Magnetism

Recent advances in the research area of 3D magnetic topological solitons (hopfions) in restricted geometries are reviewed. The description of the magnetic solitons is based on a macroscopic micromagnetic approach and the Landau–Lifshitz equation of the magnetization motion. The concepts of the gauge emergent vector potential and emergent magnetic field are widely used to calculate the 3D topological charge (the Hopf index) of magnetic textures. The relation of the magnetic hopfions with classical field theory is demonstrated, and a special role of the curvilinear toroidal coordinates in the description of the hopfions is underlined. The hopfion stability and dynamics in ferromagnetic films and dots are considered. A critical discussion of calculations of the magnetization emergent magnetic field and the Hopf index of the toroidal magnetic hopfions in restricted geometries is presented. Full article

We investigate the stability tendency of a magnetic skyrmion crystal in noncentrosymmetric tetragonal systems with the Dzyaloshinskii–Moriya interaction. We show that the stability region of the square skyrmion crystal on a square lattice depends on the Ising-type magnetic anisotropic interaction by performing the simulated annealing for the spin model. The easy-axis anisotropic interaction tends to narrow the region where the square skyrmion crystal is stabilized when the magnetic field is applied in the out-of-plane direction. In contrast, the easy-plane anisotropic interaction tends to enlarge the stability region. Meanwhile, the square skyrmion crystal induced by the easy-axis anisotropic interaction is robust compared with that induced by the easy-plane anisotropic interaction when the magnetic field is tilted from the out-of-plane to the in-plane direction. The results indicate that the instability toward the square skyrmion crystal in noncentrosymmetric crystals is sensitive to both magnetic anisotropy and magnetic fields. Full article

Rare-earth-based permanent magnets (PMs) have a vital role in numerous sustainable energy systems, such as electrical machines (EMs). However, their production can greatly harm the environment and their supply chain monopoly presents economic threats. Alternative materials are emerging, but the use of rare-earth PMs remains dominant due to their exceptional performance. Damage to magnet structure can cause loss of performance and efficiency, and propagation of cracks in PMs can result in breaking. In this context, prolonging the service life of PMs and ensuring that they remain damage-free and suitable for re-use is important both for sustainability reasons and cost management. This paper presents a new harmonic content diagnosis and motor performance analysis caused by various magnet structure defects or faults, such as cracked or broken magnets. The proposed method is used for modeling the successive physical failure of the magnet structure in the form of crack formation, crack growth, and magnet breakage. A surface-mounted permanent magnet synchronous motor (PMSM) is studied using simulation in Ansys Maxwell software (Version 2023), and different cracks and PM faults are modeled using the two-dimensional finite element method (FEM). The frequency domain simulation results demonstrate the influence of magnet cracks and their propagation on EM performance measures, such as stator current, distribution of magnetic flux density, back EMF, flux linkage, losses, and efficiency. The results show strong potential for application in health monitoring systems, which could be used to reduce the occurrence of in-service failures, thus reducing the usage of rare-earth magnet materials as well as cost. Full article

Spin Hamiltonians, like the Heisenberg model, are used to describe the magnetic properties of exchange-coupled molecules and solids. For finite clusters, physical quantities, such as heat capacities, magnetic susceptibilities or neutron-scattering spectra, can be calculated based on energies and eigenstates obtained by exact diagonalization (ED). Utilizing spin-rotational symmetry SU(2) to factor the Hamiltonian with respect to total spin S facilitates ED, but the conventional approach to spin-adapting the basis is more intricate than selecting states with a given magnetic quantum number M (the spin z-component), as it relies on irreducible tensor-operator techniques and spin-coupling coefficients. Here, we present a simpler technique based on applying a spin projector to uncoupled basis states. As an alternative to Löwdin’s projection operator, we consider a group-theoretical formulation of the projector, which can be evaluated either exactly or approximately using an integration grid. An important aspect is the choice of uncoupled basis states. We present an extension of Löwdin’s theorem for $s=\frac{1}{2}$ to arbitrary local spin quantum numbers s, which allows for the direct selection of configurations that span a complete, linearly independent basis in an S sector upon the spin projection. We illustrate the procedure with a few examples. Full article

The efficiency of Dynamic Inductive Power Transfer (DIPT) depends mainly on the coupling coefficient within the coupler. In order to improve this parameter, a novel approach has been introduced that results in a significant increase of between 25% and 36% at minimal additional cost in the case of juxtaposed rectangular coil configuration on the road. This method involves the incorporation of a passive additional short-circuit coil adjacent to the primary coil for obtaining a higher coupling coefficient, as has been theoretically demonstrated. Simulations carried out on Comsol have optimized the dimensions of this additional coil, not only for cost effectiveness and minimal space utilization, but also for optimal efficiency. Experimental validation was performed at reduced power, using a 2 kW test bench, and confirmed the estimation. The efficiency improvement proposed in this paper is crucial for improving the global DIPT efficiency and then facilitating its social acceptance. Full article

