Three-dimensional nanomagnetism

Tailoring magnon modes by extending square, kagome, and trigonal spin ice lattices vertically via interlayer coupling of trilayer nanomagnets

In this work high-frequency magnetization dynamics and statics of artificial spin-ice lattices with different geometric nanostructure array configurations are studied where the individual nanostructures are composed of ferromagnetic/non-magnetic/ferromagnetic trilayers with different non-magnetic thicknesses. These thickness variations enable additional control over the magnetic interactions within the spin-ice lattice that directly impacts the resulting magnetization dynamics and the associated magnonic modes. Specifically the geometric arrangements studied are square, kagome and trigonal spin ice configurations, where the individual lithographically patterned nanomagnets (NMs) are trilayers, made up of two magnetic layers ofNi81Fe19of 30 nm and 70 nm thickness respectively, separated by a non-magnetic copper layer of either 2 nm or 40 nm. We show that coupling via the magnetostatic interactions between the ferromagnetic layers of the NMs within square, kagome and trigonal spin-ice lattices offers fine-control over magnetization states and magnetic resonant modes. In particular, the kagome and trigonal lattices allow tuning of an additional mode and the spacing between multiple resonance modes, increasing functionality beyond square lattices. These results demonstrate the ability to move beyond quasi-2D single magnetic layer nanomagnetics via control of the vertical interlayer interactions in spin ice arrays. This additional control enables multi-mode magnonic programmability of the resonance spectra, which has potential for magnetic metamaterials for microwave or information processing applications.

Microstructure parameter-dependent non-collinear magnetic structures in scandium-doped M-type hexaferrite nanocrystals

The quest for materials with non-collinear magnetic structures has been driven by their unique properties and potential applications in advanced spintronics and data storage technologies. In this study, we investigate the induction of a non-collinear conical state in BaFe12O19 (M-type) nanocrystal fibers through the substitution of Fe3+ ions with diamagnetic Sc3+ ions. This substitution introduces an additional parameter for tuning the magnetic structure and allows precise control over the substitution amount. We demonstrate that the non-collinear conical state remains stable within a temperature range of 125 K to 325 K and can be finely adjusted by varying the Sc3+ substitution amount. The selective occupancy of Sc3+ ions at the 2a, 4f2, and 2b sites within the M-type ferrite lattice weakens the super-exchange interaction between Fe1, Fe2, and Fe5 ions. This weakening disrupts interactions between different blocks S/R (R*/S*) and stabilizes the conical state. These findings highlight a significant approach to modulating non-collinear magnetic structures in hexagonal ferrites, with implications for both fundamental research and practical applications in the development of novel magnetic materials.

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.

The 2024 magnonics roadmap

Magnonicsis a research field that has gained an increasing interest in both the fundamental and applied sciences in recent years. This field aims to explore and functionalize collective spin excitations in magnetically ordered materials for modern information technologies, sensing applications and advanced computational schemes. Spin waves, also known as magnons, carry spin angular momenta that allow for the transmission, storage and processing of information without moving charges. In integrated circuits, magnons enable on-chip data processing at ultrahigh frequencies without the Joule heating, which currently limits clock frequencies in conventional data processors to a few GHz. Recent developments in the field indicate that functional magnonic building blocks for in-memory computation, neural networks and Ising machines are within reach. At the same time, the miniaturization of magnonic circuits advances continuously as the synergy of materials science, electrical engineering and nanotechnology allows for novel on-chip excitation and detection schemes. Such circuits can already enable magnon wavelengths of 50 nm at microwave frequencies in a 5G frequency band. Research into non-charge-based technologies is urgently needed in view of the rapid growth of machine learning and artificial intelligence applications, which consume substantial energy when implemented on conventional data processing units. In its first part, the 2024 Magnonics Roadmap provides an update on the recent developments and achievements in the field of nano-magnonics while defining its future avenues and challenges. In its second part, the Roadmap addresses the rapidly growing research endeavors on hybrid structures and magnonics-enabled quantum engineering. We anticipate that these directions will continue to attract researchers to the field and, in addition to showcasing intriguing science, will enable unprecedented functionalities that enhance the efficiency of alternative information technologies and computational schemes.

Giant supermagnonic Bloch point velocities in cylindrical ferromagnetic nanowires

Achieving high velocities of magnetic domain walls is a crucial factor for their use as information carriers in modern nanoelectronic applications. In nanomagnetism and spintronics, these velocities are often limited either by internal domain wall instabilities, known as the Walker breakdown phenomenon, or by spin wave emission, known as the magnonic regime. In the rigid domain wall model, the maximum magnon velocity acts as an effective "speed of light", providing a relativistic analogy for the domain wall speed limitation. Cylindrical magnetic nanowires are an example of systems without the Walker breakdown phenomenon. Here we demonstrate that the magnonic limit could be outstandingly surpassed in cylindrical nanowires with high magnetization, such as iron. Our numerical modeling shows the Bloch point domain wall velocities as high as 14 km s-1, well above the magnonic limit estimated in the interval 1.7-2.0 km s-1. The key ingredient is the three-dimensional conical shape of the domain wall, which elongates and breaks during the dynamics, expelling backwards pairs of Bloch points. This leads to domain wall acceleration, the effect, which resembles the "jet propulsion". This effect will be very important for three-dimensional networks based on cylindrical magnetic nanowires.

Demonstration of Controlled Skyrmion Injection Across a Thickness Step

Spintronic devices incorporating magnetic skyrmions have attracted significant interest recently. Such devices traditionally focus on controlling magnetic textures in 2D thin films. However, enhanced performance of spintronic properties through the exploitation of higher dimensionalities motivates the investigation of variable-thickness skyrmion devices. We report the demonstration of a skyrmion injection mechanism that utilizes charge currents to drive skyrmions across a thickness step and, consequently, a metastability barrier. Our measurements show that under certain temperature and field conditions skyrmions can be reversibly injected from a thin region of an FeGe lamella, where they exist as an equilibrium state, into a thicker region, where they can only persist as a metastable state. This injection is achieved with a current density of 3 × 108 A m-2, nearly 3 orders of magnitude lower than required to move magnetic domain walls. This highlights the possibility to use such an element as a skyrmion source/drain within future spintronic devices.

