Magnetic vortex core reversal by excitation with short bursts of an alternating field

Stable skyrmion bundles at room temperature and zero magnetic field in a chiral magnet

Topological spin textures are characterized by magnetic topological charges, Q, which govern their electromagnetic properties. Recent studies have achieved skyrmion bundles with arbitrary integer values of Q, opening possibilities for exploring topological spintronics based on Q. However, the realization of stable skyrmion bundles in chiral magnets at room temperature and zero magnetic field - the prerequisite for realistic device applications - has remained elusive. Here, through the combination of pulsed currents and reversed magnetic fields, we experimentally achieve skyrmion bundles with different integer Q values - reaching a maximum of 24 at above room temperature and zero magnetic field - in the chiral magnet Co8Zn10Mn2. We demonstrate the field-driven annihilation of high-Q bundles and present a phase diagram as a function of temperature and field. Our experimental findings are consistently corroborated by micromagnetic simulations, which reveal the nature of the skyrmion bundle as that of skyrmion tubes encircled by a fractional Hopfion.

Topology-guided polar ordering of collective cell migration

The ability of epithelial monolayers to self-organize into a dynamic polarized state, where cells migrate in a uniform direction, is essential for tissue regeneration, development, and tumor progression. However, the mechanisms governing long-range polar ordering of motility direction in biological tissues remain unclear. Here, we investigate the self-organizing behavior of quiescent epithelial monolayers that transit to a dynamic state with long-range polar order upon growth factor exposure. We demonstrate that the heightened self-propelled activity of monolayer cells leads to formation of vortex-antivortex pairs that undergo sequential annihilation, ultimately driving the spread of long-range polar order throughout the system. A computational model, which treats the monolayer as an active elastic solid, accurately replicates this behavior, and weakening of cell-to-cell interactions impedes vortex-antivortex annihilation and polar ordering. Our findings uncover a mechanism in epithelia, where elastic solid material characteristics, activated self-propulsion, and topology-mediated guidance converge to fuel a highly efficient polar self-ordering activity.

Visualizing Nanoscale Interlayer Magnetic Interactions and Unconventional Low-Frequency Behaviors in Ferromagnetic Multishelled Structures

Precise manipulation of van der Waals forces within 2D atomic layers allows for exact control over electron-phonon coupling, leading to the exceptional quantum properties. However, applying this technique to diverse structures such as 3D materials is challenging. Therefore, investigating new hierarchical structures and different interlayer forces is crucial for overcoming these limitations and discovering novel physical properties. In this work, a multishelled ferromagnetic material with controllable shell numbers is developed. By strategically regulating the magnetic interactions between these shells, the magnetic properties of each shell are fine-tuned. This approach reveals distinctive magnetic characteristics including regulated magnetic domain configurations and enhanced effective fields. The nanoscale magnetic interactions between the shells are observed and analyzed, which shed light on the modified magnetic properties of each shell, enhancing the understanding and control of ferromagnetic materials. The distinctive magnetic interaction significantly boosts electromagnetic absorption at low-frequency frequencies used by fifth-generation wireless devices, outperforming ferromagnetic materials without multilayer structures by several folds. The application of magnetic interactions in materials science reveals thrilling prospects for technological and electronic innovation.

Coherent Magnons with Giant Nonreciprocity at Nanoscale Wavelengths

Nonreciprocal wave propagation arises in systems with broken time-reversal symmetry and is key to the functionality of devices, such as isolators or circulators, in microwave, photonic, and acoustic applications. In magnetic systems, collective wave excitations known as magnon quasiparticles have so far yielded moderate nonreciprocities, mainly observed by means of incoherent thermal magnon spectra, while their occurrence as coherent spin waves (magnon ensembles with identical phase) is yet to be demonstrated. Here, we report the direct observation of strongly nonreciprocal propagating coherent spin waves in a patterned element of a ferromagnetic bilayer stack with antiparallel magnetic orientations. We use time-resolved scanning transmission X-ray microscopy (TR-STXM) to directly image the layer-collective dynamics of spin waves with wavelengths ranging from 5 μm down to 100 nm emergent at frequencies between 500 MHz and 5 GHz. The experimentally observed nonreciprocity factor of these counter-propagating waves is greater than 10 with respect to both group velocities and specific wavelengths. Our experimental findings are supported by the results from an analytic theory, and their peculiarities are further discussed in terms of caustic spin-wave focusing.

Emergence of Stable Meron Quartets in Twisted Magnets

The investigation of twist engineering in easy-axis magnetic systems has revealed remarkable potential for generating topological spin textures. Implementing twist engineering in easy-plane magnets, we introduce a novel approach to achieving fractional topological spin textures, such as merons. Through atomistic spin simulations on twisted bilayer magnets, we demonstrate the formation of a stable double Meron pair, which we refer to as the "Meron Quartet" (MQ). Unlike a single pair, the merons within the MQ exhibit exceptional stability against pair annihilation due to the protective localization mechanism induced by the twist that prevents collision of the Meron cores. Furthermore, we showcase that the stability of the MQ can be enhanced by adjusting the twist angle, resulting in an increased resistance to external perturbations such as external magnetic fields. Our findings highlight the twisted magnet as a promising platform for achieving merons as stable magnetic quasiparticles in van der Waals magnets.