Two recently developed methods of modelling chiral magnetic soliton elliptical instability are applied in two novel scenarios: the tilted ferromagnetic phase of chiral magnets dominated by easy-plane anisotropy and the general case of the chiral magnet with tilted applied field and arbitrary uniaxial anisotropy. In the former case, the analytical predictions are found to exactly match previous numerical results. In the latter case, the instability of isolated chiral skyrmions has not yet been studied, although interestingly, the predictions correspond to previous numerical investigation into the phase diagram. Full article

This work describes an automated pilot plant for the extraction of rare-earth (RE) permanent magnets from computer hard-disk drives (HDDs), demonstrating a commercially viable way to exploit these abundant sources of end-of-life (EOL) magnets. A mobile approach is provided for the on-site destruction of the HDDs in server farms, in compliance with the European Data Protection Regulation (GDPR), enabling both separation of the magnets and automated shredding of the data carrier. This fully automated process identifies (both optically and magnetically) the location of the rare-earth magnets and cuts off the corner of the hard drive containing the rare-earth material in the voice coil motor. This allows for a significant reduction in magnet extraction time (6 s per HDD) compared to previously reported semi-automated (2 min) and manual (5 min) dismantling times. This work will also help to transfer the experience gained in the mobile pilot plant to other future sources of EOL materials such as drive motors and mixed electronic scrap. Full article

We investigate the emergence of magnetic skyrmion crystals with swirling topological spin textures in itinerant magnets with an emphasis on momentum-resolved multi-spin interactions. By performing the simulated annealing for the effective spin model with the two-spin and four-spin interactions on a two-dimensional triangular lattice, we show that various types of four-spin interactions become the microscopic origin of the magnetic skyrmion crystal with the skyrmion numbers of one and two. We find that the four-spin interactions between the different wave vectors lead to the skyrmion crystal with the skyrmion number of one, whereas those at the same wave vectors lead to the skyrmion crystals with the skyrmion number of one and two. Our results indicate that the multi-spin interactions arising from the itinerant nature of electrons provide rich topological spin textures in magnetic metals. Full article

NiO nanoparticles have garnered significant interest due to their diverse applications and unique properties, which differ markedly from their bulk counterparts. NiO nanoparticles are p-type semiconductors with a wide bandgap, high discharge capacity, and high carrier density, making them ideal for use in batteries, sensors, and catalysts. Their ability to generate reactive oxygen species also imparts disinfectant and antibiotic properties. Additionally, the higher Néel temperature of NiO compared with other antiferromagnetic materials makes it suitable for high-temperature applications in spintronic devices and industrial settings. This review focuses on the critical role of structure and composition in determining the magnetic properties of NiO nanoparticles. It examines how finite-size surface effects, morphology, crystallinity, and nickel distribution influence these properties. Fundamental physical properties and characterization techniques are discussed first. Various synthesis methods and their impact on NiO nanoparticle properties are then explored. Their magnetic phenomenology is examined in detail, highlighting the effects of finite size, particle composition and surface, and crystal quality. The review concludes with a summary of key insights and future research directions for optimizing NiO nanoparticles in technological applications. Full article

This work presents an investigation of the degradation of paracetamol via heterogeneous photocatalysis, aiming to magnetically immobilize the catalyst in a continuous process. Catalyst immobilization was conducted on aggregated flower-like structures. The CoFe₂O₄@Nb₅O₂ catalyst was characterized using a Vibrating Sample Magnetometer (VSM). The effects of the magnetic immobilization of the catalyst, flow, residence time, adsorption, and photolysis were evaluated. Additionally, catalyst reuse cycles were analyzed. The results indicated that a longer residence time favors the degradation of paracetamol due to the increase in the contact time of the effluent catalyst. At a flow rate of 20 mL·min⁻¹, a degradation of 27% was obtained. Photolysis and adsorption tests indicated that residence time was not an important factor for paracetamol degradation. For the photolysis test, in the first cycle, the values obtained were in the range of 6.0–8.5%. The adsorption results indicated ~10% removal. Full article