Symmetry Breaking-Induced Resonance Dynamics in Bloch Point Nanospheres: Unveiling Magnetic Volume Effects and Geometric Parameters for Advanced Applications in Magnetic Sensing and Spintronics

This study explores the impact of symmetry breaking on the ferromagnetic resonance of Bloch point (BP) nanospheres. Through standard Fourier analysis, we unveil two distinct oscillation mode groups characterized by low and high frequencies, respectively. Our findings emphasize the pivotal role of magnetic volume in shaping resonance amplitudes, providing new insights into the intricate dynamics of BP states. The investigation of geometric parameters reveals a quasi-monotonic decrease in resonance frequencies as a function of the asymmetry degree attributed to symmetry-breaking induced by geometric modifications. Spatial distribution analysis showcases unique resonance frequencies for the upper and lower BP hemispheres, highlighting the nuanced impact of the geometry on mode excitation. As the radius increases, additional modes emerge, demonstrating a compelling relationship between the magnetic volume and frequency. Phase analysis unveils coherent oscillations within each BP hemisphere, offering valuable insights into the rotational directions of the excitation poles. Beyond fundamental understanding, our study opens avenues for innovative applications, suggesting the potential use of nanospheres in advanced magnetic sensing, data storage, and nanoscale spintronic devices.

Ultrastrong magnon-magnon coupling and chiral spin-texture control in a dipolar 3D multilayered artificial spin-vortex ice

Strongly-interacting nanomagnetic arrays are ideal systems for exploring reconfigurable magnonics. They provide huge microstate spaces and integrated solutions for storage and neuromorphic computing alongside GHz functionality. These systems may be broadly assessed by their range of reliably accessible states and the strength of magnon coupling phenomena and nonlinearities. Increasingly, nanomagnetic systems are expanding into three-dimensional architectures. This has enhanced the range of available magnetic microstates and functional behaviours, but engineering control over 3D states and dynamics remains challenging. Here, we introduce a 3D magnonic metamaterial composed from multilayered artificial spin ice nanoarrays. Comprising two magnetic layers separated by a non-magnetic spacer, each nanoisland may assume four macrospin or vortex states per magnetic layer. This creates a system with a rich 16N microstate space and intense static and dynamic dipolar magnetic coupling. The system exhibits a broad range of emergent phenomena driven by the strong inter-layer dipolar interaction, including ultrastrong magnon-magnon coupling with normalised coupling rates ofΔ f ν = 0.57 , GHz mode shifts in zero applied field and chirality-control of magnetic vortex microstates with corresponding magnonic spectra.

Collective Spin-Wave Dynamics in Gyroid Ferromagnetic Nanostructures

Expanding upon the burgeoning discipline of magnonics, this research elucidates the intricate dynamics of spin waves (SWs) within three-dimensional nanoenvironments. It marks a shift from traditionally used planar systems to exploration of magnetization configurations and the resulting dynamics within 3D nanostructures. This study deploys micromagnetic simulations alongside ferromagnetic resonance measurements to scrutinize magnetic gyroids, periodic chiral configurations composed of chiral triple junctions with a period in nanoscale. Our findings uncover distinctive attributes intrinsic to the gyroid network, most notably the localization of collective SW excitations and the sensitivity of the gyroid's ferromagnetic response to the orientation of the static magnetic field, a correlation closely tied to the crystallographic alignment of the structure. Furthermore, we show that for the ferromagnetic resonance, multidomain gyroid films can be treated as a magnonic material with effective magnetization scaled by its filling factor. The implications of our research carry the potential for practical uses such as an effective, metamaterial-like substitute for ferromagnetic parts and lay the groundwork for radio frequency filters. The growing areas of 3D magnonics and spintronics present exciting opportunities to investigate and utilize gyroid nanostructures for signal processing purposes.

Three-dimensional spin-wave dynamics, localization and interference in a synthetic antiferromagnet

Spin waves are collective perturbations in the orientation of the magnetic moments in magnetically ordered materials. Their rich phenomenology is intrinsically three-dimensional; however, the three-dimensional imaging of spin waves has so far not been possible. Here, we image the three-dimensional dynamics of spin waves excited in a synthetic antiferromagnet, with nanoscale spatial resolution and sub-ns temporal resolution, using time-resolved magnetic laminography. In this way, we map the distribution of the spin-wave modes throughout the volume of the structure, revealing unexpected depth-dependent profiles originating from the interlayer dipolar interaction. We experimentally demonstrate the existence of complex three-dimensional interference patterns and analyze them via micromagnetic modelling. We find that these patterns are generated by the superposition of spin waves with non-uniform amplitude profiles, and that their features can be controlled by tuning the composition and structure of the magnetic system. Our results open unforeseen possibilities for the study and manipulation of complex spin-wave modes within nanostructures and magnonic devices.