Tailoring elastic and inelastic collisions of relativistic antiferromagnetic domain walls

Soliton-based computing relies on their unique properties for transporting energy and emerging intact from head-on collisions. Magnetic domain walls are often referred to as solitons disregarding the strict mathematical definition requiring the above scattering property. Here we demonstrate the conditions of elastic and inelastic scattering for spin-orbit torque-induced dynamics of relativistic domain walls on the technologically relevant Mn[Formula: see text]Au antiferromagnetic material. We show that even domain walls with opposite winding numbers can experience elastic scattering and we present the corresponding phase diagram as a function of the spin-orbit field strength and duration. The elastic collision requires minimum domain walls speed, which we explain assuming an attractive potential created by domain wall pair. On the contrary, when the domain walls move at lower speeds, their collision is inelastic and results in a dispersing breather. Our findings will be important for the development of soliton-based computing using antiferromagnetic spintronics and we discuss their prospects for building NOT and XOR gates.

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.

Dzyaloshinskii-Moriya-Interaction-Like Behavior in Confined Permalloy Nanostructures via Coupled Magnetic Vortices

Dzyaloshinskii-Moriya interaction (DMI), one of antisymmetric exchanges, originates from the combination of low structural symmetry and large spin-orbit coupling and favors magnetization rotations with fixed chirality. Herein, this work reports a DMI-like behavior in permalloy via coupled vortices in confined structures. Under the in-plane magnetic fields, continuous reversals of different coupled vortices are directly observed by in situ Lorentz transmission electron microscopy, and reproduced by complementary micromagnetic simulations. The statistical results show that coupled vortices with opposite chirality appear more frequently with the frequency up to about 60%. Such an asymmetric phenomenon mainly arises from a DMI-like behavior, associated with the increased total energy difference between different ground-state coupled vortices. Moreover, in the reversal process, the junction between disks accelerates the annihilation of vortices moving toward it and is also the starting point of vortex nucleation. These results provide an effective method to generate a DMI-like behavior in magnetic systems with symmetry breaking surface and benefit the future development of vortex-based spintronic devices.

Size driven barrier to chirality reversal in electric control of magnetic vortices in ferromagnetic nanodiscs

New high density storage media and spintronic devices come about with a progressing demand for the miniaturization of ferromagnetic structures. Vortex ordering of magnetic dipoles in such structures has been repeatedly observed as a stable state, offering the possibility of chirality in these states as a means to store information at high density. Electric pulses and magnetoelectric coupling are attractive options to control the chirality of such states in a deterministic manner. Here, we demonstrate the chirality reversal of vortex states in ferromagnetic nanodiscs via pulsed electric fields using a micromagnetic approach and focus on the analysis of the energetics of the reversal process. A strong thickness dependence of the chirality reversal in the nanodiscs is found that emanates from the anisotropy of the demagnetizing fields. Our results indicate that chiral switching of the magnetic moments in thin discs can give rise to a transient vortex-antivortex lattice not observed in thicker discs. This difference in the chirality reversal mechanism emanates from profoundly different energy barriers to overcome in thin and thicker discs. We also report the polarity-chirality correlation of a vortex that appears to depend on the aspect ratio of the nanodiscs.

Unusual Magnetic Hysteresis and Transition between Vortex and Double Pole States Arising from Interlayer Coupling in Diamond-Shaped Nanostructures

Controlling the magnetic ground states at the nanoscale is a long-standing basic research problem and an important issue in magnetic storage technologies. Here, we designed a nanostructured material that exhibits very unusual hysteresis loops due to a transition between vortex and double pole states. Arrays of 700 nm diamond-shaped nanodots consisting of Py(30 nm)/Ru(t_Ru)/Py(30 nm) (Py, permalloy (Ni₈₀Fe₂₀)) trilayers were fabricated by interference lithography and e-beam evaporation. We show that varying the Ru interlayer spacer thickness (t_Ru) governs the interaction between the Py layers. We found this interaction mainly mediated by two mechanisms: magnetostatic interaction that favors antiparallel (antiferromagnetic, AFM) alignment of the Py layers and exchange interaction that oscillates between ferromagnetic (FM) and AFM couplings. For a certain range of Ru thicknesses, FM coupling dominates and forms magnetic vortices in the upper and lower Py layers. For Ru thicknesses at which AFM coupling dominates, the magnetic state in remanence is a double pole structure. Our results showed that the interlayer exchange coupling interaction remains finite even at 4 nm Ru thickness. The magnetic states in remanence, observed by magnetic force microscopy (MFM), are in good agreement with corresponding hysteresis loops obtained by the magneto-optic Kerr effect (MOKE) and micromagnetic simulations.

Biocompatible Iron Oxide Nanoring-Labeled Mesenchymal Stem Cells: An Innovative Magnetothermal Approach for Cell Tracking and Targeted Stroke Therapy

Labeling stem cells with magnetic nanoparticles is a promising technique for in vivo tracking and magnetic targeting of transplanted stem cells, which is critical for improving the therapeutic efficacy of cell therapy. However, conventional endocytic labeling with relatively poor labeling efficiency and a short labeling lifetime has hindered the implementation of these innovative enhancements in stem-cell-mediated regenerative medicine. Herein, we describe an advanced magnetothermal approach to label mesenchymal stem cells (MSCs) efficiently by local induction of heat-enhanced membrane permeability for magnetic resonance imaging (MRI) tracking and targeted therapy of stroke, where biocompatible γ-phase, ferrimagnetic vortex-domain iron oxide nanorings (γ-FVIOs) with superior magnetoresponsive properties were used as a tracer. This approach facilitates a safe and efficient labeling of γ-FVIOs as high as 150 pg of Fe per cell without affecting the MSCs proliferation and differentiation, which is 3.44-fold higher than that by endocytosis labeling. Such a high labeling efficiency not only enables the ultrasensitive magnetic resonance imaging (MRI) detection of sub-10 cells and long-term tracking of transplanted MSCs over 10 weeks but also endows transplanted MSCs with a magnetic manipulation ability in vivo. A proof-of-concept study using a rat stroke model showed that the labeled MSCs facilitated MRI tracking and magnetic targeting for efficient replacement therapy with a significantly reduced dosage of 5 × 10⁴ transplanted cells. The findings in this study have demonstrated the great potential of the magnetothermal approach as an efficient labeling technique for future clinical usage.