In this article, a comprehensive review is presented of recent technological advancements utilizing electromagnetic sensors in the microwave range for detecting human vital signs and lung water levels. With the main objective of improving detection accuracy and system robustness, numerous advancements in front-end architecture, detection techniques, and system-level integration have been reported. The benefits of non-contact vital sign detection have garnered significant interest across a range of applications, including healthcare monitoring and search and rescue operations. Moreover, some integrated circuits and portable systems have lately been shown off. A comparative examination of various system architectures, baseband signal processing methods, system-level integration strategies, and possible applications are included in this article. Going forward, researchers will continue to focus on integrating radar chips to achieve compact form factors and employ advanced signal processing methods to further enhance detection accuracy. Full article

In 1971, Chua defined an ideal memristor that links magnetic flux φ and electric charge q. In a magnetic lump with a current-carrying conductor, we found that the direct interaction between physical magnetic flux φ and physical electric charge q is memristive by nature in terms of a time-invariant φ-q curve being nonlinear, continuously differentiable and strictly monotonically increasing. Although we succeeded in demonstrating that the “ideal/real/perfect/… memristor” needs magnetism, the structure still suffers from two serious limitations: 1. a parasitic “inductor” effect and 2. bistability and dynamic sweep of a continuous resistance range. Then, we discussed how to overcome these two limitations to make a fully functioning ideal memristor with multiple or an infinite number of stable states and no parasitic inductance. We then gave a number of innovations to the current memristor structure, such as an “open” structure, nanoscale size, magnetic materials with cubic anisotropy (or even isotropy) and sequential switching of the magnetic domains. Contrary to the conjecture that “an ideal memristor may not exist or may be a purely mathematical concept”, we remain optimistic that an ideal memristor will be discovered in nature or will be made in the laboratory. Our finding of the memristive flux–charge interaction may advance the development and application of the memristor technology. Full article

Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually required to find exact or approximate eigenstates, but for small clusters with spatial symmetry, analytical solutions exist, and a few Heisenberg systems have been solved in closed form. This paper presents a simple, generally applicable approach to analytically solve isotropic spin clusters, based on adapting the basis to both total spin and point group symmetry to factor the Hamiltonian matrix into sufficiently small blocks. We demonstrate applications to small rings and polyhedra, some of which are straightforward to solve by successive spin-coupling for Heisenberg terms only; additional interactions, such as biquadratic exchange or multi-center terms necessitate symmetry adaptation. Full article

The exact formulae for calculating the demagnetizing factors of a general ellipsoid along the three main axes a ≥ b ≥ c have been long known. According to these formulae, the demagnetizing factors depend only on the axial ratios b/a and c/a. Although the calculation of the demagnetizing factors is a straightforward task, the calculation itself is not a simple one. Therefore, tabular and graphical representations of these demagnetizing factor data have also been presented which can then be used for approximating the demagnetizing factors of a rectangular ferromagnetic slab with the same axial ratios. It turned out in our recent study, however, that, in some ranges of axial ratios (e.g., for very small c/a values), the available tables and graphs do not provide sufficient resolution for obtaining the demagnetizing factors with reasonable accuracy. It was decided to calculate these missing values, and they are presented here in both tabular and graphical form by giving instructions for how to obtain conveniently further interpolated data. In addition, the previous and current demagnetizing factor data have been replotted and fitted to a polynomial function with high accuracy. The functional form of these fitting polynomials is presented in a table for the whole range of the axial ratios b/a and c/a. By graphically displaying these functions, one can obtain, in a relatively simple manner, the demagnetizing factors of a general ellipsoid with known axial ratios without the need to directly calculate through the exact formulae. This may be helpful in obtaining a quick estimate for the demagnetizing factors of any rectangular ferromagnetic slab of interest. Full article

Multipolar bonded magnets based on a thermoset matrix provide the opportunity to expand the applications of bonded magnets, especially within the drive technology industry, in terms of the high thermal and chemical resistance, along with a higher utilisation of the magnetic potential. To realize the application of polymer bonded magnets based on thermosets within the drive technology industry, general design parameters in terms of the material, the process parameters, and the tool concept are needed. These allow for a fundamental realization of multipolar bonded magnets with complex geometries in drive technologies, based on thermosets as the matrix material. This paper investigates the impact of the material (matrix material and filler grade), the process conditions (holding pressure (p_h) and heating time (t_h)), and the tool concept (gating position and system, sleeve material, pole division, and sample thickness) on the magnetic properties in terms of the remanence (B_R) and the deviation (Δs) of the pole division, as well as the orientation of the fillers in the middle of the pole and at the pole pitch. For each parameter, an optimised value is derived. In the majority of the cases, this value is equal in terms of the magnetic properties and the orientation. In terms of the sleeve material and the sample thickness, the ideal value differs between the two criteria. Therefore, an optimised value for each criterion, as well as an overall value, is defined. In terms of the material, PF, along with a high filler grade; in terms of the process conditions, a high holding pressure (p_h) and a low heating time (t_h); and in terms of the tool concept, a two-pinpoint gating system, located in the middle of the pole, a Ferro-Titanit-Cromoni sleeve material, a high pole division, as well as small sample thickness, should be selected to improve the properties of polymer bonded magnets based on thermosets. Full article

