Retrieving spin textures on curved magnetic thin films with full-field soft X-ray microscopies

3D imaging of magnetic domains in Nd2Fe14B using scanning hard X-ray nanotomography

Nanoscale structural and electronic heterogeneities are prevalent in condensed matter physics. Investigating these heterogeneities in 3D has become an important task for understanding material properties. To provide a tool to unravel the connection between nanoscale heterogeneity and macroscopic emergent properties in magnetic materials, scanning transmission X-ray microscopy (STXM) is combined with X-ray magnetic circular dichroism. A vector tomography algorithm has been developed to reconstruct the full 3D magnetic vector field without any prior noise assumptions or knowledge about the sample. Two tomographic scans around the vertical axis are acquired on single-crystalline Nd2Fe14B pillars tilted at two different angles, with 2D STXM projections recorded using a focused 120 nm X-ray beam with left and right circular polarization. Image alignment and iterative registration have been implemented based on the 2D STXM projections for the two tilts. Dichroic projections obtained from difference images are used for the tomographic reconstruction to obtain the 3D magnetization distribution at the nanoscale.

Real space iterative reconstruction for vector tomography (RESIRE-V)

Tomography has had an important impact on the physical, biological, and medical sciences. To date, most tomographic applications have been focused on 3D scalar reconstructions. However, in some crucial applications, vector tomography is required to reconstruct 3D vector fields such as the electric and magnetic fields. Over the years, several vector tomography methods have been developed. Here, we present the mathematical foundation and algorithmic implementation of REal Space Iterative REconstruction for Vector tomography, termed RESIRE-V. RESIRE-V uses multiple tilt series of projections and iterates between the projections and a 3D reconstruction. Each iteration consists of a forward step using the Radon transform and a backward step using its transpose, then updates the object via gradient descent. Incorporating with a 3D support constraint, the algorithm iteratively minimizes an error metric, defined as the difference between the measured and calculated projections. The algorithm can also be used to refine the tilt angles and further improve the 3D reconstruction. To validate RESIRE-V, we first apply it to a simulated data set of the 3D magnetization vector field, consisting of two orthogonal tilt series, each with a missing wedge. Our quantitative analysis shows that the three components of the reconstructed magnetization vector field agree well with the ground-truth counterparts. We then use RESIRE-V to reconstruct the 3D magnetization vector field of a ferromagnetic meta-lattice consisting of three tilt series. Our 3D vector reconstruction reveals the existence of topological magnetic defects with positive and negative charges. We expect that RESIRE-V can be incorporated into different imaging modalities as a general vector tomography method. To make the algorithm accessible to a broad user community, we have made our RESIRE-V MATLAB source codes and the data freely available at https://github.com/minhpham0309/RESIRE-V .

Magnetic characterization techniques and micromagnetic simulations of magnetic nanostructures: from zero to three dimensions

The investigation of the magnetic characteristics of magnetic nanostructures (MNs) in various dimensions is a crucial direction of research in nanomagnetism, with MNs belonging to various dimensions exhibiting magnetic properties related to their geometry. A better understanding of these magnetic properties is required for MN manipulation. The primary tools for researching MNs are magnetic characterisation techniques with great spatial resolution and spin sensitivity. Micromagnetic simulation is another technique that minimises experimental costs, while providing information on the magnetic structure and magnetic behaviour, and has enormous potential for predicting, validating, and extending the magnetic characterisation results. This review first looks at the progress of research into quantitatively characterising the magnetic properties of low-dimensional (including 0D, 1D, and 2D) and 3D MNs in two directions: magnetic characterisation techniques and micromagnetic simulations, with a particular emphasis on the potential for future applications of these techniques. Single magnetic characterization techniques, single micromagnetic simulations, or a mix of both are utilised in these research studies to investigate MNs in a variety of dimensions. How the magnetic characterisation techniques and micromagnetic simulations can be better applied to MNs in various dimensions is then outlined. This discussion has significant application potential for low-dimensional and 3D MNs.

