High-resolution imaging of magnetic nanostructures is essential for understanding fundamental spin phenomena and designing advanced devices. Recent developments in three-dimensional (3D) nanomagnetism have highlighted the growing need for imaging techniques that can capture magnetic structures across curved or tilted surfaces with high sensitivity. Though widely used as a powerful technique for imaging magnetization states, conventional magneto-optical Kerr effect (MOKE) microscopy faces inherent limitations in measuring non-planar systems due to its shallow depth of field (DOF). Here, we present an extended depth of field MOKE imaging approach, combining through-focus scanning with image-stitching-based reconstruction, to obtain sharp and well-resolved magnetic domain images across non-planar sample geometries. The method is validated on both perpendicularly and in-plane magnetized films tilted on purpose for this study, enabling quantitative analysis of domain morphology and detection sensitivity. This laboratory-accessible technique provides a fast and versatile route for 3D magnetic imaging, complementing large-scale X-ray-based methods and offering a practical tool for investigating non-planar magnetic samples with tilted or curved 3D geometries.

Double-helix (DH) nanowires provide a platform to study the influence of geometric chirality on spin chirality. Their three-dimensional (3D) helical architecture and tunable inter-strand coupling enable control of spin chirality, including the stabilization of topological 3D magnetic states such as helical domains and domain walls, topological stray fields, and extended helical vortex/skyrmion tubes. So far, the study of these and other 3D nanostructures is usually confined to a limited number of magnetic microscopy experiments in large facilities. Here, we investigate the reversal mechanism of a single DH nanowire using Dark-Field magneto-optical Kerr effect (DF-MOKE) magnetometry under external 3D magnetic fields. By analyzing the angular dependence of the DF-MOKE signal, we fit the reversal process using established models for domain-wall nucleation and propagation, finding a characteristic behavior similar to that reported for cylindrical nanowires. Micromagnetic simulations indicate that the reversal process goes through nucleation of the helical vortex tube in a curling manner while ptychographic X-ray magnetic circular dichroism data reveal that this helical vortex tube state forms through a mixed nucleation-propagation process. These observations provide a consistent microscopic picture of reversal mediated by a helical vortex tube extending along the nanowire. Our work provides a comprehensive characterization of magnetization reversal in DH nanowires and demonstrates that DF-MOKE magnetometry is effective for probing reversal mechanisms in single 3D nanostructures. This lab-based approach expands the range of accessible experiments beyond large-scale facilities, enabling extensive exploration of the rich spin states supported by 3D nano-geometries.

Bloch points are three-dimensional topological singularities in magnetization that play a key role in topological transformations of spin textures, such as skyrmion creation or annihilation. While topology often enforces the existence of Bloch points in confined geometries like cylindrical nanowires, deterministic control over their position and magnetic configuration remains challenging. Here we demonstrate the generation of Bloch points with controlled spin texture by engineering geometrical boundary conditions in three-dimensional nanomagnets. By introducing a chirality interface between two three-dimensional double-helix nanowires of opposite handedness, forming a kinked, non-collinear structure, we impose competing topological constraints that uniquely define the magnetization configuration surrounding the Bloch point. A saturating magnetic field nucleates head-to-head or tail-to-tail domain configurations at the chirality interface, producing a Bloch-point domain wall with deterministic polarity, circulation and helicity. This geometrical approach enables full three-dimensional control of Bloch point domain walls allowing deterministic engineering of their spin texture and its selective coupling to current-induced Oersted fields.

X-ray photon correlation scattering measurements are undertaken on a thermally active artificial spin ice based on the square lattice, referred to as artificial square ice, to probe the fluctuation timescales as a function of temperature as the system passes through the paramagnetic-antiferromagnetic phase transition, which belongs to the two-dimensional Ising universality class. In the paramagnetic regime, a single exponential timescale is seen, whereas at and below the critical temperature, a stretched exponential decorrelation is observed, with the stretching exponent decreasing from unity down to below one-half as the temperature reduces. This trend is confirmed by kinetic Monte Carlo simulations of a simplified point-dipolar square ice system, and is in agreement with past theoretical work on the kinetic Ising model where stretched exponential relaxation due to equilibrium domain wall dynamics below the critical temperature was found.