Direct imaging of nanoscale field-driven domain wall oscillations in Landau structures

Linear oscillatory motion of domain walls (DWs) in the kHz and MHz regime is crucial when realizing precise magnetic field sensors such as giant magnetoimpedance devices. Numerous magnetically active defects lead to pinning of the DWs during their motion, affecting the overall behavior. Thus, the direct monitoring of the domain wall's oscillatory behavior is an important step to comprehend the underlying micromagnetic processes and to improve the magnetoresistive performance of these devices. Here, we report an imaging approach to investigate such DW dynamics with nanoscale spatial resolution employing conventional table-top microscopy techniques. Time-averaged magnetic force microscopy and Kerr imaging methods are applied to quantify the DW oscillations in Ni₈₁Fe₁₉ rectangular structures with Landau domain configuration and are complemented by numeric micromagnetic simulations. We study the oscillation amplitude as a function of external magnetic field strength, frequency, magnetic structure size, thickness and anisotropy and understand the excited DW behavior as a forced damped harmonic oscillator with restoring force being influenced by the geometry, thickness, and anisotropy of the Ni₈₁Fe₁₉ structure. This approach offers new possibilities for the analysis of DW motion at elevated frequencies and at a spatial resolution of well below 100 nm in various branches of nanomagnetism.

TimeMaxyne: A Shot-Noise Limited, Time-Resolved Pump-and-Probe Acquisition System Capable of 50 GHz Frequencies for Synchrotron-Based X-ray Microscopy

With the advent of modern synchrotron sources, X-ray microscopy was developed as a vigorous tool for imaging material structures with element-specific, structural, chemical and magnetic sensitivity at resolutions down to 25 nm and below. Moreover, the X-ray time structure emitted from the synchrotron source (short bunches of less than 100 ps width) provides a unique possibility to combine high spatial resolution with high temporal resolution for periodic processes by means of pump-and-probe measurements. To that end, TimeMaxyne was developed as a time-resolved acquisition setup for the scanning X-ray microscope MAXYMUS at the BESSY II synchrotron in order to perform high precision, high throughput pump-and-probe imaging. The setup combines a highly sensitive single photon detector, a real time photon sorting system and a dedicated synchronization scheme for aligning various types of sample excitations of up to 50 GHz bandwidth to the photon probe. Hence, TimeMaxyne has been demonstrated to be capable of shot-noise limited, time-resolved imaging, at time resolutions of 50 ps and below, only limited by the X-ray pulse widths of the synchrotron.

Multi-meron interactions and statistics in two-dimensional materials

As a fundamental type of topological spin textures in two-dimensional (2D) magnets, a magnetic meron carries half-integer topological charge and forms a pair with its antithesis to keep the stability in materials. However, it is challenging to quantitatively calculate merons and their dynamics by using the widely used continuum model because of the characteristic highly inhomogeneous spin textures. In this work, we develop a discrete method to address the concentrated spin structures around the core of merons. We reveal a logarithmic-scale interaction between merons when their distance is larger than twice their core size and obtain subsequent statistics of meron gas. The model also predicts how these properties of single and paired merons evolve with magnetic exchange interactions, and the results are in excellent agreement with the Monte Carlo simulations using the parameters of real 2D van der Waals magnetic materials. This discrete approach not only shows equilibrium static statistics of meron systems but also is useful to further explore the dynamic properties of merons through the quantified pairing interactions.

Continuous illumination picosecond imaging using a delay line detector in a transmission electron microscope

Progress towards analysing transitions between steady states demands improvements in time-resolved imaging, both for fundamental research and for applications in information technology. Transmission electron microscopy is a powerful technique for investigating the atomic structure, chemical composition and electromagnetic properties of materials with high spatial resolution and precision. However, the extraction of information about dynamic processes in the ps time regime is often not possible without extensive modification to the instrument while requiring careful control of the operation conditions to not compromise the beam quality. Here, we avoid these drawbacks by combining a delay line detector with continuous illumination in a transmission electron microscope. We visualize the gyration of a magnetic vortex core in real space and show that magnetization dynamics up to frequencies of 2.3 GHz can be resolved with down to ∼122ps temporal resolution by studying the interaction of an electron beam with a microwave magnetic field. In the future, this approach promises to provide access to resonant dynamics by combining high spatial resolution with sub-ns temporal resolution.

The Bloch point 3D topological charge induced by the magnetostatic interaction

A hedgehog or Bloch point is a point-like 3D magnetization configuration in a ferromagnet. Regardless of widely spread treatment of a Bloch point as a topological defect, its 3D topological charge has never been calculated. Here, applying the concepts of the emergent magnetic field and Dirac string, we calculate the 3D topological charge (Hopf index) of a Bloch point and show that due to the magnetostatic energy contribution it has a finite, non-integer value. Thus, Bloch points form a new class of hopfions-3D topological magnetization configurations. The calculated Bloch point non-zero gyrovector leads to important dynamical consequences such as the appearance of topological Hall effect.

Reversible magnetic spiral domain

The various spiral structures that exist in nature inspire humanity because of their morphological beauty, and spiral structures are used in various fields, including architecture, engineering, and art. Spiral structures have their own winding directions, and in most spirals, it is difficult to reverse the predetermined winding direction. Here, we show that a rotating spiral exists in magnetic systems for which the winding direction can be easily reversed. A magnetization vector basically has a spiral motion combining a precessional and a damping motion. The application of these basic mechanics to a system composed of magnetic vectors that are affected by a radial current and the Dzyaloshinskii–Moriya interaction forms the rotating magnetic spiral. The winding direction of the magnetic spiral has its own stability, but the direction can be changed using an external magnetic field. This magnetic spiral has a finite size, and the magnetic domain is destroyed at the edge of the spiral, which can create magnetic skyrmions.