Controlling the Interlayer Dzyaloshinskii-Moriya Interaction by Electrical Currents

The recently discovered interlayer Dzyaloshinskii-Moriya interaction (IL-DMI) in multilayers with perpendicular magnetic anisotropy favors canting of spins in the in-plane direction. It could thus stabilize intriguing spin textures such as Hopfions. A key requirement for nucleation is to control the IL-DMI. Therefore, we investigate the influence of an electric current on a synthetic antiferromagnet with growth-induced IL-DMI. The IL-DMI is quantified by using out-of-plane hysteresis loops of the anomalous Hall effect while applying a static in-plane magnetic field at varied azimuthal angles. We observe a shift in the azimuthal dependence with an increasing current, which we conclude to originate from the additional in-plane symmetry breaking introduced by the current flow. Fitting the angular dependence, we demonstrate the presence of an additive current-induced term that linearly increases the IL-DMI in the direction of current flow. This opens the possibility of easily manipulating 3D spin textures by currents.

Three-dimensional topological magnetic monopoles and their interactions in a ferromagnetic meta-lattice

Topological magnetic monopoles (TMMs), also known as hedgehogs or Bloch points, are three-dimensional (3D) non-local spin textures that are robust to thermal and quantum fluctuations due to the topology protection^1-4. Although TMMs have been observed in skyrmion lattices^1,5, spinor Bose-Einstein condensates^6,7, chiral magnets⁸, vortex rings^2,9 and vortex cores¹⁰, it has been difficult to directly measure the 3D magnetization vector field of TMMs and probe their interactions at the nanoscale. Here we report the creation of 138 stable TMMs at the specific sites of a ferromagnetic meta-lattice at room temperature. We further develop soft X-ray vector ptycho-tomography to determine the magnetization vector and emergent magnetic field of the TMMs with a 3D spatial resolution of 10 nm. This spatial resolution is comparable to the magnetic exchange length of transition metals¹¹, enabling us to probe monopole-monopole interactions. We find that the TMM and anti-TMM pairs are separated by 18.3 ± 1.6 nm, while the TMM and TMM, and anti-TMM and anti-TMM pairs are stabilized at comparatively longer distances of 36.1 ± 2.4 nm and 43.1 ± 2.0 nm, respectively. We also observe virtual TMMs created by magnetic voids in the meta-lattice. This work demonstrates that ferromagnetic meta-lattices could be used as a platform to create and investigate the interactions and dynamics of TMMs. Furthermore, we expect that soft X-ray vector ptycho-tomography can be broadly applied to quantitatively image 3D vector fields in magnetic and anisotropic materials at the nanoscale.

3D Interconnected Magnetic Nanowire Networks as Potential Integrated Multistate Memristors

Interconnected magnetic nanowire (NW) networks offer a promising platform for three-dimensional (3D) information storage and integrated neuromorphic computing. Here we report discrete propagation of magnetic states in interconnected Co nanowire networks driven by magnetic field and current, manifested in distinct magnetoresistance (MR) features. In these networks, when only a few interconnected NWs were measured, multiple MR kinks and local minima were observed, including a significant minimum at a positive field during the descending field sweep. Micromagnetic simulations showed that this unusual feature was due to domain wall (DW) pinning at the NW intersections, which was confirmed by off-axis electron holography imaging. In a complex network with many intersections, sequential switching of nanowire sections separated by interconnects was observed, along with stochastic characteristics. The pinning/depinning of the DWs can be further controlled by the driving current density. These results illustrate the promise of such interconnected networks as integrated multistate memristors.

Causal analysis and visualization of magnetization reversal using feature extended landau free energy

The magnetization reversal in nanomagnets is causally analyzed using an extended Landau free-energy model. This model draws an energy landscape in the information space using physics-based features. Thus, the origin of the magnetic effect in macroscopic pinning phenomena can be identified. The microscopic magnetic domain beyond the hierarchy can be explained using energy gradient analysis and its decomposition. Structural features from the magnetic domains are extracted using persistent homology. Extended energy is visualized using ridge regression, principal component analysis, and Hadamard products. We found that the demagnetization energy concentration near a defect causes the demagnetization effect, which quantitatively dominates the pinning phenomenon. The exchange energy inhibits pinning, promotes saturation, and shows slight interactions with the defect. Furthermore, the energy distributions are visualized in real space. Left-position defects reduce the energy barrier and are useful for the topological inverse design of recording devices.