Additive manufacturing offers manufacturing flexibility for intricate components and also allows for precise control over the microstructure. This review paper explores the current state of the art in additive manufacturing techniques for Alnico permanent magnets, emphasizing the notable advantages and challenges associated with this innovative approach. Both the LPBF and L-DED processes have demonstrated promising results in fabricating Alnico with magnetic properties comparable with conventionally processed samples. The optimization of process parameters successfully reduced porosity and cracking in the LPBF processing of Alnico. The review further explored the significance of additive manufacturing process parameter optimization in managing the temperature gradient and solidification rate for a desired microstructure and enhanced magnetic properties. Other potential additive manufacturing methods suitable for the fabrication of Alnico were discussed, along with the challenges associated with the process. The insights provided also highlight how additive manufacturing holds the potential to replace post-processing techniques like solutionization, magnetic annealing, and tempering often necessary in Alnico production. Full article

The investigation and clarification of the properties of surface-functionalized superparamagnetic nanoparticles in a biological environment are key challenges prior to their medical applications. In the present work, electron paramagnetic resonance spectroscopy (EPR) combined with the spin labeling technique was utilized to better understand the behavior of nitroxides attached to magnetite nanoparticles dispersed in body fluid. EPR spectra of spin-labeled, silane-coated Fe₃O₄ nanoparticles in human serum and whole blood were recorded and analyzed for both room- and low-temperature values. In all cases, the obtained EPR signal consisted of a broad line from magnetite cores and a characteristic signal from the attached 4-Amino-2,2,6,6-tetramethylpiperidine-1-oxyl (4-amino-TEMPO). Even for liquid samples, the anisotropic components of magnetic tensors did not fully average out, which was reflected in the differences in the intensity of three narrow hyperfine lines from nitroxide. At 230 K the irregular slow-motion signal from the attached radical was also simulated using the EasySpin toolbox, which allowed to determine the parameters related to magnetic tensors and the dynamics of the spin label. The study showed that the anisotropy of the motion of the spin label 4-amino-TEMPO reflects its interactions with the surrounding medium and the manner of the attachment of the nitroxide to the surface of nanoparticles. Full article

Inspired in pyrochlore materials presenting residual entropy and featuring collective excitation behaving like emergent monopoles, geometrically frustrated arrays of nanomagnets, denominated artificial spin ices (ASIs), were proposed as an interesting platform to investigate such excitation at room temperature. However, in such artificial systems, emergent magnetic monopoles lack the same freedom present their natural counterpart, once energetic strings connecting opposite magnetic charges arise. In this work, we aim to experimentally investigate the proposed degeneracy obtained in connected square arrays of ASIs, a characteristic that allows a reduction in the string connecting monopole–antimonopole pairs in regular non-connected ASIs and could represent an important development for technological applications of connected nanomagnets. As in general those systems are developed by nanofabrication processes involving expensive and time-consuming physical vapour deposition techniques, we also present a new nanofabrication route using an electrodeposition technique for permalloy growth in different lattice geometries as an alternative for fast and low-cost ASI system production. Full article

The structure of skyrmion and spiral solutions, investigated within the phenomenological Dzyaloshinskii model of chiral magnets near the ordering temperatures, is characterized by the strong interplay between longitudinal and angular order parameters, which may be responsible for experimentally observed precursor effects. Within the precursor regions, additional effects, such as pressure, electric fields, chemical doping, uniaxial strains and/or magnetocrystalline anisotropies, modify the energetic landscape and may even lead to the stability of such exotic phases as a square staggered lattice of half-skyrmions, the internal structure of which employs the concept of the “soft” modulus and contains points with zero modulus value. Here, we additionally alter the stiffness of the magnetization modulus to favor one- and two-dimensional modulated states with large modulations of the order parameter magnitude. The computed phase diagram, which omits any additional effects, exhibits stability pockets with a square half-skyrmion lattice, a hexagonal skyrmion lattice with the magnetization in the center of the cells parallel to the applied magnetic field, and helicoids with propagation transverse to the field, i.e., those phases in which the notion of localized defects is replaced by the picture of a smooth but more complex tiling of space. We note that the results can be adapted to metallic glasses, in which the energy contributions are the same and originate from the inherent frustration in the models, and chiral liquid crystals with a different ratio of elastic constants. Full article