Tuning the dimensional order in self-assembled magnetic nanostructures: theory, simulations, and experiments

A major obstacle to building nanoscale magnetic devices or even experimentally studying novel nanomagnetic spin textures is the present lack of a simple and robust method to fabricate various nano-structured alloys. Here, theoretical and experimental investigations were conducted to understand the underlying physical mechanisms of magnetic particle self-assembly in zero applied magnetic field. By changing the amount of NaOH added during the synthesis, we demonstrate that the resulting morphology of the assembled FeCo structure can be tuned from zero-dimensional (0D) nanoparticles to one-dimensional (1D) chains, and even three-dimensional (3D) networks. Two numerical simulations were developed to predict aspects of nanostructure formation by accounting for the magnetic interactions between individual magnetic nanoparticles. The first utilized the Boltzmann distribution to determine the equilibrium structure of a nanochain, iteratively predicting the local deviation angle θ of each particle as it attaches to a forming chain. The second simulation illustrates the differences in nanostructure arrangement and dimensionality (0D, 1D, or 3D) that arise from random interactions at various nanoparticle densities. The simulation results closely match the experimental findings, as seen from SEM images, demonstrating their ability to capture the system's structural properties. In addition, magnetic hysteresis measurements of the samples were performed along two orthogonal directions to show the influence of dimensional order on the magnetic behavior. The normalized remanence (MR/MS||) of the FeCo alloys increases as the dimensions of nanostructures are increased. Of the three cases, the FeCo 3D network structures exhibit the highest normalized nanostructure remanence of 0.33 and an increased coercivity to above 200 Oe at 300 K. This combined numerical and experimental investigation aims to shed light on the preparation of FeCo nanostructures with tailorable dimensional order and it opens new avenues for exploring the complex spin textures and coercive behavior of these multi-dimensional nanomagnetic structures.

Current-Induced Creation of Topological Vortex Rings in a Magnetic Nanocylinder

Vortex rings are ubiquitous topological structures in nature. In solid magnetic systems, their formation leads to intriguing physical phenomena and potential device applications. However, realizing these topological magnetic vortex rings and manipulating their topology on demand have still been challenging. Here, we theoretically show that topological vortex rings can be created by a current pulse in a chiral magnetic nanocylinder with a trench structure. The creation process involves the formation of a vortex ring street, i.e., a chain of magnetic vortex rings with an alternative linking manner. The created vortex rings can be bounded with monopole-antimonopole pairs and possess a rich and controllable linking topology (e.g., Hopf link and Solomon link), which is determined by the duration and amplitude of the current pulse. Our proposal paves the way for the realization and manipulation of diverse three-dimensional (3D) topological spin textures and could catalyze the development of 3D spintronic devices.

Determination of optimal experimental conditions for accurate 3D reconstruction of the magnetization vector via XMCD-PEEM

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.

The Effect of Magnetoelastic Anisotropy on the Magnetization Processes in Rapidly Quenched Amorphous Nanowires

In this paper, we report for the first time on the theoretical and experimental investigation of Fe77.5Si7.5B15 amorphous glass-coated nanowires by analyzing samples with the same diameters in both cases. The hysteresis curves, the dependence of the switching field values on nanowire dimensions, and the effect of the magnetoelastic anisotropy on the magnetization processes were analyzed and interpreted to explain the magnetization reversal in highly magnetostrictive amorphous nanowires prepared in cylindrical shape by rapid quenching from the melt. All the measured samples were found to be magnetically bistable, being characterized by rectangular hysteresis loops. The most important feature of the study is the inclusion of the magnetoelastic anisotropy term that originates in the specific production process of these amorphous nanowires. The results show that the switching field decreases when the nanowire diameter increases and this effect is due to the reduction in anisotropy and in the intrinsic mechanical stresses. Moreover, the obtained results reveal the importance of factors such as geometry and magnetoelastic anisotropy for the experimental design of cylindrical amorphous nanowires for multiple applications in miniaturized devices, like micro and nanosensors.

Voltage-Controlled ON-OFF-Switching of Magnetoresistance in FeOx/Fe/Au Aerogel Networks

Voltage control of magnetoresistance (MR) in nanoscale three-dimensional (3D) geometries is interesting from a fundamental point of view and a promising route toward novel sensors and energy-efficient computing schemes. Magneto-ionic mechanisms are favorable for low-voltage control of magnetism and room-temperature operation, but magneto-ionic control of MR has been studied only for planar geometries so far. We synthesize a 3D nanomaterial with magneto-ionic functionality by electrodepositing an iron hydroxide/iron coating on a porous nanoscale gold network (aerogel). To enable maximum magneto-ionic ON-OFF-switching, the thickness of the coating is adjusted to a few nanometers by a self-terminating electrodeposition process. In situ magnetotransport measurements during electrolytic gating of these nanostructures reveal large reversible changes in MR, including ON-OFF-switching of MR, with a small applied voltage difference (1.72 V). This effect is related to the electrochemical switching between a ferromagnetic iron shell/gold core nanostructure (negative MR at the reduction voltage) and an iron oxide shell/gold core nanostructure (negligible MR at the oxidation voltage).

3D Magnetization Textures: Toroidal Magnetic Hopfion Stability in Cylindrical Samples

Topologically non-trivial magnetization configurations in ferromagnetic materials on the nanoscale, such as hopfions, skyrmions, and vortices, have attracted considerable attention of researchers during the last few years. In this article, by applying the theory of micromagnetism, I demonstrate that the toroidal hopfion magnetization configuration is a metastable state of a thick cylindrical ferromagnetic nanodot or a nanowire of a finite radius. The existence of this state is a result of the competition among exchange, magnetostatic, and magnetic anisotropy energies. The Dzyaloshinskii-Moriya exchange interaction and surface magnetic anisotropy are of second importance for the hopfion stabilization. The toroidal hopfion metastable magnetization configuration may be reached in the process of remagnetizing the sample by applying an external magnetic field along the cylindrical axis.