Why is my image noisy? A look into the terms contributing to a time-resolved X-ray microscopy image

Through Monte Carlo simulations, we investigate how various experimental parameters can influence the quality of time-resolved scanning transmission X-ray microscopy images. In particular, the effect of the X-ray photon flux, of the thickness of the investigated samples, and of the frequency of the dynamical process under investigation on the resulting time-resolved image are investigated. The ideal sample and imaging conditions that allow for an optimal image quality are then identifed.

Propagation of Spin Waves in a 2D Vortex Network

Efficient propagation of spin waves in a magnetically coupled vortex is crucial to the development of future magnonic devices. Thus far, only a double vortex can serve as spin-wave emitter or oscillator; the propagation of spin waves in the higher-order vortex is still lacking. Here, we experimentally realize a higher-order vortex (2D vortex network) by a designed nanostructure, containing four cross-type chiral substructures. We employ this vortex network as a waveguide to propagate short-wavelength spin waves (∼100 nm) and demonstrate the possibility of guiding spin waves from one vortex to the network. It is observed that the spin waves can propagate into the network through the nanochannels formed by the Bloch-Néel-type domain walls, with a propagation decay length of several micrometers. This technique paves the way for the development of low-energy, reprogrammable, and miniaturized magnonic devices.

Motion-induced inertial effects and topological phase transitions in skyrmion transport

When the skyrmion dynamics beyond the particle-like description is considered, this topological structure can deform due to a self-induced field. In this work, we perform Monte Carlo simulations to characterize the skyrmion deformation during its steady movement. In the low-velocity regime, the deformation in the skyrmion shape is quantified by an effective inertial mass, which is related to the dissipative force. When skyrmions move faster, the large self-induced deformation triggers topological transitions. These transitions are characterized by the proliferation of skyrmions and a different total topological charge, which is obtained as a function of the skyrmion velocity. Our findings provide an alternative way to describe the dynamics of a skyrmion that accounts for the deformations of its structure. Furthermore, such motion-induced topological phase transitions make it possible to control the number of ferromagnetic skyrmions through velocity effects.

Magnonic Bending, Phase Shifting and Interferometry in a 2D Reconfigurable Nanodisk Crystal

Strongly interacting nanomagnetic systems are pivotal across next-generation technologies including reconfigurable magnonics and neuromorphic computation. Controlling magnetization states and local coupling between neighboring nanoelements allows vast reconfigurability and a host of associated functionalities. However, existing designs typically suffer from an inability to tailor interelement coupling post-fabrication and nanoelements restricted to a pair of Ising-like magnetization states. Here, we propose a class of reconfigurable magnonic crystals incorporating nanodisks as the functional element. Ferromagnetic nanodisks are crucially bistable in macrospin and vortex states, allowing interelement coupling to be selectively activated (macrospin) or deactivated (vortex). Through microstate engineering, we leverage the distinct coupling behaviors and magnonic band structures of bistable nanodisks to achieve reprogrammable magnonic waveguiding, bending, gating, and phase-shifting across a 2D network. The potential of nanodisk-based magnonics for wave-based computation is demonstrated via an all-magnon interferometer exhibiting XNOR logic functionality. Local microstate control is achieved here via topological magnetic writing using a magnetic force microscope tip.

Target Bubbles in Fe3Sn2 Nanodisks at Zero Magnetic Field

We report a vortex-like magnetic configuration in uniaxial ferromagnet Fe₃Sn₂ nanodisks using differential phase contrast scanning transmission electron microscopy. This magnetic configuration is transferred from a conventional magnetic vortex using a zero-magnetic-field warming process and is characterized by a series of concentric cylinder domains. We termed them as "target bubbles" that are identified as three-dimensional depth-modulated magnetic objects in combination with numerical simulations. Target bubbles have room-temperature stability even at zero magnetic field and multiple stable magnetic configurations. These advantages render the target bubble an ideal bit to be an information carrier and can advance magnetic target bubbles toward functionalities in the long term by incorporating emergent degrees of freedom and purely electrically controllable magnetism.

Meron-like topological spin defects in monolayer CrCl3

Noncollinear spin textures in low-dimensional magnetic systems have been studied for decades because of their extraordinary properties and promising applications derived from the chirality and topological nature. However, material realizations of topological spin states are still limited. Employing first-principles and Monte Carlo simulations, we propose that monolayer chromium trichloride (CrCl3) can be a promising candidate for observing the vortex/antivortex type of topological defects, so-called merons. The numbers of vortices and antivortices are found to be the same, maintaining an overall integer topological unit. By perturbing with external magnetic fields, we show the robustness of these meron pairs and reveal a rich phase space to tune the hybridization between the ferromagnetic order and meron-like defects. The signatures of topological excitations under external magnetic field also provide crucial information for experimental justifications. Our study predicts that two-dimensional magnets with weak spin-orbit coupling can be a promising family for realizing meron-like spin textures.

