties, behavior, and utilization in nanotechnologies. Specifically, for magnetic materials, this triggered enormous research efforts in spintronics and magnetic nanostructures. However, about ten years ago, it was realized that the extension of accomplishments from nanoscience and nanotechnology into the third-dimension will not only open new opportunities in magnetic materials1,2 due to additional levels of complexity or phenomena that can only exist in 3D, such as chirality, but will also yield substantial challenges for the synthesis, theory, and characterization of such artificially designed 3D systems. Rapid improvements in fabrication technologies,3–10 theories predicting curvature-driven novel energy terms,11–13 and new types of spin-textures that stabilize due to geometrical effects, unique topology,14 and frustration,15 as well as new experimental approaches to validate 3D spin textures and their behavior emerged. With the development of nanoscale magnetic imaging techniques16–19 that can be characterized even quantitatively, the complete 3D magnetization vector, with a precision down to magnetically relevant lengths and timescales, has helped elucidate the impact of nanoscale curvature19–21 on well-known spin textures as well as demonstrate the existence of new topological spin systems such as Bloch points,22 merons,23 and Hopfions.24..

The magneto-optical Kerr effect (MOKE) is widely exploited in laboratory-based setups for the study of thin films and nanostructures, providing magnetic characterization with good spatial and temporal resolutions. Due to the complex coupling of light with a magnetic sample, conventional MOKE magnetometers normally work by selecting a small range of incident wave-vector values, focusing the incident light beam to a small spot, and recording the reflected intensity at that angular range by means of photodetectors. Using this approach, additional methodologies and measurements are required for full vectorial magnetic characterization. Here, we computationally investigate a Fourier-space MOKE setup, where a focused beam ellipsometer using high numerical aperture optics and a camera detector is employed to simultaneously map the intensity distribution for a wide range of incident and reflected wave vectors. We employ circularly incident polarized light and no analyzing optics, in combination with a fitting procedure of the light intensity maps to the analytical expression of the Kerr effect under linear approximation. In this way, we are able to retrieve the three unknown components of the magnetization vector as well as the material' s optical and magneto-optical constants with high accuracy and short acquisition times, with the possibility of single-shot measurements. Fourier MOKE is thus proposed as a powerful method to perform generalized magneto-optical ellipsometry for a wide range of magnetic materials and devices.

In this study, we demonstrate an enhancement of the measured spin Seebeck coefficient in Fe3O4/Pt bilayer films due to an increase in Fe nanodroplets formed by pulsed laser deposition. Four bilayer films were deposited at the same time from a highly textured target, resulting in a general increase in droplet formation that was confirmed to be Fe rich by scanning electron microscope and transmission electron microscope-dispersive x-ray spectroscopy. Of these four films, there were two distinct groupings with differing density of α-Fe droplets, where the bilayer with higher droplet density exhibited a 64% increase in the measured spin Seebeck coefficient from 38 to 63 nV m/W.

The interlayer Dzyaloshinskii–Moriya interaction (IL-DMI) chirally couples spins in different ferromagnetic layers of multilayer heterostructures. So far, samples with IL-DMI have been investigated utilizing magnetometry and magnetotransport techniques, where the interaction manifests as a tunable chiral exchange bias field. Here, we investigate the nanoscale configuration of the magnetization vector in a synthetic anti-ferromagnet (SAF) with IL-DMI, after applying demagnetizing field sequences. We add different global magnetic field offsets to the demagnetizing sequence in order to investigate the states that form when the IL-DMI exchange bias field is fully or partially compensated. For magnetic imaging and vector reconstruction of the remanent magnetic states, we utilize x-ray magnetic circular dichroism photoemission electron microscopy, evidencing the formation of 360° domain wall rings of typically 0.5–3.0 μm in diameter. These spin textures are only observed when the exchange bias field due to the IL-DMI is not perfectly compensated by the magnetic field offset. From a combination of micromagnetic simulations, magnetic charge distribution, and topology arguments, we conclude that a non-zero remanent effective field with components both parallel and perpendicular to the anisotropy axis of the SAF is necessary to observe the rings. This work shows how the exchange bias field due to IL-DMI can lead to complex metastable spin states during reversal, important for the development of future spintronic devices.

This work presents a detailed analysis of the performance of X-ray magnetic circular dichroism photoemission electron microscopy (XMCD-PEEM) as a tool for vector reconstruction of magnetization. For this, 360° domain wall ring structures which form in a synthetic antiferromagnet are chosen as the model to conduct the quantitative analysis. An assessment is made of how the quality of the results is affected depending on the number of projections that are involved in the reconstruction process, as well as their angular distribution. For this a self-consistent error metric is developed which allows an estimation of the optimum azimuthal rotation angular range and number of projections. This work thus proposes XMCD-PEEM as a powerful tool for vector imaging of complex 3D magnetic structures.

Three-dimensional magnetic metamaterials feature interesting phenomena that arise from a delicate interplay of material properties, local anisotropy, curvature, and connectivity. A particularly interesting magnetic lattice that combines these aspects is that of nanoscale gyroids, with a highly interconnected chiral network with local three-connectivity reminiscent of three-dimensional artificial spin ices. Here, we use finite-element micromagnetic simulations to elucidate the anisotropic behavior of nanoscale nickel gyroid networks at applied fields and at remanence. We simplify the description of the micromagnetic spin states with a macrospin model to explain the anisotropic global response, to quantify the extent of icelike correlations, and to discuss qualitative features of the anisotropic magnetoresistance in the three-dimensional network. Our results demonstrate the large variability of the magnetic order in extended gyroid networks, which might enable future spintronic functionalities, including neuromorphic computing and nonreciprocal transport.