Template-free generation and integration of functional 1D magnetic nanostructures

The direct integration of 1D magnetic nanostructures into electronic circuits is crucial for realizing their great potential as components in magnetic storage, logical devices, and spintronic applications. Here, we present a novel template-free technique for producing magnetic nanochains and nanowires using directed self-assembly of gas-phase-generated metallic nanoparticles. The 1D nanostructures can be self-assembled along most substrate surfaces and can be freely suspended over micrometer distances, allowing for direct incorporation into different device architectures. The latter is demonstrated by a one-step integration of nanochains onto a pre-patterned Si chip and the fabrication of devices exhibiting magnetoresistance. Moreover, fusing the nanochains into nanowires by post-annealing significantly enhances the magnetic properties, with a 35% increase in the coercivity. Using magnetometry, X-ray microscopy, and micromagnetic simulations, we demonstrate how variations in the orientation of the magnetocrystalline anisotropy and the presence of larger multi-domain particles along the nanochains play a key role in the domain formation and magnetization reversal. Furthermore, it is shown that the increased coercivity in the nanowires can be attributed to the formation of a uniform magnetocrystalline anisotropy along the wires and the onset of exchange interactions.

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.

Hopfion-Driven Magnonic Hall Effect and Magnonic Focusing

Hopfions are localized and topologically nontrivial magnetic configurations that have received considerable attention in recent years. In this Letter, we use a micromagnetic approach to analyze the scattering of spin waves (SWs) by magnetic hopfions. Our results evidence that SWs experience an electromagnetic field generated by the hopfion and sharing its topological properties. In addition, SWs propagating along the hopfion symmetry axis are deflected by the magnetic texture, which acts as a convergent or divergent lens, depending on the SWs' propagation direction. Assuming that SWs propagate along the plane perpendicular to the symmetry axis, the scattering is closely related to the Aharonov-Bohm effect, allowing us to identify the magnetic hopfion as a scattering center.

Magneto-optical diffraction of visible light as a probe of nanoscale displacement of domain walls at femtosecond timescales

Using diffraction of femtosecond laser pulses of visible light by a magnetic domain pattern in an iron garnet, we demonstrate a proof of concept of time-resolved measurements of domain pattern movements with nanometer spatial and femtosecond temporal resolution. In this method, a femtosecond laser (pump) pulse initiates magnetization dynamics in a sample that is initially in a labyrinth domain state, while an equally short linearly polarized laser pulse (probe) is diffracted by the domain pattern. The components of the diffracted light that are polarized orthogonally to the incident light generate several concentric diffraction rings. Nanometer small changes in the relative sizes of domains with opposite magnetization result in observable changes in the intensities of the rings. We demonstrate that the signal-to-noise ratio is high enough to detect a 6 nm domain wall displacement with 100 fs temporal resolution using visible light. We also discuss possible artifacts, such as pump-induced changes of optical properties, that can affect the measurements.

Observation of magnetic vortex configuration in non-stoichiometric Fe3O4 nanospheres

Theoretical and micromagnetic simulation studies of magnetic nanospheres with vortex configurations suggest that such nanostructured materials have technological advantages over conventional nanosystems for applications based on high-power-rate absorption and subsequent emission. However, full experimental evidence of magnetic vortex configurations in spheres of submicrometer size is still lacking. Here, we report the microwave irradiation fabrication of Fe3O4 nanospheres and establish their magnetic vortex configuration based on experimental results, theoretical analysis, and micromagnetic simulations. Detailed magnetic and electrical measurements, together with Mössbauer spectroscopy data, provide evidence of a loss of stoichiometry in vortex nanospheres owing to the presence of a surface oxide layer, defects, and a higher concentration of cation vacancies. The results indicate that the magnetic vortex spin configuration can be established in bulk spherical magnetite materials. This study provides crucial information that can aid the synthesis of magnetic nanospheres with magnetically tailored properties; consequently, they may be promising candidates for future technological applications based on three-dimensional magnetic vortex structures.

Realization and Control of Bulk and Surface Modes in 3D Nanomagnonic Networks by Additive Manufacturing of Ferromagnets

The high-density integration in information technology fuels the research on functional 3D nanodevices. Particularly ferromagnets promise multifunctional 3D devices for nonvolatile data storage, high-speed data processing, and non-charge-based logic operations via spintronics and magnonics concepts. However, 3D nanofabrication of ferromagnets is extremely challenging. In this work, an additive manufacturing methodology is reported, and unprecedented 3D ferromagnetic nanonetworks with a woodpile-structure unit cell are fabricated. The collective spin dynamics (magnons) at frequencies up to 25 GHz are investigated by Brillouin Light Scattering (BLS) microscopy and micromagnetic simulations. A clear discrepancy of about 10 GHz is found between the bulk and surface modes, which are engineered by different unit cell sizes in the Ni-based nanonetworks. The angle- and spatially-dependent modes demonstrate opportunities for multi-frequency signal processing in 3D circuits via magnons. The developed synthesis route will allow one to create 3D magnonic crystals with chiral unit cells, which are a prerequisite toward surface modes with topologically protected properties.

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.

3D Magnonic Conduits by Direct Write Nanofabrication

Magnonics is a rapidly developing domain of nanomagnetism, with application potential in information processing systems. Realisation of this potential and miniaturisation of magnonic circuits requires their extension into the third dimension. However, so far, magnonic conduits are largely limited to thin films and 2D structures. Here, we introduce 3D magnonic nanoconduits fabricated by the direct write technique of focused-electron-beam induced deposition (FEBID). We use Brillouin light scattering (BLS) spectroscopy to demonstrate significant qualitative differences in spatially resolved spin-wave resonances of 2D and 3D nanostructures, which originates from the geometrically induced non-uniformity of the internal magnetic field. This work demonstrates the capability of FEBID as an additive manufacturing technique to produce magnetic 3D nanoarchitectures and presents the first report of BLS spectroscopy characterisation of FEBID conduits.