Reviewing Magnetic Particle Preparation: Exploring the Viability in Biosensing

In this review article, we conceptually investigated the requirements of magnetic nanoparticles for their application in biosensing and related them to example systems of our thin-film portfolio. Analyzing intrinsic magnetic properties of different magnetic phases, the size range of the magnetic particles was determined, which is of potential interest for biosensor technology. Different e-beam lithography strategies are utilized to identify possible ways to realize small magnetic particles targeting this size range. Three different particle systems from 500 μm to 50 nm are produced for this purpose, aiming at tunable, vertically magnetized synthetic antiferromagnets, martensitic transformation in a single elliptical, disc-shaped Heusler Ni₅₀Mn_32.5Ga_17.5 particle and nanocylinders of Co₂MnSi-Heusler compound. Perspectively, new applications for these particle systems in combination with microfluidics are addressed. Using the concept of a magnetic on–off ratchet, the most suitable particle system of these three materials is validated with respect to magnetically-driven transport in a microfluidic channel. In addition, options are also discussed for improving the magnetic ratchet for larger particles.

Deterministic reversal of single magnetic vortex circulation by an electric field

The ability to control magnetic vortex is critical for their potential applications in spintronic devices. Traditional methods including magnetic field, spin-polarized current etc. have been used to flip the core and/or reverse circulation of vortex. However, it is challenging for deterministic electric-field control of the single magnetic vortex textures with time-reversal broken symmetry and no planar magnetic anisotropy. Here it is reported that a deterministic reversal of single magnetic vortex circulation can be driven back and forth by a space-varying strain in multiferroic heterostructures, which is controlled by using a bi-axial pulsed electric field. Phase-field simulation reveals the mechanism of the emerging magnetoelastic energy with the space variation and visualizes the reversal pathway of the vortex. This deterministic electric-field control of the single magnetic vortex textures demonstrates a new approach to integrate the low-dimensional spin texture into the magnetoelectric thin film devices with low energy consumption.

Spontaneous creation and annihilation dynamics and strain-limited stability of magnetic skyrmions

Magnetic skyrmions are topological magnetic spin structures exhibiting particle-like behaviour. They are of strong interest from a fundamental viewpoint and for application, where they have potential to act as information carriers in future low-power computing technologies. Importantly, skyrmions have high physical stability because of topological protection. However, they have potential to deform according to their local energy environment. Here we demonstrate that, in regions of high exchange energy density, skyrmions may exhibit such extreme deformation that spontaneous merging with nearest neighbours or spawning new skyrmions is favoured to attain a lower energy state. Using transmission electron microscopy and a high-speed imaging detector, we observe dynamics involving distinct configurational states, in which transitions are accompanied by spontaneous creation or annihilation of skyrmions. These observations raise important questions regarding the limits of skyrmion stability and topological charge conservation, while also suggesting a means of control of skyrmion creation and annihilation.

Tunable Magnetic Vortex Dynamics in Ion-Implanted Permalloy Disks

Nanoscale, low-phase-noise, tunable transmitter-receiver links are key for enabling the progress of wireless communication. We demonstrate that vortex-based spin-torque nano-oscillators, which are intrinsically low-noise devices because of their topologically protected magnetic structure, can achieve frequency tunability when submitted to local ion implantation. In the experiments presented here, the gyrotropic mode is excited with spin-polarized alternating currents and anisotropic magnetoresistance measurements yield discrete frequencies from a single device. Indeed, chromium-implanted regions of permalloy disks exhibit different saturation magnetization than neighboring, non-irradiated areas, and thus different resonance frequency, corresponding to the specific area where the core is gyrating. Our study proves that such devices can be fabricated without the need for further lithographical steps, suggesting ion irradiation can be a viable and cost-effective fabrication method for densely packed networks of oscillators.

Fast and deterministic switching of a vortex core induced by an out-of-plane current in notch disks

The magnetic vortex, as one of the most interesting magnetic solitons, has attracted great interest over the past two decades. A fast and reliable method to switch vortex polarity and chirality is one of the key issues for various applications. Based on micromagnetic simulation, here we report a fast, low energy cost and deterministic switching of a vortex core, by the designing of a notch structure in disks and the use of out-of-plane current geometry. We demonstrate that with such a design, the multiple switching problems found in notch disk systems can be avoided. Furthermore, the switching time can be reduced by more than 50% compared with disks without notches.

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.

Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications

The field of magnetic skyrmions has been actively investigated across a wide range of topics during the last decades. In this topical review, we mainly review and discuss key results and findings in skyrmion research since the first experimental observation of magnetic skyrmions in 2009. We particularly focus on the theoretical, computational and experimental findings and advances that are directly relevant to the spintronic applications based on magnetic skyrmions, i.e. their writing, deleting, reading and processing driven by magnetic field, electric current and thermal energy. We then review several potential applications including information storage, logic computing gates and non-conventional devices such as neuromorphic computing devices. Finally, we discuss possible future research directions on magnetic skyrmions, which also cover rich topics on other topological textures such as antiskyrmions and bimerons in antiferromagnets and frustrated magnets.

Magnetic Properties of Electrospun Magnetic Nanofiber Mats after Stabilization and Carbonization

Magnetic nanofibers are of great interest in basic research, as well as for possible applications in spintronics and neuromorphic computing. Here we report on the preparation of magnetic nanofiber mats by electrospinning polyacrylonitrile (PAN)/nanoparticle solutions, creating a network of arbitrarily oriented nanofibers with a high aspect ratio. Since PAN is a typical precursor for carbon, the magnetic nanofiber mats were stabilized and carbonized after electrospinning. The magnetic properties of nanofiber mats containing magnetite or nickel ferrite nanoparticles were found to depend on the nanoparticle diameters and the potential after-treatment, as compared with raw nanofiber mats. Micromagnetic simulations underlined the different properties of both magnetic materials. Atomic force microscopy and scanning electron microscopy images revealed nearly unchanged morphologies after stabilization without mechanical fixation, which is in strong contrast to pure PAN nanofiber mats. While carbonization at 500 °C left the morphology unaltered, as compared with the stabilized samples, stronger connections between adjacent fibers were formed during carbonization at 800 °C, which may be supportive of magnetic data transmission.

