BUSCADOR RECOLECTA

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

[Description of methods used for collection/generation of data] Experiments obtained using magneto-optical Kerr effect, This work was supported by the European Community under the Horizon 2020 Program, Contract no. 101001290, 3DNANOMAG., Peer reviewed

[Description of methods used for collection/generation of data] Data was generated utilizing the code and model described in the main text of the publication.

[Methods for processing the data] Self-developed python code provided with data., Raw data for this publication, including Fourier-resolved magneto-optical Kerr effect maps and selected analysis of them, as shown in the paper., This work was supported by UKRI through an EPSRC studentship, 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 (PRTR-C17.I1), and the Aragon Government through the Project Q-MAD., The data is structured in different folders for each of the figures: - Figure4: contains HDF5 file "ParticularCases.h5", with the necessary data to generate the maps shown in figure 4. - Figure5: contains as ".npy" files the values for the optical and magneto-optical parameters for figure (a), as well as the error as a function of the number of averages for figure (c). - ResultsTable: contains the files necessary to generate the results shown in table II. The files "sstate" correspond to the "S" error results, whereas the "shared" correspond to the "SC" error results of the table. - SM1: contains the HDF5 files to generate the maps shown in figure 1 of the supplementary material for the different materials specified in the text. - SM2: contains the HDF5 files to generate the maps shown in figure 2 of the supplementary material for linear polarization and the magnetic configurations specified in the text. - SM4: contains the data needed to generate the uniqueness plot. "One theta" and "Two theta" are the data-sets when using respectively one or two different incidence angles for different optical plane values. The numpy arrays inside contain the fit values for each of the variables as a function of the number of fits as described in the supplementary text. These should be compared with the Permalloy values written in the main text, an incidence angle of 60 degrees and an optical plane angle of 13 degrees., Peer reviewed

The magneto-optical Kerr effect (MOKE) is a widely used lab-based technique 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. This generally provides signals proportional to a mixture of magnetization components, requiring additional methodologies 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 EP-SRC studentship, 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 (PRTR-C17.I1), and the Aragon Government
through the Project Q-MAD. Aurelio Hierro-Rodríguez acknowledges the support by Spanish MICIN under
grant PID2019-104604RB/AEI/10.13039/501100011033 and by Asturias FICYT under grant AYUD/2021/51185 with the support of FEDER funds. Dédalo Sanz-Hernández acknowledges funding from ANR/CNRS un-
der the French "Plan Relance de l’etat" for the preservation of R&D. Luka Skoric acknowledges support from the EPSRC Cambridge NanoDTC EP/L015978/1. Charles N. Christensen acknowledges the UK EPSRC Centre for Doctoral Training in Sensor Technologies for a Healthy and Sustainable Future. Claire Donnelly acknowledges funding from the Max Planck Society Lise Meitner Excellence Program., No

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

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.

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.

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.