Layer-Dependent Magnetic Domains in Atomically Thin Fe5GeTe2

Magnetic domain formation in two-dimensional (2D) materials gives perspectives into the fundamental origins of 2D magnetism and also motivates the development of advanced spintronics devices. However, the characterization of magnetic domains in atomically thin van der Waals (vdW) flakes remains challenging. Here, we employ X-ray photoemission electron microscopy (XPEEM) to perform layer-resolved imaging of the domain structures in the itinerant vdW ferromagnet Fe5GeTe2 which shows near room temperature bulk ferromagnetism and a weak perpendicular magnetic anisotropy (PMA). In the bulk limit, we observe the well-known labyrinth-type domains. Thinner flakes, on the other hand, are characterized by increasingly fragmented domains. While PMA is a characteristic property of Fe5GeTe2, we observe a spin-reorientation transition with the spins canting in-plane for flakes thinner than six layers. Notably, a bubble phase emerges in four-layer flakes. This thickness dependence, which clearly deviates from the single-domain behavior observed in other 2D magnetic materials, demonstrates the exciting prospect of stabilizing complex spin textures in 2D vdW magnets at relatively high temperatures.

Unveiling the three-dimensional magnetic texture of skyrmion tubes

Magnetic skyrmions are stable topological solitons with complex non-coplanar spin structures. Their nanoscopic size and the low electric currents required to control their motion has opened a new field of research, skyrmionics, that aims for the usage of skyrmions as information carriers. Further advances in skyrmionics call for a thorough understanding of their three-dimensional (3D) spin texture, skyrmion-skyrmion interactions and the coupling to surfaces and interfaces, which crucially affect skyrmion stability and mobility. Here, we quantitatively reconstruct the 3D magnetic texture of Bloch skyrmions with sub-10-nanometre resolution using holographic vector-field electron tomography. The reconstructed textures reveal local deviations from a homogeneous Bloch character within the skyrmion tubes, details of the collapse of the skyrmion texture at surfaces and a correlated modulation of the skyrmion tubes in FeGe along their tube axes. Additionally, we confirm the fundamental principles of skyrmion formation through an evaluation of the 3D magnetic energy density across these magnetic solitons.

Geometrically stabilized skyrmionic vortex in FeGe tetrahedral nanoparticles

The concept of topology has dramatically expanded the research landscape of magnetism, leading to the discovery of numerous magnetic textures with intriguing topological properties. A magnetic skyrmion is an emergent topological magnetic texture with a string-like structure in three dimensions and a disk-like structure in one and two dimensions. Skyrmions in zero dimensions have remained elusive due to challenges from many competing orders. Here, by combining electron holography and micromagnetic simulations, we uncover the real-space magnetic configurations of a skyrmionic vortex structure confined in a B20-type FeGe tetrahedral nanoparticle. An isolated skyrmionic vortex forms at the ground state and this texture shows excellent robustness against temperature without applying a magnetic field. Our findings shed light on zero-dimensional geometrical confinement as a route to engineer and manipulate individual skyrmionic metastructures.

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures

Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.

Creating Ferroic Micropatterns through Geometrical Transformation

The functionality of a ferroic device is intimately coupled to the configuration of domains, domain boundaries, and the possibility for tailoring them. Exemplified with a ferromagnetic system, we present a novel approach which allows the creation of new, metastable multidomain patterns with tailored wall configurations through a self-assembled geometrical transformation. By preparing a magnetic layer system on a polymeric platform including swelling layer, a repeated self-assembled rolling into a multiwinding tubular structure and unrolling of the functional membrane is obtained. When polarizing the rolled-up 3D structure in a simple homogeneous magnetic field, the imprinted configuration translates into a regularly arranged multidomain configuration once the tubular structure is unwound. The process is linked to the employed magnetic anisotropy with respect to the surface normal, and the geometrical transformation connects the angular with the lateral degrees of freedom. This combination offers unparalleled possibilities for designing new magnetic or other ferroic micropatterns.