Nucleation and Stability of Toron Chains in Non-Centrosymmetric Magnetic Nanowires

This work analyzes the magnetic configurations of cylindrical nanowires with a bulk Dzyaloshinskii-Moriya interaction and easy-plane anisotropy. We show that this system allows the nucleation of a metastable toron chain even when no out-of-plane anisotropy exists in the nanowire's top and bottom surfaces, as usually required. The number of nucleated torons depends on the nanowire length and the strength of an external magnetic field applied to the system. The size of each toron depends on the fundamental magnetic interactions and can be controlled by external stimuli, allowing the use of these magnetic textures as information carriers or nano-oscillator elements. Our results evidence that the topology and structure of the torons yield a wide variety of behaviors, revealing the complex nature of these topological textures, which should present an exciting interaction dynamic, depending on the initial conditions.

Domain wall propagation and pinning induced by current pulses in cylindrical modulated nanowires

The future developments in 3D magnetic nanotechnology require the control of domain wall dynamics by means of current pulses. While this has been extensively studied in 2D magnetic strips (planar nanowires), few reports on this exist in cylindrical geometry, where Bloch point domain walls are expected to have intriguing properties. Here, we report an investigation on cylindrical magnetic Ni nanowires with geometrical notches. An experimental work based on synchrotron X-ray magnetic circular dichroism (XMCD) combined with photoemission electron microscopy (PEEM) indicates that large current densities induce domain wall nucleation, while smaller currents move domain walls preferably antiparallel to the current direction. In the region where no pinning centers are present, we found a domain wall velocity of about 1 km s^-1. Thermal modelling indicates that large current densities temporarily raise the temperature in the nanowire above the Curie temperature, leading to nucleation of domain walls during the system cooling. Micromagnetic modelling with a spin-torque effect shows that for intermediate current densities, Bloch point domain walls with chirality parallel to the Oersted field propagate antiparallel to the current direction. In other cases, domain walls can be bounced from the notches and/or get pinned outside their positions. We thus found that current is not only responsible for domain wall propagation, but also is a source of pinning due to the Oersted field action.

Exchange Bias Effect of Ni@(NiO,Ni(OH)2) Core/Shell Nanowires Synthesized by Electrochemical Deposition in Nanoporous Alumina Membranes

Tuning and controlling the magnetic properties of nanomaterials is crucial to implement new and reliable technologies based on magnetic hyperthermia, spintronics, or sensors, among others. Despite variations in the alloy composition as well as the realization of several post material fabrication treatments, magnetic heterostructures as ferromagnetic/antiferromagnetic coupled layers have been widely used to modify or generate unidirectional magnetic anisotropies. In this work, a pure electrochemical approach has been used to fabricate core (FM)/shell (AFM) Ni@(NiO,Ni(OH)₂) nanowire arrays, avoiding thermal oxidation procedures incompatible with integrative semiconductor technologies. Besides the morphology and compositional characterization of these core/shell nanowires, their peculiar magnetic properties have been studied by temperature dependent (isothermal) hysteresis loops, thermomagnetic curves and FORC analysis, revealing the existence of two different effects derived from Ni nanowires' surface oxidation over the magnetic performance of the array. First of all, a magnetic hardening of the nanowires along the parallel direction of the applied magnetic field with respect their long axis (easy magnetization axis) has been found. The increase in coercivity, as an effect of surface oxidation, has been observed to be around 17% (43%) at 300 K (50 K). On the other hand, an increasing exchange bias effect on decreasing temperature has been encountered when field cooling (3T) the oxidized Ni@(NiO,Ni(OH)₂) nanowires below 100 K along their parallel lengths.

Ingestion of microplastics by silver carp (Hypophthalmichthys molitrix) larvae: Quantification of ingestion and assessment of microbiota dysbiosis

The adverse effects of microplastics ingested by aquatic organisms have been reported previously. However, most studies are primarily qualitative; therefore, it is challenging to determine the direct interactions between microplastics and organisms. In this study, for the first time, the microplastic intake behavior of silver carp (Hypophthalmichthys molitrix) larvae, a popular fish in China, as well as intestine accumulation and excretion of the microplastics were quantitatively investigated. The results showed that the intake of microplastics by silver carp larvae was negatively correlated with the particle size of microplastics but positively correlated with the exposure concentration. After intaking microplastics of different sizes, small-sized microplastics (≤ 150 μm) were rapidly excreted from the intestine of silver carp, whereas some large-sized microplastics (≥ 300 μm) remained in the intestine for a long time. The presence of food significantly increased the intake of large-sized microplastics, while small-sized microplastics intake was unaffected by the food. More importantly, the ingested microplastics caused specific changes in the diversity of intestinal microflora, potentially leading to abnormal immune and metabolic functions. The results of this study provide a new understanding on the potential impacts of microplastics on aquatic organisms.

Site-Selective Chemical Vapor Deposition on Direct-Write 3D Nanoarchitectures

Recent advancements in additive manufacturing have enabled the preparation of free-shaped 3D objects with feature sizes down to and below the micrometer scale. Among the fabrication methods, focused electron beam- and focused ion beam-induced deposition (FEBID and FIBID, respectively) associate a high flexibility and unmatched accuracy in 3D writing with a wide material portfolio, thereby allowing for the growth of metallic to insulating materials. The combination of the free-shaped 3D nanowriting with established chemical vapor deposition (CVD) techniques provides attractive opportunities to synthesize complex 3D core-shell heterostructures. Hence, this hybrid approach enables the fabrication of morphologically tunable layer-based nanostructures with the great potential of unlocking further functionalities. Here, the fundamentals of such a hybrid approach are demonstrated by preparing core-shell heterostructures using 3D FEBID scaffolds for site-selective CVD. In particular, 3D microbridges are printed by FEBID with the (CH₃)₃CH₃C₅H₄Pt precursor and coated by thermal CVD using the Nb(NMe₂)₃(N-t-Bu) and HFeCo₃(CO)₁₂ precursors. Two model systems on the basis of CVD layers consisting of a superconducting NbC-based layer and a ferromagnetic Co₃Fe layer are prepared and characterized with regard to their composition, microstructure, and magneto-transport properties.