The expansion of nanomagnetism to the third dimension leads to phenomena such as curvature-induced magnetochirality and anisotropy, which can significantly influence the behavior of magnetic textures. One of the most promising systems is the magnetic nanotube – where intrinsic curvature effects are present. However, studies of magnetic nanotubes remain limited to straight systems, and little is known about the influence of 3D geometries. In this work, three dimensional (3D) complex-shaped nanotubes are fabricated by combining nanoprinting with the conformal deposition of magnetic films. Specifically, 3D conductive non-magnetic tungsten scaffolds are fabricated using focused electron beam induced deposition and subsequently coated with a nickel magnetic shell, resulting in complex-shaped magnetic nanotubes whose geometry can be controlled by tuning the electron-beam parameters and electrodeposition conditions. Performing X-ray microscopy revealed that nanotubes of various geometries host a vortex-like azimuthal state, and that the energy landscape of the magnetic configuration can be tailored geometrically. Specifically, the pinning of magnetic domain walls at curved vertices is observed experimentally and confirmed with micromagnetic simulations, offering geometrical control of magnetic configurations in nanotube architectures. This approach provides a new pathway to fabricate and study complex 3D core-shell magnetic structures, facilitating experimental investigations of their fundamental properties, key for the next-generation of spintronic devices.

This work was supported by the EPSRC and the
Centre for Doctoral Training (CDT) in Photonic Integration
and Advanced Data Storage (PIADS), RCUK Grant No. EP/
L015323/1, the European Community under the Horizon
2020 Program, Contract No. 101001290 (3DNANOMAG),
the MCIN with funding from European Union NextGener-
ationEU (PRTR-C17.I1), and the Aragon Government
through the Project Q-MAD. AH-R acknowledges the support from European Union’s Horizon 2020 research and
innovation program under Marie Skłodowska-Curie Grant
ref. H2020-MSCA-IF-2016-746958, from the Spanish
MICIN under Grant PID2019-104604RB/AEI/10.13039/
501100011033 and from the Asturias FICYT under Grant
AYUD/2021/51185 with the support of FEDER funds.
CINN (CSIC—Universidad de Oviedo), El Entrego, Spain LS acknowledges support from the University of Cambridge
(EPSRC Cambridge NanoDTC EP/L015978/1) DH
acknowledges Unité Mixte de Physique, CNRS, Thales,
Université Paris-Saclay, 91767, Palaiseau, France. CD
acknowledges funding from the Max Planck Society Lise
Meitner Excellence Program.

This project received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 101001290). A.H.-R. and S.M.
acknowledge support from the European Union’s Horizon 2020 research and innovation
programme under Marie Skłodowska-Curie grant H2020-MSCA-IF-2016-746958.
A.H.-R. acknowledges funding from the Spanish AEI under project PID2019–104604RB/
AEI/10.13039/501100011033, Donnelly, C; Hierro-Rodriguez, A; Abert, C; Witte, K; Skoric, L; Sanz-Hernandez, D; Finizio, S; Meng, FF; McVitie, S; Raabe, J; Suess, D; Cowburn, R; Fernandez-Pacheco, A

This work was supported by the European Community under the Horizon 2020 Program, Contract No. 101001290 (3DNANOMAG) the MCIN with funding from European Union NextGenerationEU (PRTR-C17.I1), and the Aragón Government
through the Project Q-MAD. A.H.-R. acknowledges the
support by Spanish MICIN under Grant No. PID2019-
104604RB/AEI/10.13039/501100011033 and by Asturias
FICYT under Grant No. AYUD/2021/51185 with the support of FEDER funds (...)

S. R-G., P. M-F, C. F-G and C.D. acknowledge funding
from the Max Planck Society Lise Meitner Excellence Program and funding from the European Research Council (ERC) under the ERC Starting Grant No. 3DNANOQUANT 101116043. (...) S. R-G acknowledges support from the Humboldt foundation grant 1223621 and Marie Curie fellowship grant GAP-101061612. (...) MF and MAN acknowledge funding through MICIN, project PID2021-122980OB-C54. N.B and S. R.-G. acknowledge funding through Advanced Materials program supported by MCIN with funding from the European Union NextGenerationEU (PRTR-C17.I1) and by the Generalitat de Catalunya. A. F.-P. Acknowledges funding from the European Community under the Horizon 2020 program. Contract NO 101001290 (3DNANOMAG). G.S.-S. acknowledges financial support from Grant RYC2022-038027-I funded by MICIU/AEI/10.13039/501100011033 and by ESF + . Electron microscopy observations at ICTS ELECMI (Centro
Nacional de Microscopia Electrónica) sponsored by grants Spanish MICINN PID2021-122980OB-C51 and Comunidad de Madrid “Materiales avanzados” MAD2D-UCM3., Ruiz-Gómez S., Abert C., Morales-Fernández P., Fernández-González C., Koraltan S., Danesi L., Suess D., Varela M., Sánchez-Santolino G., Bagués N., Foerster M., Niño M.Á., Mandziak A., Wilgocka-Ślęzak D., Nita P., Koenig M., Seifert S., Hierro-Rodriguez A., Fernández-Pacheco A., Donnelly C.

EU Horizon 2020 Program [730872, 101001290]; Spanish AEI [PID2019-104604RB/AEI/10.13039/501100011033] (...)