Multi-domain states of square artificial spin ice show a range of different morphologies ranging from simple stripe-like domains to more organically shaped coral domains. To model the relevant dynamics leading to the emergence of such diverse domain structures, simplified descriptions of the switching behavior of individual nanomagnets are necessary. In this work, we employ kinetic Monte Carlo simulations of the demagnetization of square artificial spin ice toward its ground state, and compare how the choice of transition barriers affect the emergence of mesoscale domains. We find that the commonly used mean-field barrier model (informed by equilibrium energetics only) results in propagation of ground-state string avalanches. In contrast, taking into account chiral barrier splitting enabled by state-dependent local torques supports the emergence of complex-shaped coral domains and their successful relaxation towards the ground state in later relaxation stages. Our results highlight that intrinsic contributions to switching barriers, in addition to the effect of extrinsic defects often attributed to nanofabrication irregularities, can subtly shift favored transition pathways and result in different emergent mesoscale features. Future kinetic Monte Carlo models that describe the evolution of artificial spin systems should thus account for these effects.

Magnetoelectric multiferroics promise direct cross-control between coexisting ferroelectric and ferromagnetic orders, which is of interest for applications in magnetism and spintronics. A particularly interesting type of cross-control is found in spin-spiral multiferroic Mn_2GeO_4, where a ferroelectric multi-domain distribution can be globally inverted by a single magnetic field sweep. In this work we consider the initial domain evolution from zero-field cooling, imaging the evolution of domains under both magnetic and electric fields via optical second harmonic generation. We find that polarization and magnetization domains form independently when entering the multiferroic phase, and a single deterministic initialisation procedure, spanning three quarters of a field cycle, is required to achieve reliable magnetoelectric cross-coupling. This initialisation behaviour originates from a deterministic pathway from metastable to equilibrium domain patterns, in contrast to more common and less reliable domain "training" procedures that require repeated field cycles. Understanding the initial domain evolution thus enables reliable cross-control in magnetoelectric devices with highly interlinked order parameters.

The spin-orbit field and interfacial exchange field are two major interface phenomena, and the detection and manipulation of these fields can enable a variety of nanoscale spintronics devices. Optimizing the interfacial exchange field, which governs the spin-dependent scattering asymmetry at (ferromagnetic insulator)-(normal metal) interfaces, will pave the way for next-generation nanoscale, low-power insulator spintronics devices. Here, we demonstrate an experimental pathway to detect an interfacial exchange field between insulating ferromagnet EuS and non-magnetic Cu using magnetoresistance measurements, and show that the spin-dependent scattering at the common interface can lead to a significant current-in-plane magnetoresistance in Py|Cu|EuS trilayer Hall-bar device. Our experiment suggests that simple magnetoresistance measurements can be used to experimentally detect the interfacial exchange field and thereby the magnetic state of a ferromagnetic insulator.

Magnetic skyrmions are chiral spin textures with rich physics and great potential for unconventional computing. Typically, skyrmions form in bulk crystals with reduced symmetry or ultrathin film multilayers involving heavy metals. Here, we demonstrate the formation of fractional Bloch skyrmion tubes at room temperature by 3D printing ferromagnetic double-helix nanowires with two regions of opposite chirality. Using X-ray microscopy and micromagnetic simulations, we show that the coexistence of vortex and anti-parallel spin states induces the formation of fractional skyrmion tubes at zero magnetic fields, minimising the energy cost of breaking the coupling between geometric and magnetic chirality. We also demonstrate control over zero-field states, including pure vortex, or mixed skyrmion-vortex states, highlighting the magnetic reconfigurability of these 3D nanowires. This work shows how interfacing chiral geometries at the nanoscale can enable advanced forms of topological spintronics.

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

Femtosecond (fs) time-resolved magneto-optics is applied to investigate laser-excited ultrafast dynamics of one-dimensional nickel gratings on fused silica and silicon substrates for a wide range of periodicities Λ = 400-1500 nm. Multiple surface acoustic modes with frequencies up to a few tens of GHz are generated. Nanoscale acoustic wavelengths Λ/n have been identified as nth-spatial harmonics of Rayleigh surface acoustic wave (SAW) and surface skimming longitudinal wave (SSLW), with acoustic frequencies and lifetimes being in agreement with theoretical calculations. Resonant magnetoelastic excitation of the ferromagnetic resonance (FMR) by SAW's third spatial harmonic, and, most interestingly fingerprints of the parametric resonance at 1/2 SAW frequency have been observed. Numerical solutions of Landau-Lifshitz-Gilbert (LLG) equation magnetoelastically driven by complex polychromatic acoustic fields quantitatively reproduce all resonances at once. Thus, our results provide a solid experimental and theoretical base for a quantitative understanding of ultrafast fs-laser-driven magnetoacoustics and tailoring the magnetic-grating-based metasurfaces at the nanoscale.