Fast and Efficient Simulation of the FEBID Process with Thermal Effects

Focused electron-beam-induced deposition (FEBID) is a highly versatile direct-write approach with particular strengths in the 3D nanofabrication of functional materials. Despite its apparent similarity to other 3D printing approaches, non-local effects related to precursor depletion, electron scattering and sample heating during the 3D growth process complicate the shape-true transfer from a target 3D model to the actual deposit. Here, we describe an efficient and fast numerical approach to simulate the growth process, which allows for a systematic study of the influence of the most important growth parameters on the resulting shape of the 3D structures. The precursor parameter set derived in this work for the precursor Me₃PtCpMe enables a detailed replication of the experimentally fabricated nanostructure, taking beam-induced heating into account. The modular character of the simulation approach allows for additional future performance increases using parallelization or drawing on the use of graphics cards. Ultimately, beam-control pattern generation for 3D FEBID will profit from being routinely combined with this fast simulation approach for optimized shape transfer.

Curvature-induced stabilization and field-driven dynamics of magnetic hopfions in toroidal nanorings

Three dimensional magnetic textures are a cornerstone in magnetism research. In this work, we analyze the stabilization and dynamic response of a magnetic hopfion hosted in a toroidal nanoring with intrinsic Dzyaloshinskii-Moriya interaction simulating FeGe. Our results evidence that unlike their planar counterparts, where perpendicular magnetic anisotropies are necessary to stabilize hopfions, the shape anisotropy originated on the torus symmetry naturally yields the nucleation of these topological textures. We also analyze the magnetization dynamical response by applying a magnetic field pulse to differentiate among several magnetic patterns. Finally, to understand the nature of spin wave modes, we analyze the spatial distributions of the resonant mode amplitudes and phases and describe the differences among bulk and surface modes. Importantly, hopfions lying in toroidal nanorings present a non-circularly symmetric poloidal resonant mode, which is not observed in other systems hosting hopfions.

Controlled evolution of three-dimensional magnetic states in strongly coupled cylindrical nanowire pairs

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.

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.

Emergent Magnetomultipoles and Nonlinear Responses of a Magnetic Hopfion

The three-dimensional emergent magnetic field B^{e} of a magnetic hopfion gives rise to emergent magnetomultipoles in a similar manner to the multipoles of classical electromagnetic field. Here, we show that the nonlinear responses of a hopfion are characterized by its emergent magnetic toroidal moment T_{z}^{e}=1/2∫(r×B^{e})_{z}dV and emergent magnetic octupole component Γ^{e}=∫[(x^{2}+y^{2})B_{z}^{e}-xzB_{x}^{e}-yzB_{y}^{e}]dV. The hopfion exhibits nonreciprocal dynamics (nonlinear hopfion Hall effect) under an ac driving current applied along (perpendicular to) the direction of T_{z}^{e}. The sign of nonreciprocity and nonlinear Hall angle is determined by the polarity and chirality of hopfion. The nonlinear electrical transport induced by a magnetic hopfion is also discussed. This Letter reveals the vital roles of emergent magnetomultipoles in nonlinear hopfion dynamics and could stimulate further investigations on the dynamical responses of topological spin textures induced by emergent electromagnetic multipoles.

Optimization and fabrication of programmable domains for soft magnetic robots: A review

Driven by the aim of realizing functional robotic systems at the milli- and submillimetre scale for biomedical applications, the area of magnetically driven soft devices has received significant recent attention. This has resulted in a new generation of magnetically controlled soft robots with patterns of embedded, programmable domains throughout their structures. This type of programmable magnetic profiling equips magnetic soft robots with shape programmable memory and can be achieved through the distribution of discrete domains (voxels) with variable magnetic densities and magnetization directions. This approach has produced highly compliant, and often bio-inspired structures that are well suited to biomedical applications at small scales, including microfluidic transport and shape-forming surgical catheters. However, to unlock the full potential of magnetic soft robots with improved designs and control, significant challenges remain in their compositional optimization and fabrication. This review considers recent advances and challenges in the interlinked optimization and fabrication aspects of programmable domains within magnetic soft robots. Through a combination of improvements in the computational capacity of novel optimization methods with advances in the resolution, material selection and automation of existing and novel fabrication methods, significant further developments in programmable magnetic soft robots may be realized.

Three-dimensional skyrmionic cocoons in magnetic multilayers

Three-dimensional spin textures emerge as promising quasi-particles for encoding information in future spintronic devices. The third dimension provides more malleability regarding their properties and more flexibility for potential applications. However, the stabilization and characterization of such quasi-particles in easily implementable systems remain a work in progress. Here we observe a three-dimensional magnetic texture that sits in the interior of magnetic thin films aperiodic multilayers and possesses a characteristic ellipsoidal shape. Interestingly, these objects that we call skyrmionic cocoons can coexist with more standard tubular skyrmions going through all the multilayer as evidenced by the existence of two very different contrasts in room temperature magnetic force microscopy. The presence of these novel skyrmionic textures as well as the understanding of their layer resolved chiral and topological properties have been investigated by micromagnetic simulations. Finally, we show that the skyrmionic cocoons can be electrically detected using magneto-transport measurements.