Revealing 3D magnetization of thin films with soft X-ray tomography: magnetic singularities and topological charges

The knowledge of how magnetization looks inside a ferromagnet is often hindered by the limitations of the available experimental methods which are sensitive only to the surface regions or limited in spatial resolution. Here we report a vector tomographic reconstruction based on soft X-ray transmission microscopy and magnetic dichroism data, which has allowed visualizing the three-dimensional magnetization in a ferromagnetic thin film heterostructure. Different non-trivial topological textures have been resolved and the determination of their topological charge has allowed us to identify a Bloch point and a meron-like texture. Our method relies only on experimental data and might be of wide application and interest in 3D nanomagnetism.

Although magnetic tomography has been used in the past to determine the 3D magnetization of materials its application to thin films remains challenging. Here the authors reconstruct the magnetization of a thin film, enabling the measurement of topological charges of magnetic singularities.

Spin-wave spectroscopy of individual ferromagnetic nanodisks

The increasing demand for nanoscale magnetic devices requires development of 3D magnetic nanostructures. In this regard, focused electron beam induced deposition (FEBID) is a technique of choice for direct-writing of complex nano-architectures with applications in nanomagnetism, magnon spintronics, and superconducting electronics. However, intrinsic properties of nanomagnets are often poorly known and can hardly be assessed by local optical probe techniques. Here, an original spatially resolved approach is demonstrated for spin-wave spectroscopy of individual circular magnetic elements with sample volumes down to about 10-3 μm3. The key component of the setup is a coplanar waveguide whose microsized central part is placed over a movable substrate with well-separated CoFe-FEBID nanodisks which exhibit standing spin-wave resonances. The circular symmetry of the disks allows for the deduction of the saturation magnetization and the exchange stiffness of the material using an analytical theory. A good correspondence between the results of analytical calculations and micromagnetic simulations is revealed, indicating a validity of the used analytical model going beyond the initial thin-disk approximation used in the theoretical derivation. The presented approach is especially valuable for the characterization of direct-write magnetic elements opening new horizons for 3D nanomagnetism and magnonics.

Artificial Double-Helix for Geometrical Control of Magnetic Chirality

Chirality plays a major role in nature, from particle physics to DNA, and its control is much sought-after due to the scientific and technological opportunities it unlocks. For magnetic materials, chiral interactions between spins promote the formation of sophisticated swirling magnetic states such as skyrmions, with rich topological properties and great potential for future technologies. Currently, chiral magnetism requires either a restricted group of natural materials or synthetic thin-film systems that exploit interfacial effects. Here, using state-of-the-art nanofabrication and magnetic X-ray microscopy, we demonstrate the imprinting of complex chiral spin states via three-dimensional geometric effects at the nanoscale. By balancing dipolar and exchange interactions in an artificial ferromagnetic double-helix nanostructure, we create magnetic domains and domain walls with a well-defined spin chirality, determined solely by the chiral geometry. We further demonstrate the ability to create confined 3D spin textures and topological defects by locally interfacing geometries of opposite chirality. The ability to create chiral spin textures via 3D nanopatterning alone enables exquisite control over the properties and location of complex topological magnetic states, of great importance for the development of future metamaterials and devices in which chirality provides enhanced functionality.

Perspective: Ferromagnetic Liquids

Mechanical jamming of nanoparticles at liquid-liquid interfaces has evolved into a versatile approach to structure liquids with solid-state properties. Ferromagnetic liquids obtain their physical and magnetic properties, including a remanent magnetization that distinguishes them from ferrofluids, from the jamming of magnetic nanoparticles assembled at the interface between two distinct liquids to minimize surface tension. This perspective provides an overview of recent progress and discusses future directions, challenges and potential applications of jamming magnetic nanoparticles with regard to 3D nano-magnetism. We address the formation and characterization of curved magnetic geometries, and spin frustration between dipole-coupled nanostructures, and advance our understanding of particle jamming at liquid-liquid interfaces.

