Magnetism

We conduct a numerical investigation into the stability of a quadruple-Q skyrmion crystal, a structure generated by the superposition of four spin density waves traveling in distinct directions within three-dimensional space, hosted on a centrosymmetric body-centered tetragonal lattice. Using simulated annealing applied to an effective spin model that includes momentum-resolved bilinear and biquadratic interactions, we construct a magnetic phase diagram spanning a broad range of model parameters. Our study finds that a quadruple-Q skyrmion crystal does not emerge within the phase diagram when varying the biquadratic interaction and external magnetic field. Instead, three distinct quadruple-Q states with topologically trivial spin textures are stabilized. However, we demonstrate that the quadruple-Q skyrmion crystal can become the ground state when an additional high-harmonic wave–vector interaction is considered. Depending on the magnitude of this interaction, we obtain two types of quadruple-Q skyrmion crystals exhibiting the skyrmion numbers of one and two. These findings highlight the emergence of diverse three-dimensional multiple-Q spin states in centrosymmetric body-centered tetragonal magnets. Full article

The present work aspires to contribute to the discussion on the relationship between macroscopic measurements and microstructure, helping establish a methodology that will allow the quantitative assessment of the effect of strain on magnetic properties in the plastic deformation regime. In particular, we study the effect of strain on the magnetization process as a result of varying the anisotropy profile at the grain level. Results on micromagnetic calculations of hysteresis loops for various configurations of magnetic anisotropy are shown and discussed against the interplay between the energy terms involved in the calculations, namely anisotropy, demagnetizing, and exchange. The results are in line with previously obtained results using vector Preisach modeling with the Stoner–Wohlfarth model acting both as a switching and rotation mechanism. The hysteresis loop phenomenology is consistent with the emergence of a hard phase in the form of a boundary around soft grains which is assumed to be the result of the onset of compressive stresses in the plastic region. Future research will be oriented toward the study of the effect of the secondary peak in differential permeability, which is observed experimentally in the plastic deformation region, and its dependence on the angle of misalignment between the hard boundary and the soft grain. Full article

We investigate the instability toward a double-Q state, which consists of a superposition of two spin density waves at different wave vectors, on a two-dimensional noncentrosymmetric square lattice in an in-plane external magnetic field. By performing the simulated annealing for the spin model with the Dzyaloshinskii–Moriya interaction and bond-dependent anisotropic interaction, we obtain four types of double-Q states depending on the sign of the bond-dependent anisotropic interaction. On the other hand, only the single-Q spiral state appears in the absence of the bond-dependent anisotropic interaction. The present results suggest that the interplay between the Dzyaloshinskii–Moriya interaction and bond-dependent anisotropic interaction can give rise to multiple-Q states for both zero and nonzero in-plane magnetic fields. Full article

All-d metallic Heusler compounds are promising materials for nanoelectronic applications. Such materials combining 3d, 4d, and 5d atoms have not yet been studied. In this respect, we perform ab initio electronic structure calculations and focus on ${\mathrm{Co}}_2$MnZ, ${\mathrm{Rh}}_2$MnZ, and ${\mathrm{Ru}}_2$MnZ compounds, where Z represents transition metal atoms from groups 3B, 4B, 5B, and 6B of the periodic table. Our results demonstrate that most of these compounds exhibit a distinctive region of very low minority-spin state density at the Fermi level when crystallized in the $L{2}_1$ lattice structure. The Co-based compounds follow a Slater–Pauling behavior for their total spin magnetic moments, while the Ru-based compounds consistently deviate from the predicted Slater–Pauling values. Rh-based compounds show similarities to Co-based compounds for lighter Z atoms and to Ru-based compounds for heavier Z atoms. We find that the choice of the Z element within the same periodic table column has only a minor effect on the results, except for the ${\mathrm{Rh}}_2$Mn(Cr, Mo, W) compounds. Our findings suggest that these compounds hold significant promise for applications in spintronics and magnetoelectronics. Full article

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