Reversing the circulation of ferromagnetic nanodisks with a local circular magnetic field

Ferromagnetic nanodisks have a unique closed-flux vortex state with two degrees of freedom that results in four different magnetization states that are degenerate in energy and stable against thermal fluctuations. Such disks could be interesting for magnetic memory devices if the independent switching of each degree of freedom can be realized. Polarity switching of the vortex core has been demonstrated, but it is difficult to manipulate switching of the vortex due to the high symmetry of the structure. In this work, we reverse the circulation direction of a circular ferromagnetic nanodisk by applying a local circular Oersted field via a metallic atomic force microscope tip placed at the center of the disk. The resulting field reverses the circulation of the vortex without switching the orientation of the core. Switching of the vortex is accomplished by the sudden increase in the current that occurs when there is dielectric breakdown of a thin insulating layer on top of the disk. Micromagnetic simulations indicate that a line current concentrated in the center of a nanodisk can reverse the magnetization of the disk at a value over one order of magnitude smaller than the current required if the current is instead uniformly distributed across the cross section of disk. These results can be applied to reducing the switching current in circularly symmetric device structures.

Voltage-driven annihilation and creation of magnetic vortices in Ni discs

Using photoemission electron microscopy (PEEM) to image ferromagnetism in polycrystalline Ni disks, and ferroelectricity in their single-crystal BaTiO₃ substrates, we find that voltage-driven 90° ferroelectric domain switching serves to reversibly annihilate each magnetic vortex via uniaxial compressive strain, and that the orientation of the resulting bi-domain reveals the chirality of the annihilated vortex. Micromagnetic simulations reveal that only 60% of this strain is required for annihilation. Voltage control of magnetic vortices is novel, and should be energetically favourable with respect to the use of a magnetic field or an electrical current. In future, stray field from bi-domains could be exploited to read vortex chirality. Given that core polarity can already be read via stray field, our work represents a step towards four-state low-power memory applications.

Chiral asymmetry detected in a 2D array of permalloy square nanomagnets using circularly polarized x-ray resonant magnetic scattering

The sensitivity of circularly polarized x-ray resonant magnetic scattering (CXRMS) to chiral asymmetry has been demonstrated. The study was performed on a 2D array of Permalloy (Py) square nanomagnets of 700 nm lateral size arranged in a chess pattern, in a square lattice of 1000 nm lattice parameter. Previous x-ray magnetic circular dichroism photoemission electron microscopy (XMCD-PEEM) images on this sample showed the formation of vortices at remanence and a preference in their chiral state. The magnetic hysteresis loops of the array along the diagonal axis of the squares indicate a non-negligible and anisotropic interaction between vortices. The intensity of the magnetic scattering using circularly polarized light along one of the diagonal axes of the square magnets becomes asymmetric in intensity in the direction transversal to the incident plane at fields where the vortex states are formed. The asymmetry sign is inverted when the direction of the applied magnetic field is inverted. The result is the expected in the presence of an unbalanced chiral distribution. The effect is observed by CXRMS due to the interference between the charge scattering and the magnetic scattering.

Magnetization dynamics in artificial spin ice

In this topical review, we present key results of studies on magnetization dynamics in artificial spin ice (ASI), which are arrays of magnetically interacting nanostructures. Recent experimental and theoretical progress in this emerging area, which is at the boundary between research on frustrated magnetism and high-frequency studies of artificially created nanomagnets, is reviewed. The exploration of ASI structures has revealed fascinating discoveries in correlated spin systems. Artificially created spin ice lattices offer unique advantages as they allow for a control of the interactions between the elements by their geometric properties and arrangement. Magnonics, on the other hand, is a field that explores spin dynamics in the gigahertz frequency range in magnetic micro- and nanostructures. In this context, magnonic crystals are particularly important as they allow the modification of spin-wave properties and the observation of band gaps in the resonance spectra. Very recently, there has been considerable progress, experimentally and theoretically, in combining aspects of both fields-artificial spin ice and magnonics-enabling new functionalities in magnonic and spintronic applications using ASI, as well as providing a deeper understanding of geometrical frustration in the gigahertz range. Different approaches for the realization of ASI structures and their experimental characterization in the high-frequency range are described and the appropriate theoretical models and simulations are reviewed. Special attention is devoted to linking these findings to the quasi-static behavior of ASI and dynamic investigations in magnonics in an effort to bridge the gap between both areas further and to stimulate new research endeavors.

Creation and annihilation of topological meron pairs in in-plane magnetized films

Merons which are topologically equivalent to one-half of skyrmions can exist only in pairs or groups in two-dimensional (2D) ferromagnetic (FM) systems. The recent discovery of meron lattice in chiral magnet Co₈Zn₉Mn₃ raises the immediate challenging question that whether a single meron pair, which is the most fundamental topological structure in any 2D meron systems, can be created and stabilized in a continuous FM film? Utilizing winding number conservation, we develop a new method to create and stabilize a single pair of merons in a continuous Py film by local vortex imprinting from a Co disk. By observing the created meron pair directly within a magnetic field, we determine its topological structure unambiguously and explore the topological effect in its creation and annihilation processes. Our work opens a pathway towards developing and controlling topological structures in general magnetic systems without the restriction of perpendicular anisotropy and Dzyaloshinskii–Moriya interaction.

A meron is one half of a skyrmion but whether a single meron pair can be created and stabilized remains a challenging question. Here, Gao et al. develop a method to create and stabilize individual pairs of merons in a continuous Py film by local vortex imprinting from Co disks.