Imaging three-dimensional magnetic systems with x-rays

Recent progress in nanofabrication and additive manufacturing have facilitated the building of nanometer-scale three-dimensional (3D) structures, that promise to lead to an emergence of new functionalities within a number of fields, compared to state-of-the-art two dimensional systems. In magnetism, the move to 3D systems offers the possibility for novel magnetic properties not available in planar systems, as well as enhanced performance, both of which are key for the development of new technological applications. In this review paper we will focus our attention on 3D magnetic systems and how their magnetic configuration can be retrieved using x-ray magnetic nanotomography. We will start with an introduction to magnetic materials, and their relevance to our everyday life, along with the growing impact that they will have in the coming years in, for example, reducing energy consumption. We will then briefly introduce common methods used to study magnetic materials, such as electron holography, neutron and x-ray imaging. In particular, we will focus on x-ray magnetic circular dichroism (XMCD) and how it can be used to image magnetic moment configurations. As a next step we will introduce tomography for 3D imaging, and how it can be adapted to study magnetic materials. Particular attention will be given to explaining the reconstruction algorithms that can be used to retrieve the magnetic moment configuration from the experimental data, as these represent one of the main challenges so far, as well as the different experimental geometries that are available. Recent experimental results will be used as specific examples to guide the reader through each step in order to make sure that the paper will be accessible for those interested in the topic that do not have a specialized background on magnetic imaging. Finally, we will describe the future prospects of such studies, identifying the current challenges facing the field, and how these can be tackled. In particular we will highlight the exciting possibilities offered by the next generation of synchrotron sources which will deliver diffraction limited beams, as well as with the extension of well-established methodologies currently implemented for the study of two-dimensional magnetic materials to achieve higher dimensional investigations.

Time-resolved imaging of three-dimensional nanoscale magnetization dynamics

Understanding and control of the dynamic response of magnetic materials with a three-dimensional magnetization distribution is important both fundamentally and for technological applications. From a fundamental point of view, the internal magnetic structure and dynamics in bulk materials still need to be mapped¹, including the dynamic properties of topological structures such as vortices², magnetic singularities³ or skyrmion lattices⁴. From a technological point of view, the response of inductive materials to magnetic fields and spin-polarized currents is essential for magnetic sensors and data storage devices⁵. Here, we demonstrate time-resolved magnetic laminography, a pump-probe technique, which offers access to the temporal evolution of a three-dimensional magnetic microdisc with nanoscale resolution, and with a synchrotron-limited temporal resolution of 70 ps. We image the dynamic response to a 500 MHz magnetic field of the complex three-dimensional magnetization in a two-phase bulk magnet with a lateral spatial resolution of 50 nm. This is achieved with a stroboscopic measurement consisting of eight time steps evenly spaced over 2 ns. These measurements map the spatial transition between domain wall motion and the dynamics of a uniform magnetic domain that is attributed to variations in the magnetization state across the phase boundary. Our technique, which probes three-dimensional magnetic structures with temporal resolution, enables the experimental investigation of functionalities arising from dynamic phenomena in bulk and three-dimensional patterned nanomagnets⁶.

From 2D STXM to 3D Imaging: Soft X-ray Laminography of Thin Specimens

X-ray tomography has become an indispensable tool for studying complex 3D interior structures with high spatial resolution. Three-dimensional imaging using soft X-rays offers powerful contrast mechanisms but has seen limited success with tomography due to the restrictions imposed by the much lower energy of the probe beam. The generalized geometry of laminography, characterized by a tilted axis of rotation, provides nm-scale 3D resolution for the investigation of extended (mm range) but thin (μm to nm) samples that are well suited to soft X-ray studies. This work reports on the implementation of soft X-ray laminography (SoXL) at the scanning transmission X-ray spectromicroscope of the PolLux beamline at the Swiss Light Source, Paul Scherrer Institut, which enables 3D imaging of extended specimens from 270 to 1500 eV. Soft X-ray imaging provides contrast mechanisms for both chemical sensitivity to molecular bonds and oxidation states and magnetic dichroism due to the much stronger attenuation of X-rays in this energy range. The presented examples of applications range from functionalized nanomaterials to biological photonic crystals and sophisticated nanoscaled magnetic domain patterns, thus illustrating the wide fields of research that can benefit from SoXL.