Magneto-toroidal order, also called ferrotoroidicity, is the most recently established type of ferroic state. It is based on a spontaneous and uniform alignment of unit-cell-sized magnetic whirls, called magneto-toroidal moments, associated with a macroscopic toroidization. Because of its intrinsic magnetoelectric coupling, this new ferroic state could be useful in the development of spintronic devices. We exploit two-dimensional periodic arrays of magnetostatically coupled nanomagnets as model systems for the investigation of long-range magneto-toroidal order. We present two pathways promoting this order, namely (i), structures comprising a ring of uniformly magnetized sub-micrometer-sized bar magnets and (ii), structures in which each magnetic building block itself hosts a magnetic vortex. For both cases calculations of the magnetic-dipole interaction and micromagnetic simulations reveal the conditions for the formation of spontaneous magneto-toroidal order. We confirm this order and the formation of magneto-toroidal domains in our arrays by magnetic force microscopy. We identify the presence of two types of domain-wall states emerging from the competition of two intrinsic microscopic couplings. Our work not only identifies the microscopic conditions promoting spontaneous magneto-toroidal order but also highlights the possibility tailor mesoscale magnetic arrays towards elusive types of ferroic order.

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

Nanomagnetic logic, in which the outcome of a computation is embedded into the energy hierarchy of magnetostatically coupled nanomagnets, offers an attractive pathway to implement in-memory computation. This computational paradigm avoids separate energy costs associated with transporting and storing the outcome of a computational operation. Thermally-driven nanomagnetic logic gates, which are driven solely by the ambient thermal energy, hold great promise for energy-efficient operation, but have the disadvantage of slow operating speeds due to the lack of spatial selectivity of currently-employed global heating methods. As has been shown recently, this disadvantage can be removed by employing local plasmon-assisted photo-heating. Here, we show by means of micromagnetic and finite-elements simulations how such local heating can be exploited to design reconfigurable nanomagnetic Boolean logic gates. The reconfigurability of operation is achieved either by modifying the initialising field protocol or optically, by changing the order in which horizontally and vertically polarised laser pulses are applied. Our results thus demonstrate that nanomagnetic logic offers itself as a fast (up to GHz), energy-efficient and reconfigurable platform for in-memory computation that can be controlled via optical means.

The triangular lattice with Ising magnetic moments is an archetypical example of geometric frustration. In the case of dipolar-coupled out-of-plane moments, the geometric frustration results in a disordered classical spin-liquid state at higher temperatures while the system is predicted to transition to an anti-ferromagnetic stripe ground state at low temperatures. In this work we fabricate artificial triangular Ising spin systems without and with uniaxial in-plane compression to tune the nature and temperature of the correlations. We probe the energy scale and nature of magnetic correlations by grazing-incidence small-angle neutron scattering. In particular, we apply a newly-developed empirical structure-factor model to describe the measured short-range correlated spin-liquid state, and find good agreement with theoretical predictions. We demonstrate that grazing-incidence neutron scattering on our high-quality samples, in conjunction with detailed modeling of the scattering using the Distorted Wave Born Approximation, can be used to experimentally quantify the spin-liquid-like correlations in highly-frustrated artificial spin systems.

Ferromagnet (FM)\ifmmode\text{\textcelsius}\else\textcelsius\fi{}heavy-metal (HM) nanostructures can be used for magnetic state readout in the proposed magnetoelectric spin-orbit logic by locally injecting a spin-polarized current and measuring the spin-to-charge conversion via the spin Hall effect. However, this local configuration is prone to spurious signals. Here, we address spurious Hall effects that can contaminate the spin Hall signal in these FM/HM T-shaped nanostructures. The most pronounced Hall effects in our ${\mathrm{Co}}_{50}{\mathrm{Fe}}_{50}/\mathrm{Pt}$ nanostructures are the planar Hall effect and the anomalous Hall effect generated in the ferromagnetic nanowire. We find that the planar Hall effect, induced by misalignment between magnetization and current direction in the ferromagnetic wire, is manifested as a shift in the measured baseline resistance, but does not alter the spin Hall signal. In contrast, the anomalous Hall effect, arising from the charge-current distribution within the FM, adds to the spin Hall signal. However, the effect can be made insignificant by minimizing the shunting effect via proper design of the device. We conclude that local spin injection in FM/HM nanostructures is a suitable tool for measuring spin Hall signals and, therefore, a valid method for magnetic state readout in prospective spin-based logic.