Current-Driven Dynamics of Magnetic Hopfions

Topological magnetic textures have attracted considerable interest since they exhibit new properties and might be useful in information technology. Magnetic hopfions are three-dimensional (3D) spatial variations in the magnetization with a nontrivial Hopf index. We find that, in ferromagnetic materials, two types of hopfions, Bloch-type and Néel-type hopfions, can be excited as metastable states in the presence of bulk and interfacial Dzyaloshinskii-Moriya interactions, respectively. We further investigate how hopfions can be driven by currents via spin-transfer torques (STTs) and spin-Hall torques (SHTs). Distinct from 2D ferromagnetic skyrmions, hopfions have a vanishing gyrovector. Consequently, there are no undesirable Hall effects. Néel-type hopfions move along the current direction via both STT and SHT, while Bloch-type hopfions move either transverse to the current direction via SHT or parallel to the current direction via STT. Our findings open the door to utilizing hopfions as information carriers.

Quantitative magnetic force microscopy using calibration on superconducting flux quanta

We present a new procedure that takes advantage of the magnetic flux quantization of superconducting vortices to calibrate the magnetic properties of tips for magnetic force microscopy (MFM). Indeed, a superconducting vortex, whose quantized flux is dependent upon Plank constant, speed of light and electron charge, behaves as a very well defined magnetic reference object. The proposed calibration procedure has been tested on new and worn tips and shows that the monopole point-like approximation of the probe is a reliable model. This procedure has been then applied to perform quantitative MFM experiments on a soft ferromagnetic thin film of permalloy, leading to the determination of the local out-of-plane component of the canted magnetization, together with its spatial variations across a few μm² scan area.

Twisted magnon beams carrying orbital angular momentum

Low-energy eigenmode excitations of ferromagnets are spin waves or magnons that can be triggered and guided in magnonic circuits without Ohmic losses and hence are attractive for communicating and processing information. Here we present new types of spin waves that carry a definite and electrically controllable orbital angular momentum (OAM) constituting twisted magnon beams. We show how twisted beams emerge in magnonic waveguides and how to topologically quantify and steer them. A key finding is that the topological charge associated with OAM of a particular beam is tunable externally and protected against magnetic damping. Coupling to an applied electric field via the Aharanov-Casher effect allows for varying the topological charge. This renders possible OAM-based robust, low-energy consuming multiplex magnonic computing, analogously to using photonic OAM in optical communications, and high OAM-based entanglement studies, but here at shorter wavelengths, lower energy consumption, and ready integration in magnonic circuits.

Magnetic Nanofiber Mats for Data Storage and Transfer

Electrospun nanofiber mats may serve as new hardware for neuromorphic computing. To enable data storage and transfer in them, they should be magnetic, possibly electrically conductive and able to respond to further external impulses. Here we report on creating magnetic nanofiber mats, consisting of magnetically doped polymer nanofibers for data transfer and polymer beads containing larger amounts of magnetic nanoparticles for storage purposes. Using magnetite and iron nickel oxide nanoparticles, a broad range of doping ratios could be electrospun with a needleless technique, resulting in magnetic nanofiber mats with varying morphologies and different amounts of magnetically doped beads.

Fabrication of Magnetic Nanostructures on Silicon Nitride Membranes for Magnetic Vortex Studies Using Transmission Microscopy Techniques

Electron and x-ray magnetic microscopies allow for high-resolution magnetic imaging down to tens of nanometers. However, the samples need to be prepared on transparent membranes which are very fragile and difficult to manipulate. We present processes for the fabrication of samples with magnetic micro- and nanostructures with spin configurations forming magnetic vortices suitable for Lorentz transmission electron microscopy and magnetic transmission x-ray microscopy studies. The samples are prepared on silicon nitride membranes and the fabrication consists of a spin coating, UV and electron-beam lithography, the chemical development of the resist, and the evaporation of the magnetic material followed by a lift-off process forming the final magnetic structures. The samples for the Lorentz transmission electron microscopy consist of magnetic nanodiscs prepared in a single lithography step. The samples for the magnetic x-ray transmission microscopy are used for time-resolved magnetization dynamic experiments, and magnetic nanodiscs are placed on a waveguide which is used for the generation of repeatable magnetic field pulses by passing an electric current through the waveguide. The waveguide is created in an extra lithography step.

Optical manipulation of magnetic vortices visualized in situ by Lorentz electron microscopy

Understanding the fundamental dynamics of topological vortex and antivortex naturally formed in microscale/nanoscale ferromagnetic building blocks under external perturbations is crucial to magnetic vortex-based information processing and spintronic devices. All previous studies have focused on magnetic vortex-core switching via external magnetic fields, spin-polarized currents, or spin waves, which have largely prohibited the investigation of novel spin configurations that could emerge from the ground states in ferromagnetic disks and their underlying dynamics. We report in situ visualization of femtosecond laser quenching-induced magnetic vortex changes in various symmetric ferromagnetic Permalloy disks by using Lorentz phase imaging of four-dimensional electron microscopy that enables in situ laser excitation. Besides the switching of magnetic vortex chirality and polarity, we observed with distinct occurrence frequencies a plenitude of complex magnetic structures that have never been observed by magnetic field- or current-assisted switching. These complex magnetic structures consist of a number of newly created topological magnetic defects (vortex and antivortex) strictly conserving the topological winding number, demonstrating the direct impact of topological invariants on magnetization dynamics in ferromagnetic disks. Their spin configurations show mirror or rotation symmetry due to the geometrical confinement of the disks. Combined micromagnetic simulations with the experimental observations reveal the underlying magnetization dynamics and formation mechanism of the optical quenching-induced complex magnetic structures. Their distinct occurrence rates are pertinent to their formation-growth energetics and pinning effects at the disk edge. On the basis of these findings, we propose a paradigm of optical quenching-assisted fast switching of vortex cores for the control of magnetic vortex-based information recording and spintronic devices.