Magnetic Materials and Systems: Domain Structure Visualization and Other Characterization Techniques for the Application in the Materials Science and Biomedicine

Magnetic structures have attracted a great interest due to their multiple applications, from physics to biomedicine. Several techniques are currently employed to investigate magnetic characteristics and other physicochemical properties of magnetic structures. The major objective of this review is to summarize the current knowledge on the usage, advances, advantages, and disadvantages of a large number of techniques that are currently available to characterize magnetic systems. The present review, aiming at helping in the choice of the most suitable method as appropriate, is divided into three sections dedicated to characterization techniques. Firstly, the magnetism and magnetization (hysteresis) techniques are introduced. Secondly, the visualization methods of the domain structures by means of different probes are illustrated. Lastly, the characterization of magnetic nanosystems in view of possible biomedical applications is discussed, including the exploitation of magnetism in imaging for cell tracking/visualization of pathological alterations in living systems (mainly by magnetic resonance imaging, MRI).

Co/Pd-Based synthetic antiferromagnetic thin films on Au/resist underlayers: towards biomedical applications

Thin film stacks consisting of multiple repeats M of synthetic antiferromagnetic (SAF) [Co/Pd]N/Ru/[Co/Pd]N units with perpendicular magnetic anisotropy were explored as potential starting materials to fabricate free-standing micro/nanodisks, which represent a promising candidate system for theranostic applications. The films were directly grown on a sacrificial resist layer spin-coated on SiOx/Si(100) substrates, required for the preparation of free-standing disks after its dissolution. Furthermore, the film stack was sandwiched between two Au layers to allow further bio-functionalization. For M ≤ 5, the samples fulfill all the key criteria mandatory for biomedical applications, i.e., zero remanence, zero field susceptibility at small fields and sharp switching to saturation, together with the ability to vary the total magnetic moment at saturation by changing the number of repetitions of the multi-stack. Moreover, the samples show strong perpendicular magnetic anisotropy, which is required for applications relying on the transduction of a mechanical force through the micro/nano-disks under a magnetic field, such as the mechanical cell disruption, which is nowadays considered a promising alternative to the more investigated magnetic hyperthermia approach for cancer treatment. In a further step, SAF microdisks were prepared from the continuous multi-stacks by combining electron beam lithography and Ar ion milling, revealing similar magnetic properties as compared to the continuous films.

Soft X-ray magnetic scattering studies of 3D magnetic morphology along buried interfaces in NiFe/CoPd/NiFe nanostructures

With the continuing interest in new magnetic materials for sensor devices and data storage applications, the community needs reliable and sensitive tools for the characterization of such materials. Soft X-rays tuned to elemental absorption edges are a depth and element sensitive probe of magnetic structure at the nanoscale, and scattering measurements have the potential to provide 3D magnetic structural information of the material. In this work we develop a methodology in transmission geometry that allows one to probe the spatial distribution of the magnetization along the different layers of magnetic heterostructures. We study the in-plane/out-of-plane transition of magnetic domains in multilayer thin film systems consisting of two layers of NiFe top and bottom, and a 50 repeat Co/Pd multilayer in the centre. The experimental data are analysed by simulating scattering data starting from micromagnetic simulations, and we find that the out of plane domains of the Co/Pd multilayer intrude into the NiFe layers to a greater extent than would be expected from micromagnetic simulations performed using the standard magnetically isotropic input parameters for the NiFe layers.

Tensorial neutron tomography of three-dimensional magnetic vector fields in bulk materials

Knowing the distribution of a magnetic field in bulk materials is important for understanding basic phenomena and developing functional magnetic materials. Microscopic imaging techniques employing X-rays, light, electrons, or scanning probe methods have been used to quantify magnetic fields within planar thin magnetic films in 2D or magnetic vector fields within comparable thin volumes in 3D. Some years ago, neutron imaging has been demonstrated to be a unique tool to detect magnetic fields and magnetic domain structures within bulk materials. Here, we show how arbitrary magnetic vector fields within bulk materials can be visualized and quantified in 3D using a set of nine spin-polarized neutron imaging measurements and a novel tensorial multiplicative algebraic reconstruction technique (TMART). We first verify the method by measuring the known magnetic field of an electric coil and then investigate the unknown trapped magnetic flux within the type-I superconductor lead.

Mapping the distribution of magnetic fields inside bulk materials is challenging but crucial to understand and develop functional magnetic materials. Here the authors demonstrate the capability to visualize 3D vector magnetic fields inside materials using spin-polarized neutron tomography and tensorial reconstruction techniques.