Bending Modulated Ultralarge Magnetoresistance in Flexible La0.67Ba0.33MnO3 Thin Film Based Device

Magnetoresistance based information devices have attracted much attention due to the ability to utilize spins as information carriers. To promote the magnetoresistance-based devices, ultrahigh magnetoresistance ratios are highly desirable for magnetic sensing, memory, and artificial intelligent devices, etc. However, today the magnetoresistance devices are facing the challenge of limited magnetoresistance ratio, low work temperature, or high magnetic field, which calls for proper theories and mechanisms. To address it, we first introduce the flexible bending-controlled magnetoresistance device based on the La_0.67Ba_0.33MnO₃ film. Due to the anisotropic resistance of the La_0.67Ba_0.33MnO₃ film and the nonlinear amplification effect of the Zener diode, the device has exhibited strong magnetoresistive performance (∼8725% at 1 T, 300 K). Combining the assist from mechanical bending and diode, high magnetic field sensitivity with large magnetoresistance ratio (∼1.7 × 10⁴% at 1 T, 300 K) and low work current (∼0.15 mA) is simultaneously achieved at room temperature, which is over 10⁴ times larger than that of the planar La_0.67Ba_0.33MnO₃ film. Based on the above results, we propose one but not the only possible application as tunable multistage switch. Our findings may pave a strategy to develop flexible diode-enhanced magnetoresistance device with ultrahigh magnetoresistance ratios and bending tunable performances.

Interwire and Intrawire Magnetostatic Interactions in Fe-Au Barcode Nanowires with Alternating Ferromagnetically Strong and Weak Segments

Metallic barcode nanowires (BNWs) composed of repeating heterogeneous segments fabricated by template-assisted electrodeposition can offer extended functionality in magnetic, electrical, mechanical, and biomedical applications. The authors consider such nanostructures as a 3D system of magnetically interacting elements with magnetic behavior strongly affected by complex magnetostatic interactions. This study discusses the influence of geometrical parameters of segments on the character of their interactions and the overall magnetic behavior of the array of BNWs having alternating magnetization, because the Fe and Au segments are made of Fe-Au alloys with high and low magnetizations. By controlling the applied current densities and the elapsed time in the electrodeposition, the dimension of the Fe-Au BNWs can be regulated. This study reveals that the influence of the length of magnetically weak Au segments on the interaction field between nanowires is different for samples with magnetically strong 100 and 200 nm long Fe segments using the first-order reversal curve (FORC) diagram method. With the help of micromagnetic simulations, three types of magnetostatic interactions in the BNW arrays are discovered and analy. This study demonstrates that the dominating type of interaction depends on the geometric parameters of the Fe and Au segments and the interwire and intrawire distances.

Spatial magnetic imaging of non-axially symmetric vortex domains in cylindrical nanowire by transmission X-ray microscopy

The spatial magnetization texture of a cylindrical nanowire has been determined by Transmission X-ray Microscopy (TXM) and X-ray magnetic circular dichroism (XMCD). For this purpose, nanowires with designed geometry, consisting of CoNi/Ni periodic segments, have been grown by designed electrodeposition into alumina templates. Experimental data allow one to conclude the presence of mono- and trivortex magnetic domains in CoNi segments but, unusually, these states are characterized by an asymmetric XMCD contrast across the nanowire's section. Micromagnetic modelling shows non-trivial three-dimensional structures with ellipsoidal vortex cores and non-axially symmetric magnetization along the nanowire direction. The modelled TXM contrast of micromagnetic structures allows to correlate the experimental asymmetric XMCD contrast to the easy axis direction of the uniaxial magnetocrystalline anisotropy.

Evolution in Lithography Techniques: Microlithography to Nanolithography

In this era, electronic devices such as mobile phones, computers, laptops, sensors, and many more have become a necessity in healthcare, for a pleasant lifestyle, and for carrying out tasks quickly and easily. Different types of temperature sensors, biosensors, photosensors, etc., have been developed to meet the necessities of people. All these devices have chips inside them fabricated using diodes, transistors, logic gates, and ICs. The patterning of the substrate which is used for the further development of these devices is done with the help of a technique known as lithography. In the present work, we have carried out a review on different types of lithographic techniques such as optical lithography, extreme ultraviolet lithography, electron beam lithography, X-ray lithography, and ion beam lithography. The evolution of these techniques with time and their application in device fabrication are discussed. The different exposure tools developed in the past decade to enhance the resolution of these devices are also discussed. Chemically amplified and non-chemically amplified resists with their bonding and thickness are discussed. Mask and maskless lithography techniques are discussed along with their merits and demerits. Device fabrication at micro and nano scale has been discussed. Advancements that can be made to improve the performance of these techniques are also suggested.

Effect of Multilayered Structure on the Static and Dynamic Properties of Magnetic Nanospheres

The development of flexible and lightweight electromagnetic interference (EMI)-shielding materials and microwave absorbers requires precise control and optimization of core-shell constituents within composite materials. Here, a theoretical model is proposed to predict the static and dynamic properties of multilayered core-shell particles comprised of exchange-coupled layers, as in the case of a spherical iron core coupled to an oxide shell across a spacer layer. The theory of exchange resonance in homogeneous spheres is shown to be a limiting special case of this more general theory. Nucleation of magnetization reversal occurs through either quasi-uniform or curling magnetization processes in core-shell particles, where a purely homogeneous magnetization configuration is forbidden by the multilayered morphology. The energy is minimized through mixing of modes for specific interface conditions, leading to many inhomogeneous solutions, which grow as 2ⁿ with increasing layers, where n represents the number of magnetic layers. The analytical predictions are confirmed using numerical simulations.

Electrodeposited Magnetic Nanowires with Radial Modulation of Composition

In the last few years, magnetic nanowires have gained attention due to their potential implementation as building blocks in spintronics applications and, in particular, in domain-wall- based devices. In these devices, the control of the magnetic properties is a must. Cylindrical magnetic nanowires can be synthesized rather easily by electrodeposition and the control of their magnetic properties can be achieved by modulating the composition of the nanowire along the axial direction. In this work, we report the possibility of introducing changes in the composition along the radial direction, increasing the degrees of freedom to harness the magnetization. In particular, we report the synthesis, using template-assisted deposition, of FeNi (or Co) magnetic nanowires, coated with a Au/Co (Au/FeNi) bilayer. The diameter of the nanowire as well as the thickness of both layers can be tuned at will. In addition to a detailed structural characterization, we report a preliminary study on the magnetic properties, establishing the role of each layer in the global collective behavior of the system.