Direct Observation of Magnetocrystalline Anisotropy Tuning Magnetization Configurations in Uniaxial Magnetic Nanomaterials

Discovering the effect of magnetic anisotropy on the magnetization configurations of magnetic nanomaterials is essential and significant for not only enriching the fundamental knowledge of magnetics but also facilitating the designs of desired magnetic nanostructures for diverse technological applications, such as data storage devices, spintronic devices, and magnetic nanosensors. Herein, we present a direct observation of magnetocrystalline anisotropy tuning magnetization configurations in uniaxial magnetic nanomaterials with hexagonal structure by means of three modeled samples. The magnetic configuration in polycrystalline BaFe₁₂O₁₉ nanoslice is a curling structure, revealing that the effect of magnetocrystalline anisotropy in uniaxial magnetic nanomaterials can be broken by forming an amorphous structure or polycrystalline structure with tiny grains. Both single crystalline BaFe₁₂O₁₉ nanoslice and individual particles of single-particle-chain BaFe₁₂O₁₉ nanowire appear in a single domain state, revealing a dominant role of magnetocrystalline anisotropy in the magnetization configuration of uniaxial magnetic nanomaterials. These observations are further verified by micromagnetic computational simulations.

Composition and diameter modulation of magnetic nanowire arrays fabricated by a novel approach

Straight magnetic nanowires composed of nickel and permalloy segments having different diameters are synthesized using a promising approach. This approach involves the controlled electrodeposition of each magnetic material into specially designed diameter-modulated porous alumina templates. Standard alumina templates are exposed to pore widening followed by a protective coating of the pore wall with ultrathin silica and further anodization. Micromagnetic simulations are employed to investigate the process of magnetization reversal in the fabricated nanowires when the magnetic materials exchange their places in the thick and thin segments. It is found that the magnetization reversal occurs by the propagation of transverse domain wall (DW) when the thick segment is composed of permalloy. However, the reversal process proceeds by the propagation of vortex DW when permalloy is located at the thin segment.

Tunable geometrical frustration in magnonic vortex crystals

A novel approach to investigate geometrical frustration is introduced using two-dimensional magnonic vortex crystals. The frustration of the crystal can be manipulated and turned on and off dynamically on the timescale of milliseconds. The vortices are studied using scanning transmission x-ray microscopy and ferromagnetic resonance spectroscopy. They are arranged analogous to the nanomagnets in artificial spin-ice systems. The polarization state of the vortices is tuned in a way that geometrical frustration arises. We demonstrate that frustrated polarization states and non-frustrated states can be tuned to the crystal by changing the frequency of the state formation process.

Nanoscale magnetic imaging using circularly polarized high-harmonic radiation

This work demonstrates nanoscale magnetic imaging using bright circularly polarized high-harmonic radiation. We utilize the magneto-optical contrast of worm-like magnetic domains in a Co/Pd multilayer structure, obtaining quantitative amplitude and phase maps by lensless imaging. A diffraction-limited spatial resolution of 49 nm is achieved with iterative phase reconstruction enhanced by a holographic mask. Harnessing the exceptional coherence of high harmonics, this approach will facilitate quantitative, element-specific, and spatially resolved studies of ultrafast magnetization dynamics, advancing both fundamental and applied aspects of nanoscale magnetism.

Magneto-actuated cell apoptosis by biaxial pulsed magnetic field

We report on a highly efficient magneto-actuated cancer cell apoptosis method using a biaxial pulsed magnetic field configuration, which maximizes the induced magnetic torque. The light transmissivity dynamics show that the biaxial magnetic field configuration can actuate the magnetic nanoparticles with higher responsiveness over a wide range of frequencies as compared to uniaxial field configurations. Its efficacy was demonstrated in in vitro cell destruction experiments with a greater reduction in cell viability. Magnetic nanoparticles with high aspect ratios were also found to form a triple vortex magnetization at remanence which increases its low field susceptibility. This translates to a larger magneto-mechanical actuated force at low fields and 12% higher efficacy in cell death as compared to low aspect ratio nanoparticles.

Characteristics and controllability of vortices in ferromagnetics, ferroelectrics, and multiferroics

Topological defects in condensed matter are attracting e significant attention due to their important role in phase transition and their fascinating characteristics. Among the various types of matter, ferroics which possess a switchable physical characteristic and form domain structure are ideal systems to form topological defects. In particular, a special class of topological defects-vortices-have been found to commonly exist in ferroics. They often manifest themselves as singular regions where domains merge in large systems, or stabilize as novel order states instead of forming domain structures in small enough systems. Understanding the characteristics and controllability of vortices in ferroics can provide us with deeper insight into the phase transition of condensed matter and also exciting opportunities in designing novel functional devices such as nano-memories, sensors, and transducers based on topological defects. In this review, we summarize the recent experimental and theoretical progress in ferroic vortices, with emphasis on those spin/dipole vortices formed in nanoscale ferromagnetics and ferroelectrics, and those structural domain vortices formed in multiferroic hexagonal manganites. We begin with an overview of this field. The fundamental concepts of ferroic vortices, followed by the theoretical simulation and experimental methods to explore ferroic vortices, are then introduced. The various characteristics of vortices (e.g. formation mechanisms, static/dynamic features, and electronic properties) and their controllability (e.g. by size, geometry, external thermal, electrical, magnetic, or mechanical fields) in ferromagnetics, ferroelectrics, and multiferroics are discussed in detail in individual sections. Finally, we conclude this review with an outlook on this rapidly developing field.