Experimental Evidence of Chiral Ferrimagnetism in Amorphous GdCo Films

Inversion symmetry breaking has become a vital research area in modern magnetism with phenomena including the Rashba effect, spin Hall effect, and the Dzyaloshinskii-Moriya interaction (DMI)-a vector spin exchange. The latter one may stabilize chiral spin textures with topologically nontrivial properties, such as Skyrmions. So far, chiral spin textures have mainly been studied in helimagnets and thin ferromagnets with heavy-element capping. Here, the concept of chirality driven by interfacial DMI is generalized to complex multicomponent systems and demonstrated on the example of chiral ferrimagnetism in amorphous GdCo films. Utilizing Lorentz microscopy and X-ray magnetic circular dichroism spectroscopy, and tailoring thickness, capping, and rare-earth composition, reveal that 2 nm thick GdCo films preserve ferrimagnetism and stabilize chiral domain walls. The type of chiral domain walls depends on the rare-earth composition/saturation magnetization, enabling a possible temperature control of the intrinsic properties of ferrimagnetic domain walls.

Origin and Manipulation of Stable Vortex Ground States in Permalloy Nanotubes

We present a detailed study on the static magnetic properties of individual permalloy nanotubes (NTs) with hexagonal cross-sections. Anisotropic magnetoresistance (AMR) measurements and scanning transmission X-ray microscopy (STXM) are used to investigate their magnetic ground states and its stability. We find that the magnetization in zero applied magnetic field is in a very stable vortex state. Its origin is attributed to a strong growth-induced anisotropy with easy axis perpendicular to the long axis of the tubes. AMR measurements of individual NTs in combination with micromagnetic simulations allow the determination of the magnitude of the growth-induced anisotropy for different types of NT coatings. We show that the strength of the anisotropy can be controlled by introducing a buffer layer underneath the magnetic layer. The magnetic ground states depend on the external magnetic field history and are directly imaged using STXM. Stable vortex domains can be introduced by external magnetic fields and can be erased by radio-frequency magnetic fields applied at the center of the tubes via a strip line antenna.

Imaging Stray Magnetic Field of Individual Ferromagnetic Nanotubes

We use a scanning nanometer-scale superconducting quantum interference device to map the stray magnetic field produced by individual ferromagnetic nanotubes (FNTs) as a function of applied magnetic field. The images are taken as each FNT is led through magnetic reversal and are compared with micromagnetic simulations, which correspond to specific magnetization configurations. In magnetic fields applied perpendicular to the FNT long axis, their magnetization appears to reverse through vortex states, that is, configurations with vortex end domains or in the case of a sufficiently short FNT with a single global vortex. Geometrical imperfections in the samples and the resulting distortion of idealized magnetization configurations influence the measured stray-field patterns.

Transmission XMCD-PEEM imaging of an engineered vertical FEBID cobalt nanowire with a domain wall

Using focused electron-beam-induced deposition, we fabricate a vertical, platinum-coated cobalt nanowire with a controlled three-dimensional structure. The latter is engineered to feature bends along the height: these are used as pinning sites for domain walls, which are obtained at remanence after saturation of the nanostructure in a horizontally applied magnetic field. The presence of domain walls is investigated using x-ray magnetic circular dichroism (XMCD) coupled to photoemission electron microscopy (PEEM). The vertical geometry of our sample combined with the low incidence of the x-ray beam produce an extended wire shadow which we use to recover the wire's magnetic configuration. In this transmission configuration, the whole sample volume is probed, thus circumventing the limitation of PEEM to surfaces. This article reports on the first study of magnetic nanostructures standing perpendicular to the substrate with XMCD-PEEM. The use of this technique in shadow mode enabled us to confirm the presence of a domain wall without direct imaging of the nanowire.