Domain Wall Automotion in Three-Dimensional Magnetic Helical Interconnectors

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.

Toggle-like current-induced Bloch point dynamics of 3D skyrmion strings in a room temperature nanowire

Research into practical applications of magnetic skyrmions, nanoscale solitons with interesting topological and transport properties, has traditionally focused on two dimensional (2D) thin-film systems. However, the recent observation of novel three dimensional (3D) skyrmion-like structures, such as hopfions, skyrmion strings (SkS), skyrmion bundles, and skyrmion braids, motivates the investigation of new designs, aiming to exploit the third spatial dimension for more compact and higher performance spintronic devices in 3D or curvilinear geometries. A crucial requirement of such device schemes is the control of the 3D magnetic structures via charge or spin currents, which has yet to be experimentally observed. In this work, we utilise real-space imaging to investigate the dynamics of a 3D SkS within a nanowire of Co₈Zn₉Mn₃ at room temperature. Utilising single current pulses, we demonstrate current-induced nucleation of a single SkS, and a toggle-like positional switching of an individual Bloch point at the end of a SkS. The observations highlight the possibility to locally manipulate 3D topological spin textures, opening up a range of design concepts for future 3D spintronic devices.

In three dimensional systems with broken bulk inversion symmetry, skyrmions can form extended string-like structures. Here, Birch et al use scanning transmission x-ray microscopy to demonstrate the current induced generation and motion of these three dimensional skyrmion strings.

Toggle-like current-induced Bloch point dynamics of 3D skyrmion strings in a room temperature nanowire

Research into practical applications of magnetic skyrmions, nanoscale solitons with interesting topological and transport properties, has traditionally focused on two dimensional (2D) thin-film systems. However, the recent observation of novel three dimensional (3D) skyrmion-like structures, such as hopfions, skyrmion strings (SkS), skyrmion bundles, and skyrmion braids, motivates the investigation of new designs, aiming to exploit the third spatial dimension for more compact and higher performance spintronic devices in 3D or curvilinear geometries. A crucial requirement of such device schemes is the control of the 3D magnetic structures via charge or spin currents, which has yet to be experimentally observed. In this work, we utilise real-space imaging to investigate the dynamics of a 3D SkS within a nanowire of Co₈Zn₉Mn₃ at room temperature. Utilising single current pulses, we demonstrate current-induced nucleation of a single SkS, and a toggle-like positional switching of an individual Bloch point at the end of a SkS. The observations highlight the possibility to locally manipulate 3D topological spin textures, opening up a range of design concepts for future 3D spintronic devices.

Topological transitions in ac/dc-driven superconductor nanotubes

Extending of nanostructures into the third dimension has become a major research avenue in condensed-matter physics, because of geometry- and topology-induced phenomena. In this regard, superconductor 3D nanoarchitectures feature magnetic field inhomogeneity, non-trivial topology of Meissner currents and complex dynamics of topological defects. Here, we investigate theoretically topological transitions in the dynamics of vortices and slips of the phase of the order parameter in open superconductor nanotubes under a modulated transport current. Relying upon the time-dependent Ginzburg–Landau equation, we reveal two distinct voltage regimes when (i) a dominant part of the tube is in either the normal or superconducting state and (ii) a complex interplay between vortices, phase-slip regions and screening currents determines a rich FFT voltage spectrum. Our findings unveil novel dynamical states in superconductor open nanotubes, such as paraxial and azimuthal phase-slip regions, their branching and coexistence with vortices, and allow for control of these states by superimposed dc and ac current stimuli.

Asymmetric Motion of Magnetic Skyrmions in Ferromagnetic Nanotubes Induced by a Magnetic Field

Magnetic skyrmions, featuring topological stability and low driving current density, are believed to be a promising candidate of information carriers. One of the obstacles to application is the skyrmion Hall effect, which can lead to the annihilation of moving skyrmions at the lateral boundary of thin-film tracks. In order to resolve this issue, it was recently proposed to exploit ferromagnetic nanotubes as alternative skyrmion guides. In this work, we investigate the field-effect of current-driven skyrmion motion in nanotubes using micromagnetic simulations. It is found that, in the presence of an axial field, the skyrmion motion becomes asymmetric in tubes. This is fundamentally different from the flat strip, in which a field has little influence on the skyrmion dynamics. Based on the dissipation tensor determined by the spin texture of the skyrmions, the solution of the Thiele equation is obtained, yielding a perfect match with simulations. We argue that the asymmetry of the skyrmion dynamics originates from the curvature of the nanotube.

Size-Specific Magnetic Configurations in Electrodeposited Epitaxial Iron Nanocuboids: From Landau Pattern to Vortex and Single Domain States

As the size of magnetic devices continuously decreases, the creation of three-dimensional nanomagnets and the understanding of their magnetic configurations become increasingly important for modern applications. Here, by progressive nucleation during epitaxial nanoelectrodeposition, we synthesize single-crystal iron nanocuboids with sizes ranging 10 to 200 nm on one sample. The size-dependent magnetic configurations of these nanocuboids are studied by quantitative magnetic force microscopy and electron holography. In conjunction, a "magnetic configuration versus size" phase diagram is established via micromagnetic simulations. Both experiment and theory reveal a sequential transition from Landau pattern to vortex and finally single domain when decreasing the sizes of the nanocuboids. The combinatorial-like approach leads to a quantitative understanding of the magnetic configurations of the nanomagnets in a broad size range. It can be transferred to other materials and shapes and thereby presents an advanced route to enrich the material library for future nanodevice design.