Collective dynamics in lithographically-defined artificial spin ices offer profound insights into emergent correlations and phase transitions of geometrically-frustrated Ising spin systems. Their temporal and spatial evolution are often simulated using kinetic Monte Carlo (kMC) simulations, which rely on the precise knowledge of the switching barriers to obtain predictive results in agreement with experimental observations. In many cases, however, the barriers are derived from simplified assumptions only, and do not take into account the full physical picture of nanomagnetic switching. Here we describe how the immediate magnetic square- or kagome-ice environment of a nanomagnet reversing via quasi-coherent rotation can induce clockwise and counter-clockwise switching channels with different barrier energies. This energy splitting for chiral reversal channels can be sizeable and, as string-method micromagnetic simulations show, is relevant for artificial spin ice systems made of both exchange- as well as magnetostatically-dominated units. Due to the barrier splitting and further reductions due to non-uniform reversal, transition rates can be exponentially enhanced by several orders of magnitude compared to mean-field predictions, especially in the limit of rare switching events where thermal excitation is less likely. This leads to significantly faster relaxation time scales and modified spatial correlations. Our findings are thus of integral importance to achieve realistic kMC simulations of emergent correlations in artificial spin systems, magnonic crystals, or the evolution of nanomagnetic logic circuits.

We perform micromagnetic simulations to study the switching barriers in square artificial spin ice systems consisting of elongated single domain magnetic islands arranged on a square lattice. By considering a double vertex composed of one central island and six nearest neighbor islands, we calculate the energy barriers between two types of double vertices by applying the simplified and improved string method. We investigate by means of micromagnetic simulations the consequences of the neighboring islands, the inhomogeneities in the magnetization of the islands and the reversal mechanisms on the energy barrier by comparing three different approaches with increasing complexity. The micromagnetic models, where the string method is applied, are compared to a method commonly in use, the mean barrier approximation. Our investigations indicate that a proper micromagnetic modeling of the switching process leads to significantly lower energy barriers, by up to 35% compared to the mean-barrier approximation, so decreasing the expected average life time up to seven orders of magnitude. Hereby, we investigate the influence of parallel switching channels and the conceptional approach of using a mean-barrier to calculate the corresponding rates.

The driving force in materials to spontaneously form states with magnetic or electric order is of fundamental importance for basic research and device technology. The macroscopic properties and functionalities of these ferroics depend on the size, distribution and morphology of domains; that is, of regions across which such uniform order is maintained1. Typically, extrinsic factors such as strain profiles, grain size or annealing procedures control the size and shape of the domains2–5, whereas intrinsic parameters are often difficult to extract due to the complexity of a processed material. Here, we achieve this separation by building artificial crystals of planar nanomagnets that are coupled by well-defined, tuneable and competing magnetic interactions6–9. Aside from analysing the domain configurations, we uncover fundamental intrinsic correlations between the microscopic interactions establishing magnetically compensated order and the macroscopic manifestations of these interactions in basic physical properties. Experiment and simulations reveal how competing interactions can be exploited to control ferroic hallmark properties such as the size and morphology of domains, topological properties of domain walls or their thermal mobility. Both extrinsic and intrinsic factors determine the properties of ferroic materials and are difficult to disentangle. This study on artificial crystals of planar nanomagnets with well-defined, tuneable magnetic interactions unveils the intrinsic correlations between microscopic interactions and macroscopic properties such as the domain size and morphology or the domain-wall mobility.

Artificial kagome spin ice exhibits exotic magnetic correlations driven by a combination of geometric frustration and dipolar interactions that, at low-enough temperature, can result in ordered phases. This order, whether it is the ground state of several kagome rings, or the theoretically predicted long-range order of an extended array, has yet to be experimentally observed. By introducing an interfacial Dzyaloshinskii-Moriya interaction, we are able to reduce the blocking temperature of the individual nanomagnets, allowing a system of 30 kagome nanomagnets to explore its vast manifold of microstates and find its ground state. Furthermore, the extracted magnetic correlations in an extended artificial kagome spin ice are found to exhibit quantitative signatures of long-range charge order, providing evidence of the theoretically predicted continuous phase transition to the charge-ordered state. The significant lowering of the blocking temperature in nanomagnets is important for the exploitation of superparamagnetism in artificial spin systems and devices.