Mesoscale Dzyaloshinskii-Moriya interaction: geometrical tailoring of the magnetochirality

Crystals with broken inversion symmetry can host fundamentally appealing and technologically relevant periodical or localized chiral magnetic textures. The type of the texture as well as its magnetochiral properties are determined by the intrinsic Dzyaloshinskii-Moriya interaction (DMI), which is a material property and can hardly be changed. Here we put forth a method to create new artificial chiral nanoscale objects with tunable magnetochiral properties from standard magnetic materials by using geometrical manipulations. We introduce a mesoscale Dzyaloshinskii-Moriya interaction that combines the intrinsic spin-orbit and extrinsic curvature-driven DMI terms and depends both on the material and geometrical parameters. The vector of the mesoscale DMI determines magnetochiral properties of any curved magnetic system with broken inversion symmetry. The strength and orientation of this vector can be changed by properly choosing the geometry. For a specific example of nanosized magnetic helix, the same material system with different geometrical parameters can acquire one of three zero-temperature magnetic phases, namely, phase with a quasitangential magnetization state, phase with a periodical state and one intermediate phase with a periodical domain wall state. Our approach paves the way towards the realization of a new class of nanoscale spintronic and spinorbitronic devices with the geometrically tunable magnetochirality.

Three-dimensional nanomagnetism

Magnetic nanostructures are being developed for use in many aspects of our daily life, spanning areas such as data storage, sensing and biomedicine. Whereas patterned nanomagnets are traditionally two-dimensional planar structures, recent work is expanding nanomagnetism into three dimensions; a move triggered by the advance of unconventional synthesis methods and the discovery of new magnetic effects. In three-dimensional nanomagnets more complex magnetic configurations become possible, many with unprecedented properties. Here we review the creation of these structures and their implications for the emergence of new physics, the development of instrumentation and computational methods, and exploitation in numerous applications.

Nanoscale magnetic devices play a key role in modern technologies but current applications involve only 2D structures like magnetic discs. Here the authors review recent progress in the fabrication and understanding of 3D magnetic nanostructures, enabling more diverse functionalities.

Magnetically Patterned Rolled-Up Exchange Bias Tubes: A Paternoster for Superparamagnetic Beads

We realized a deterministic transport system for superparamagnetic microbeads through micrometer-sized tubes acting as channels. Beads are moved stepwise in a paternoster-like manner through the tube and back on top of it by weak magnetic field pulses without changing the field pulse polarity and taking advantage of the magnetic stray field emerging from the tubular structures. The microtubes are engineered by rolling up exchange bias layer systems, magnetically patterned into parallel stripe magnetic domains. In this way, the tubes possess distinct azimuthally aligned magnetic domain patterns. This transport mechanism features high step velocities and remote control of not only the direction and trajectory but also the velocity of the transport without the need of fuel or catalytic material. Therefore, this approach has the potential to impact several fields of 3D applications in biotechnology, including particle transport related phenomena in lab-on-a-chip and lab-in-a-tube devices.

Rashba Torque Driven Domain Wall Motion in Magnetic Helices

Manipulation of the domain wall propagation in magnetic wires is a key practical task for a number of devices including racetrack memory and magnetic logic. Recently, curvilinear effects emerged as an efficient mean to impact substantially the statics and dynamics of magnetic textures. Here, we demonstrate that the curvilinear form of the exchange interaction of a magnetic helix results in an effective anisotropy term and Dzyaloshinskii-Moriya interaction with a complete set of Lifshitz invariants for a one-dimensional system. In contrast to their planar counterparts, the geometrically induced modifications of the static magnetic texture of the domain walls in magnetic helices offer unconventional means to control the wall dynamics relying on spin-orbit Rashba torque. The chiral symmetry breaking due to the Dzyaloshinskii-Moriya interaction leads to the opposite directions of the domain wall motion in left- or right-handed helices. Furthermore, for the magnetic helices, the emergent effective anisotropy term and Dzyaloshinskii-Moriya interaction can be attributed to the clear geometrical parameters like curvature and torsion offering intuitive understanding of the complex curvilinear effects in magnetism.

Self-Assembled On-Chip-Integrated Giant Magneto-Impedance Sensorics

A novel method relying on strain engineering to realize arrays of on-chip-integrated giant magneto-impedance (GMI) sensors equipped with pick-up coils is put forth. The geometrical transformation of an initially planar layout into a tubular 3D architecture stabilizes favorable azimuthal magnetic domain patterns. This work creates a solid foundation for further development of CMOS compatible GMI sensorics for magnetoencephalography.